research paper for stocks

A systematic review of fundamental and technical analysis of stock market predictions

• Published: 20 August 2019
• Volume 53 , pages 3007–3057, ( 2020 )

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• Isaac Kofi Nti   ORCID: orcid.org/0000-0001-9257-4295 1 , 2 ,
• Adebayo Felix Adekoya   ORCID: orcid.org/0000-0002-5029-2393 2 &
• Benjamin Asubam Weyori   ORCID: orcid.org/0000-0001-5422-4251 2  

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The stock market is a key pivot in every growing and thriving economy, and every investment in the market is aimed at maximising profit and minimising associated risk. As a result, numerous studies have been conducted on the stock-market prediction using technical or fundamental analysis through various soft-computing techniques and algorithms. This study attempted to undertake a systematic and critical review of about one hundred and twenty-two (122) pertinent research works reported in academic journals over 11 years (2007–2018) in the area of stock market prediction using machine learning. The various techniques identified from these reports were clustered into three categories, namely technical, fundamental, and combined analyses. The grouping was done based on the following criteria: the nature of a dataset and the number of data sources used, the data timeframe, the machine learning algorithms used, machine learning task, used accuracy and error metrics and software packages used for modelling. The results revealed that 66% of documents reviewed were based on technical analysis; whiles 23% and 11% were based on fundamental analysis and combined analyses, respectively. Concerning the number of data source, 89.34% of documents reviewed, used single sources; whiles 8.2% and 2.46% used two and three sources respectively. Support vector machine and artificial neural network were found to be the most used machine learning algorithms for stock market prediction.

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Nti, I.K., Adekoya, A.F. & Weyori, B.A. A systematic review of fundamental and technical analysis of stock market predictions. Artif Intell Rev 53 , 3007–3057 (2020). https://doi.org/10.1007/s10462-019-09754-z

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Stock Market Volatility and Return Analysis: A Systematic Literature Review

Roni bhowmik.

1 School of Economics and Management, Jiujiang University, Jiujiang 322227, China

2 Department of Business Administration, Daffodil International University, Dhaka 1207, Bangladesh

Shouyang Wang

3 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China; nc.ca.ssma@gnawys

In the field of business research method, a literature review is more relevant than ever. Even though there has been lack of integrity and inflexibility in traditional literature reviews with questions being raised about the quality and trustworthiness of these types of reviews. This research provides a literature review using a systematic database to examine and cross-reference snowballing. In this paper, previous studies featuring a generalized autoregressive conditional heteroskedastic (GARCH) family-based model stock market return and volatility have also been reviewed. The stock market plays a pivotal role in today’s world economic activities, named a “barometer” and “alarm” for economic and financial activities in a country or region. In order to prevent uncertainty and risk in the stock market, it is particularly important to measure effectively the volatility of stock index returns. However, the main purpose of this review is to examine effective GARCH models recommended for performing market returns and volatilities analysis. The secondary purpose of this review study is to conduct a content analysis of return and volatility literature reviews over a period of 12 years (2008–2019) and in 50 different papers. The study found that there has been a significant change in research work within the past 10 years and most of researchers have worked for developing stock markets.

1. Introduction

In the context of economic globalization, especially after the impact of the contemporary international financial crisis, the stock market has experienced unprecedented fluctuations. This volatility increases the uncertainty and risk of the stock market and is detrimental to the normal operation of the stock market. To reduce this uncertainty, it is particularly important to measure accurately the volatility of stock index returns. At the same time, due to the important position of the stock market in the global economy, the beneficial development of the stock market has become the focus. Therefore, the knowledge of theoretical and literature significance of volatility are needed to measure the volatility of stock index returns.

Volatility is a hot issue in economic and financial research. Volatility is one of the most important characteristics of financial markets. It is directly related to market uncertainty and affects the investment behavior of enterprises and individuals. A study of the volatility of financial asset returns is also one of the core issues in modern financial research and this volatility is often described and measured by the variance of the rate of return. However, forecasting perfect market volatility is difficult work and despite the availability of various models and techniques, not all of them work equally for all stock markets. It is for this reason that researchers and financial analysts face such a complexity in market returns and volatilities forecasting.

The traditional econometric model often assumes that the variance is constant, that is, the variance is kept constant at different times. An accurate measurement of the rate of return’s fluctuation is directly related to the correctness of portfolio selection, the effectiveness of risk management, and the rationality of asset pricing. However, with the development of financial theory and the deepening of empirical research, it was found that this assumption is not reasonable. Additionally, the volatility of asset prices is one of the most puzzling phenomena in financial economics. It is a great challenge for investors to get a pure understanding of volatility.

A literature reviews act as a significant part of all kinds of research work. Literature reviews serve as a foundation for knowledge progress, make guidelines for plan and practice, provide grounds of an effect, and, if well guided, have the capacity to create new ideas and directions for a particular area [ 1 ]. Similarly, they carry out as the basis for future research and theory work. This paper conducts a literature review of stock returns and volatility analysis based on generalized autoregressive conditional heteroskedastic (GARCH) family models. Volatility refers to the degree of dispersion of random variables.

Financial market volatility is mainly reflected in the deviation of the expected future value of assets. The possibility, that is, volatility, represents the uncertainty of the future price of an asset. This uncertainty is usually characterized by variance or standard deviation. There are currently two main explanations in the academic world for the relationship between these two: The leverage effect and the volatility feedback hypothesis. Leverage often means that unfavorable news appears, stock price falls, leading to an increase in the leverage factor, and thus the degree of stock volatility increases. Conversely, the degree of volatility weakens; volatility feedback can be simply described as unpredictable stock volatility that will inevitably lead to higher risk in the future.

There are many factors that affect price movements in the stock market. Firstly, there is the impact of monetary policy on the stock market, which is extremely substantial. If a loose monetary policy is implemented in a year, the probability of a stock market index rise will increase. On the other hand, if a relatively tight monetary policy is implemented in a year, the probability of a stock market index decline will increase. Secondly, there is the impact of interest rate liberalization on risk-free interest rates. Looking at the major global capital markets, the change in risk-free interest rates has a greater correlation with the current stock market. In general, when interest rates continue to rise, the risk-free interest rate will rise, and the cost of capital invested in the stock market will rise simultaneously. As a result, the economy is expected to gradually pick up during the release of the reform dividend, and the stock market is expected to achieve a higher return on investment.

Volatility is the tendency for prices to change unexpectedly [ 2 ], however, all kinds of volatility is not bad. At the same time, financial market volatility has also a direct impact on macroeconomic and financial stability. Important economic risk factors are generally highly valued by governments around the world. Therefore, research on the volatility of financial markets has always been the focus of financial economists and financial practitioners. Nowadays, a large part of the literature has studied some characteristics of the stock market, such as the leverage effect of volatility, the short-term memory of volatility, and the GARCH effect, etc., but some researchers show that when adopting short-term memory by the GARCH model, there is usually a confusing phenomenon, as the sampling interval tends to zero. The characterization of the tail of the yield generally assumes an ideal situation, that is, obeys the normal distribution, but this perfect situation is usually not established.

Researchers have proposed different distributed models in order to better describe the thick tail of the daily rate of return. Engle [ 3 ] first proposed an autoregressive conditional heteroscedasticity model (ARCH model) to characterize some possible correlations of the conditional variance of the prediction error. Bollerslev [ 4 ] has been extended it to form a generalized autoregressive conditional heteroskedastic model (GARCH model). Later, the GARCH model rapidly expanded and a GARCH family model was created.

When employing GARCH family models to analyze and forecast return volatility, selection of input variables for forecasting is crucial as the appropriate and essential condition will be given for the method to have a stationary solution and perfect matching [ 5 ]. It has been shown in several findings that the unchanged model can produce suggestively different results when it is consumed with different inputs. Thus, another key purpose of this literature review is to observe studies which use directional prediction accuracy model as a yardstick from a realistic point of understanding and has the core objective of the forecast of financial time series in stock market return. Researchers estimate little forecast error, namely measured as mean absolute deviation (MAD), root mean squared error (RMSE), mean absolute error (MAE), and mean squared error (MSE) which do not essentially interpret into capital gain [ 6 , 7 ]. Some others mention that the predictions are not required to be precise in terms of NMSE (normalized mean squared error) [ 8 ]. It means that finding the low rate of root mean squared error does not feed high returns, in another words, the relationship is not linear between two.

In this manuscript, it is proposed to categorize the studies not only by their model selection standards but also for the inputs used for the return volatility as well as how precise it is spending them in terms of return directions. In this investigation, the authors repute studies which use percentage of success trades benchmark procedures for analyzing the researchers’ proposed models. From this theme, this study’s authentic approach is compared with earlier models in the literature review for input variables used for forecasting volatility and how precise they are in analyzing the direction of the related time series. There are other review studies on return and volatility analysis and GARCH-family based financial forecasting methods done by a number of researchers [ 9 , 10 , 11 , 12 , 13 ]. Consequently, the aim of this manuscript is to put forward the importance of sufficient and necessary conditions for model selection and contribute for the better understanding of academic researchers and financial practitioners.

Systematic reviews have most notable been expanded by medical science as a way to synthesize research recognition in a systematic, transparent, and reproducible process. Despite the opportunity of this technique, its exercise has not been overly widespread in business research, but it is expanding day by day. In this paper, the authors have used the systematic review process because the target of a systematic review is to determine all empirical indication that fits the pre-decided inclusion criteria or standard of response to a certain research question. Researchers proved that GARCH is the most suitable model to use when one has to analysis the volatility of the returns of stocks with big volumes of observations [ 3 , 4 , 6 , 9 , 13 ]. Researchers observe keenly all the selected literature to answer the following research question: What are the effective GARCH models to recommend for performing market volatility and return analysis?

The main contribution of this paper is found in the following four aspects: (1) The best GARCH models can be recommended for stock market returns and volatilities evaluation. (2) The manuscript considers recent papers, 2008 to 2019, which have not been covered in previous studies. (3) In this study, both qualitative and quantitative processes have been used to examine the literature involving stock returns and volatilities. (4) The manuscript provides a study based on journals that will help academics and researchers recognize important journals that they can denote for a literature review, recognize factors motivating analysis stock returns and volatilities, and can publish their worth study manuscripts.

2. Methodology

A systematic literature examination of databases should recognize as complete a list as possible of relevant literature while keeping the number of irrelevant knocks small. The study is conducted by a systematic based literature review, following suggestions from scholars [ 14 , 15 ]. This manuscript was led by a systematic database search, surveyed by cross-reference snowballing, as demonstrated in Figure 1 , which was adapted from Geissdoerfer et al. [ 16 ]. Two databases were selected for the literature search: Scopus and Web-of-Science. These databases were preferred as they have some major depositories of research and are usually used in literature reviews for business research [ 17 ].

Literature review method.

At first stage, a systematic literature search is managed. The keywords that were too broad or likely to be recognized in literature-related keywords with other research areas are specified below. As shown in Table 1 , the search string “market return” in ‘Title‘ respectively “stock market return”, “stock market volatility”, “stock market return volatility”, “GARCH family model* for stock return”, “forecasting stock return”, and GARCH model*, “financial market return and volatility” in ‘Topic’ separately ‘Article title, Abstract, Keywords’ were used to search for reviews of articles in English on the Elsevier Scopus and Thomson Reuters Web-of-Science databases. The asterisk (*) is a commonly used wildcard symbol that broadens a search by finding words that start with the same letters.

Literature search strings for database.

At second stage, suitable cross-references were recognized in this primary sample by first examining the publications’ title in the reference portion and their context and cited content in the text. The abstracts of the recognized further publications were examined to determine whether the paper was appropriate or not. Appropriate references were consequently added to the sample and analogously scanned for appropriate cross-references. This method was continual until no additional appropriate cross-references could be recognized.

At the third stage, the ultimate sample was assimilated, synthesized, and compiled into the literature review presented in the subsequent section. The method was revised a few days before the submission.

Additionally, the list of affiliation criteria in Table 2 , which is formed on discussions of the authors, with the summaries of all research papers were independently checked in a blind system method. Evaluations were established on the content of the abstract, with any extra information unseen, and were comprehensive rather than exclusive. In order to check for inter-coder dependability, an initial sample of 30 abstracts were studied for affiliation by the authors. If the abstract was not satisfactorily enough, the whole paper was studied. Simply, 4.61 percent of the abstract resulted in variance between the researchers. The above-mentioned stages reduced the subsequent number of full papers for examination and synthesis to 50. In order to recognize magnitudes, backgrounds, and moderators, these residual research papers were reviewed in two rounds of reading.

Affiliation criteria.

3. Review of Different Studies

In this paper, a large amount of articles were studied but only a few were well thought out to gather the quality developed earlier. For every published article, three groups were specified. Those groups were considered as index and forecast time period, input elements, econometric models, and study results. The first group namely “index and forecast time period with input elements” was considered since market situation like emerging, frontier, and developed markets which are important parameters of forecast and also the length of evaluation is a necessary characteristic for examining the robustness of the model. Furthermore, input elements are comparatively essential parameters for a forecast model because the analytical and diagnostic ability of the model is mainly supported on the inputs that a variable uses. In the second group, “model” was considered forecast models proposed by authors and other models for assessment. The last group is important to our examination for comparing studies in relationships of proper guiding return and volatility, acquired by using recommended estimate models, named the “study results” group.

Measuring the stock market volatility is an incredibly complex job for researchers. Since volatility tends to cluster, if today’s volatility is high, it is likely to be high tomorrow but they have also had an attractive high hit rate with major disasters [ 4 , 7 , 11 , 12 ]. GARCH models have a strong background, recently having crossed 30 years of the fast progress of GARCH-type models for investigating the volatility of market data. Literature of eligible papers were clustered in two sub groups, the first group containing GARCH and its variations model, and the second group containing bivariate and other multivariate GARCH models, summarized in a table format for future studies. Table 3 explains the review of GARCH and its variations models. The univariate GARCH model is for a single time series. It is a statistical model that is used to analyze a number of different kinds of financial data. Financial institutions and researchers usually use this model to estimate the volatility of returns for stocks, bonds, and market indices. In the GARCH model, current volatility is influenced by past innovation to volatility. GARCH models are used to model for forecast volatility of one time series. The most widely used GARCH form is GARCH (1, 1) and this has some extensions.

Different literature studies based on generalized autoregressive conditional heteroskedastic (GARCH) and its variations models.

Notes: APARCH (Asymmetric Power ARCH), AIC (Akaike Information Criterion), OHLC (Open-High-Low-Close Chart), NSE (National Stock Exchange of India), EWMA (Exponentially Weighted Moving Average), CGARCH (Component GARCH), BDS (Brock, Dechert & Scheinkman) Test, ARCH-LM (ARCH-Lagrange Multiplier) test, VAR (Vector Autoregression) model, VEC (Vector Error Correction) model, ARFIMA (Autoregressive Fractional Integral Moving Average), FIGARCH (Fractionally Integrated GARCH), SHCI (Shanghai Stock Exchange Composite Index), SZCI (Shenzhen Stock Exchange Component Index), ADF (Augmented Dickey–Fuller) test, BSE (Bombay Stock Exchange), and PGARCH (Periodic GARCH) are discussed.

In a simple GARCH model, the squared volatility σ t 2 is allowed to change on previous squared volatilities, as well as previous squared values of the process. The conditional variance satisfies the following form: σ t 2 = α 0 + α 1 ϵ t − 1 2 + … + α q ϵ t − q 2 + β 1 σ t − 1 2 + … + β p σ t − p 2 where, α i > 0 and β i > 0 . For the GARCH model, residuals’ lags can substitute by a limited number of lags of conditional variances, which abridges the lag structure and in addition the estimation method of coefficients. The most often used GARCH model is the GARCH (1, 1) model. The GARCH (1, 1) process is a covariance-stationary white noise process if and only if α 1 + β < 1 . The variance of the covariance-stationary process is given by α 1   /   ( 1 − α 1 − β ) . It specifies that σ n 2     is based on the most recent observation of φ t 2   and the most recent variance rate σ n − 1 2 . The GARCH (1, 1) model can be written as σ n 2 = ω + α φ n − 1 2 + β σ n − 1 2 and this is usually used for the estimation of parameters in the univariate case.

Though, GARCH model is not a complete model, and thus could be developed, these developments are detected in the form of the alphabet soup that uses GARCH as its key component. There are various additions of the standard GARCH family models. Nonlinear GARCH (NGARCH) was proposed by Engle and Ng [ 18 ]. The conditional covariance equation is in the form: σ t 2 = γ + α ( ε t − 1 − ϑ σ t − 1   ) 2 + β σ t − 1 2 , where α ,   β ,   γ > 0 . The integrated GARCH (IGARCH) is a restricted version of the GARCH model, where the sum of all the parameters sum up to one and this model was introduced by Engle and Bollerslev [ 19 ]. Its phenomenon might be caused by random level shifts in volatility. The simple GARCH model fails in describing the “leverage effects” which are detected in the financial time series data. The exponential GARCH (EGARCH) introduced by Nelson [ 5 ] is to model the logarithm of the variance rather than the level and this model accounts for an asymmetric response to a shock. The GARCH-in-mean (GARCH-M) model adds a heteroskedasticity term into the mean equation and was introduced by Engle et al. [ 20 ]. The quadratic GARCH (QGARCH) model can handle asymmetric effects of positive and negative shocks and this model was introduced by Sentana [ 21 ]. The Glosten-Jagannathan-Runkle GARCH (GJR-GARCH) model was introduced by Glosten et al. [ 22 ], its opposite effects of negative and positive shocks taking into account the leverage fact. The threshold GARCH (TGARCH) model was introduced by Zakoian [ 23 ], this model is also commonly used to handle leverage effects of good news and bad news on volatility. The family GARCH (FGARCH) model was introduced by Hentschel [ 24 ] and is an omnibus model that is a mix of other symmetric or asymmetric GARCH models. The COGARCH model was introduced by Klüppelberg et al. [ 25 ] and is actually the stochastic volatility model, being an extension of the GARCH time series concept to continuous time. The power-transformed and threshold GARCH (PTTGARCH) model was introduced by Pan et al. [ 26 ], this model is a very flexible model and, under certain conditions, includes several ARCH/GARCH models.

Based on the researchers’ articles, the symmetric GARCH (1, 1) model has been used widely to forecast the unconditional volatility in the stock market and time series data, and has been able to simulate the asset yield structure and implied volatility structure. Most researchers show that GARCH (1, 1) with a generalized distribution of residual has more advantages in volatility assessment than other models. Conversely, the asymmetry influence in stock market volatility and return analysis was beyond the descriptive power of the asymmetric GARCH models, as the models could capture more specifics. Besides, the asymmetric GARCH models can incompletely measure the effect of positive or negative shocks in stock market return and volatility, and the GARCH (1, 1) comparatively failed to accomplish this fact. In asymmetric effect, the GJR-GARCH model performed better and produced a higher predictable conditional variance during the period of high volatility. In addition, among the asymmetric GARCH models, the reflection of EGARCH model appeared to be superior.

Table 4 has explained the review of bivariate and other multivariate GARCH models. Bivariate model analysis was used to find out if there is a relationship between two different variables. Bivariate model uses one dependent variable and one independent variable. Additionally, the Multivariate GARCH model is a model for two or more time series. Multivariate GARCH models are used to model for forecast volatility of several time series when there are some linkages between them. Multivariate model uses one dependent variable and more than one independent variable. In this case, the current volatility of one time series is influenced not only by its own past innovation, but also by past innovations to volatilities of other time series.

Different literature studies based on bivariate and other multivariate GARCH models.

The most recognizable use of multivariate GARCH models is the analysis of the relations between the volatilities and co-volatilities of several markets. A multivariate model would create a more dependable model than separate univariate models. The vector error correction (VEC) models is the first MGARCH model which was introduced by Bollerslev et al. [ 66 ]. This model is typically related to subsequent formulations. The model can be expressed in the following form: v e c h   ( H t ) = ℂ + ∑ j = 1 q X j   v e c h   ( ϵ t − j   ϵ t − j ' ) + ∑ j = 1 p Y j   v e c h   ( H t − j   )   where v e c h is an operator that stacks the columns of the lower triangular part of its argument square matrix and H t is the covariance matrix of the residuals. The regulated version of the VEC model is the DVEC model and was also recommended by Bollerslev et al. [ 66 ]. Compared to the VEC model, the estimation method proceeded far more smoothly in the DVEC model. The Baba-Engle-Kraft-Kroner (BEKK) model was introduced by Baba et al. [ 67 ] and is an innovative parameterization of the conditional variance matrix H t . The BEKK model accomplishes the positive assurance of the conditional covariance by conveying the model in a way that this property is implied by the model structure. The Constant Conditional Correlation (CCC) model was recommended by Bollerslev [ 68 ], to primarily model the conditional covariance matrix circuitously by estimating the conditional correlation matrix. The Dynamic Conditional Correlation (DCC) model was introduced by Engle [ 69 ] and is a nonlinear mixture of univariate GARCH models and also a generalized variety of the CCC model. To overcome the inconveniency of huge number of parameters, the O-GARCH model was recommended by Alexander and Chibumba [ 70 ] and consequently developed by Alexander [ 71 , 72 ]. Furthermore, a multivariate GARCH model GO-GARCH model was introduced by Bauwens et al. [ 73 ].

The bivariate models showed achieve better in most cases, compared with the univariate models [ 85 ]. MGARCH models could be used for forecasting. Multivariate GARCH modeling delivered a realistic but parsimonious measurement of the variance matrix, confirming its positivity. However, by analyzing the relative forecasting accuracy of the two formulations, BEKK and DCC, it could be deduced that the forecasting performance of the MGARCH models was not always satisfactory. By comparing it with the other multivariate GARCH models, BEKK-GARCH model was comparatively better and flexible but it needed too many parameters for multiple time series. Conversely, for the area of forecasting, the DCC-GARCH model was more parsimonious. In this regard, it was significantly essential to balance parsimony and flexibility when modeling multivariate GARCH models.

The current systematic review has identified 50 research articles for studies on significant aspects of stock market return and volatility, review types, and GARCH model analysis. This paper noticed that all the studies in this review used an investigational research method. A literature review is necessary for scholars, academics, and practitioners. However, assessing various kinds of literature reviews can be challenging. There is no use for outstanding and demanding literature review articles, since if they do not provide a sufficient contribution and something that is recent, it will not be published. Too often, literature reviews are fairly descriptive overviews of research carried out among particular years that draw data on the number of articles published, subject matter covered, authors represented, and maybe methods used, without conducting a deeper investigation. However, conducting a literature review and examining its standard can be challenging, for this reason, this article provides some rigorous literature reviews and, in the long run, to provide better research.

4. Conclusions

Working on a literature review is a challenge. This paper presents a comprehensive literature which has mainly focused on studies on return and volatility of stock market using systematic review methods on various financial markets around the world. This review was driven by researchers’ available recommendations for accompanying systematic literature reviews to search, examine, and categorize all existing and accessible literature on market volatility and returns [ 16 ]. Out of the 435 initial research articles located in renowned electronic databases, 50 appropriate research articles were extracted through cross-reference snowballing. These research articles were evaluated for the quality of proof they produced and were further examined. The raw data were offered by the authors from the literature together with explanations of the data and key fundamental concepts. The outcomes, in this research, delivered future magnitudes to research experts for further work on the return and volatility of stock market.

Stock market return and volatility analysis is a relatively important and emerging field of research. There has been plenty of research on financial market volatility and return because of easily increasing accessibility and availability of researchable data and computing capability. The GARCH type models have a good model on stock market volatilities and returns investigation. The popularity of various GARCH family models has increased in recent times. Every model has its specific strengths and weaknesses and has at influence such a large number of GARCH models. To sum up the reviewed papers, many scholars suggest that the GARCH family model provides better results combined with another statistical technique. Based on the study, much of the research showed that with symmetric information, GARCH (1, 1) could precisely explain the volatilities and returns of the data and when under conditions of asymmetric information, the asymmetric GARCH models would be more appropriate [ 7 , 32 , 40 , 47 , 48 ]. Additionally, few researchers have used multivariate GARCH model statistical techniques for analyzing market volatility and returns to show that a more accurate and better results can be found by multivariate GARCH family models. Asymmetric GARCH models, for instance and like, EGARCH, GJR GARCH, and TGARCH, etc. have been introduced to capture the effect of bad news on the change in volatility of stock returns [ 42 , 58 , 62 ]. This study, although short and particular, attempted to give the scholar a concept of different methods found in this systematic literature review.

With respect to assessing scholars’ articles, the finding was that rankings and specifically only one GARCH model was sensitive to the different stock market volatilities and returns analysis, because the stock market does not have similar characteristics. For this reason, the stock market and model choice are little bit difficult and display little sensitivity to the ranking criterion and estimation methodology, additionally applying software is also another matter. The key challenge for researchers is finding the characteristics in stock market summarization using different kinds of local stock market returns, volatility detection, world stock market volatility, returns, and other data. Additional challenges are modeled by differences of expression between different languages. From an investigation perception, it has been detected that different authors and researchers use special datasets for the valuation of their methods, which may put boundary assessments between research papers.

Whenever there is assurance that scholars build on high accuracy, it will be easier to recognize genuine research gaps instead of merely conducting the same research again and again, so as to progress better and create more appropriate hypotheses and research questions, and, consequently, to raise the standard of research for future generation. This study will be beneficial for researchers, scholars, stock exchanges, regulators, governments, investors, and other concerned parties. The current study also contributes to the scope of further research in the area of stock volatility and returns. The content analysis can be executed taking the literature of the last few decades. It determined that a lot of methodologies like GARCH models, Johansen models, VECM, Impulse response functions, and Granger causality tests are practiced broadly in examining stock market volatility and return analysis across countries as well as among sectors with in a country.

Author Contributions

R.B. and S.W. proposed the research framework together. R.B. collected the data, and wrote the document. S.W. provided important guidance and advice during the process of this research. All authors have read and agreed to the published version of the manuscript.

This research received no external funding.

Conflicts of Interest

The authors declare no conflict of interest.

SYSTEMATIC REVIEW article

Covid and world stock markets: a comprehensive discussion.

• 1 Department of Management Sciences, Lahore College for Women University, Lahore, Pakistan
• 2 Department of Management Sciences, National University of Modern Languages, Islamabad, Pakistan

The COVID-19 outbreak has disturbed the victims' economic conditions and posed a significant threat to economies worldwide and their respective financial markets. The majority of the world stock markets have suffered losses in the trillions of dollars, and international financial institutions were forced to reduce their forecasted growth for 2020 and the years to come. The current research deals with the impact of the COVID-19 pandemic on the global stock markets. It has focused on the contingent effects of previous and current pandemics on the financial markets. It has also elaborated on the pandemic impact on diverse pillars of the economy. Irrespective of all these destructive effects of the pandemic, still hopes are there for a sharp rise and speedy improvement in global stock markets' performance.

Introduction

The world is experiencing the worst health and economic disaster in the shape of COVID-19 pandemic. Dealing with this pandemic is the most challenging task being faced by human beings since the Second World War ( Maqsood et al., 2021 ). Coronavirus has pushed the markets toward the danger zone. The market panic has been started. This disease is contagious even before it shows obvious symptoms. It is quite difficult to hold people in quarantine in this outbreak. That's the narrative, and we haven't gotten very far into it yet. So, the potential for market disruption because of a scary narrative is quite high.

—Robert James Shriller, Nobel Memorial Prize Winner in Economic Sciences, 2013.

The epidemiological perspectives are not required to be understood here. Currently, well-informed individuals ought to have some know-how about the basics of contagious diseases. Times of fear are also times of rumor and misinformation; knowledge is the antidote ( Baldwin et al., 2020 ). The COVID-19 outbreak was officially reported in the Wuhan City of China in December 2019 and covered all continents of this globe other than Antarctica ( Hui et al., 2020 ). COVID-19 is a distinctive black swan event, and we are unaware of its existence, expansion, breadth, depth, magnitude, and even its disappearance ( He P. et al., 2020 ; He Q. et al., 2020 ). World Health Organization (WHO) officially declared COVID-19 a pandemic on 11th March 2020 ( Cucinotta and Vanelli, 2020 ). The pandemic has severely hit global economies ( Shafi et al., 2020 ). It has disrupted the life and lifestyle of almost everyone ( Aqeel et al., 2021 ). Almost no one has been left untouched. Another pandemic of information and misinformation is keeping pace with it during this pandemic, spreading fear and anxiety ( Koley and Dhole, 2020 ). The outbreak has changed the outlook of this globe within no time at all. Human beings are struggling with the long-lasting effects of this disease and the unforgettable reality of their existence which has never happened before. The pandemic affected more than 107 million people, with around 2.3 million causalities, and the numbers of cases are escalated day by day. The alarming point is the growth factor of this disease, where 100 contaminated cases create another 10,000 within a very limited time ( Bagchi et al., 2020 ).

The people from this generation have seen wars. They have seen the collapse of the Soviet Union. They have seen extremely dangerous terrorist attacks. They have seen the burst of financial bubbles, and they have seen the effects of climate change. However, they had not seen anything like the coronavirus before. A similar case has not existed for more than one hundred years. They were not ready for it, and they did not know how to respond to it. Since it was something that no one had any prior experience with, the pandemic has also led to reconsidering some things which were always previously thought either right or wrong ( Sharma, 2021 ).

The COVID-19 pandemic has spread globally, has made millions of people sick, and triggered an international response spearheaded by the World Health Organization to stop its spread. From Wuhan, China, it spread like wildfire. The virus has now visited almost every nation in the world, bringing helplessness and death with it. None are spared, and in some way or another, almost everyone has become a victim. In a recent message, the WHO warned that the worst is yet to come. The coronavirus has not only triggered disease and death, and it has affected almost every aspect human life. There is a long list of disruptions to daily life in the cities and states with lockdown, global sporting events, weddings, social events, post-poned ceremonies; all this has elicited the global crisis. Moreover, industries worldwide have been affected; stock markets have been reported in record downfall; airlines, travel, tourism, and hospitality sectors are the major victims of this pandemic. A significant disaster is job loss in various sectors ( Koley and Dhole, 2020 ).

Crucial and groundbreaking strategies are required to protect not only human lives but also to safeguard economies and uplift economic growth and financial health. Nations are exposed to a global health crisis, the like of which has not occurred for a century. This crisis is killing human beings, enhancing human distress, and upsetting the lives of individuals. This can be considered a sort of human, social, and economic crisis ( Mishra, 2020 ). The best efforts by governments from every country have failed to halt its spread: cities were put under lockdown; people were advised to stay at home; international borders were closed; travel bans at local, national and international level were imposed; markets, schools, universities and shopping complexes were closed. Quarantine and self-isolation have been advised to stop the spread of COVID-19. The virus has triggered an unprecedented global crisis which led the WHO to provide technical guidance for government authorities, healthcare workers, and other key stakeholders to respond to community spread ( Koley and Dhole, 2020 ).

In the intermingled economies, the Covid-19 pandemic came as a global distress that affects both the demand and supply side concurrently. Rapidly growing infectivity limits labor supply and badly affects productivity, whereas supply disruptions are also caused by social distancing, lockdowns and industry closures. On the other hand, disruption on the demand side is caused by reduced consumption, unemployment, and income loss and these economic prospects result in reduced company investment. The unpredictability about the path, instance, enormity and impact of Covid-19 could create a vicious cycle of redundancy, less consumption, and business closures, leading to financial distress. To identify and determine this extraordinary shock is the key challenge for the experiential analysis of this pandemic. The unprecedented nature of COVID-19 makes it difficult to recognize its non-linear effects, cross-country spillovers, and quantify unobserved factors to compose forecasts ( Chudik et al., 2020 ).

International institutions including the FAO, ILO, IFAD, and WHO jointly declared this pandemic a global challenge to food systems, public health, trade, and industry. Overwhelming social and economic disruptions put tens of millions of individuals at risk of falling below the poverty line. According to another approximation, by the end of this year, the number of undernourished people could increase by up to 32 million, which are ~690 million at present. It also poses an existential threat to a considerable number of business ventures. The world has a 3.3 billion workforce and ~50% of which are near to being unemployed. Significant individuals are informal workers with limited access to productive assets, quality health, and the majority lack social protection. Due to lockdowns, they lost their means to earn money and became incapable of feeding themselves and their families because for most their daily food depends upon their daily wages earned. Such a devastating effect on the entire food chain has exposed the vulnerability of this pandemic. Farmers have no access to markets, nor can buy inputs or sell their output and result in a reduced harvest. In addition to market shutdown, trade limitations, border closures, and detention measures dislocate food supply chains nationally and internationally, which badly influenced a healthy diet. Small scale farmers are the soft target of COVID-19 and placed nutrition and food security of the most marginalized population under threat, as income producers fall ill, die, or otherwise lose their work ( Chriscaden, 2020 ).

It is still difficult to understand the recovery due to the development of vaccines. To understand corona's economic impact, the following charts and maps exhibit real statistics so far.

Impact on Jobs

A report published by the OECD (2020) shows the impact of COVID-19 and containment measures on OECD economies where people were prohibited from going to work, resulting in a significant drop in business activity and extraordinary job losses. In some countries, millions have been moved to reduced hours and most people worked up to ten times fewer hours. Moreover, the rate of entire job loss is also very high. Some people are more exposed to this pandemic than others. As young people and women workers are at greater risk due to less secured and unskilled jobs. They are also associated with the industries most affected by this unprecedented shock, including restaurants, cafés and tourism.

Causing Recession

Worldwide economic downturn caused by the COVID-19 pandemic forced the Organization for Economic Cooperation and Development (OECD), International Monetary Fund (IMF), and World Bank (WB) to revise their forecasts and reported a significant decline in the projected rate of growth in late 2019 and mid-2020. Such deterioration can be seen in the IMF figures in which global economic growth forecasts declined from +3.4% to −4.4% during October 2019 and October 2020. In the same way, OECD also revised its forecast and lowered the growth rate from positive 2.9% in November to −4.5% in September 2020. In June 2020, OECD anticipated the blow of another wave of infections.

Impact on Travel

The travel industry is one of those acutely damaged industries due to lockdowns, border closures, and abandoned flight operations. Airlines are not only canceling flights, but customers also restrict themselves from holidays and business trips. A recently discovered subsequent wave of COVID-19 has forced national and international airlines to promulgate new travel restrictions and tighten their policies. While providing data of 2020, Flight tracking service Flight Radar 24 reveals a huge hit in number of flights worldwide and requires a long way to recover ( Jones et al., 2021 ).

Impact on Tourism

Tourism is another badly affected industry due to this unprecedented pandemic. The World Tourism Organization, also known as UNWTO (2020) marked this pandemic as a serious threat to the travel and tourism sector. Many jurisdictions put restrictions on international travel to restrict the spread of the virus; some fully closed their borders, resulting in a massive decline in demand. In 2020, tourism reported a loss of ~1 billion tourists, equivalent to US$ 1.1 trillion in international tourism receipts. This decline in international tourism could cause an ~$2 trillion loss in global GDP, over 2% of the global GDP in 2019. While predicting a rebound in the global tourism industry, UNWTO presented an extended scenario for the year 2021 to the year 2024. According to them, global tourism will start recovery from the second half of the year 2021 but it will take 2.5 to 4 years to return to 2019.

Impact on Stock Markets

The capital markets are at the front line of any country's economy, and the stock markets are considered the indicator of any economy ( He P. et al., 2020 ; He Q. et al., 2020 ). The COVID-19 outbreak has disturbed the victims' economic conditions and posed a significant threat to the worldwide economies and their respective financial markets ( Barro et al., 2020 ; Ramelli and Wagner, 2020 ). The majority of the world stock markets have suffered in terms of trillion-dollar losses ( Lyócsa et al., 2020 ) and international financial institutions were forced to reduce their forecasted growth for 2020 and the years to come ( Boone et al., 2020 ). The root cause of this severe decline is the exposure of stock markets to several risks, for instance, the global financial crisis of 2008, which had pushed these markets in a melting position ( Dang and Nguyen, 2020 ). The current pandemic has affected the global stock markets significantly compared to the SARS virus, which was spread in 2003 as China has got tremendous development in comparison to the last 17 years and recognized as a leading economy of the world and also a global production hub, manufacturing the highly demanded technology products ( Alameer et al., 2019 ).

Effects of Previous Pandemics on Stock Markets

Scholars have argued that previous pandemics triggered fragile stock markets ( Chen et al., 2018 ) and impeded stock market participants' decision-making capacity by reducing their active involvement in stock market trading ( Dong and Heo, 2014 ). The literature has provided empirical evidence of the stock market reactions to significant systematic events. The research has shown the cyclical nature of the stock market reactions and the factors that affected the stock markets ( Keating, 2001 ). The historical performance of stock markets has been documented in the previous literature regarding influenza and other major epidemics. Similarly, the scholars have examined the influences of significant events on the stock markets, i.e., Severe Acute Respiratory Syndrome (SARS), ( Chen et al., 2018 ), natural disasters ( Caporale et al., 2019 ), corporate events ( Ranju and Mallikarjunappa, 2019 ), public news, and political events ( Bash and Alsaifi, 2019 ). Some other studies have also demonstrated that SARS in 2003 weakened the Taiwanese economy ( Chen et al., 2007 ) and regional stock markets ( Chen et al., 2018 ).

The previous studies have comprehensively examined the association between outbreaks and stock market performance. Kalra et al. (1993) investigated the disaster of the Soviet Chernobyl nuclear power plant. Delisle (2003) recognized that effects were of greater intensity after SARS (2003) than the Asian financial crisis. Nippani and Washer (2004) investigated the effects of SARS on global financial markets and found that it influenced the markets of China and Vietnam. Lee and and McKibbin (2004) reported the strong effect of SARS on human beings and financial integration. Loh (2006) explained a robust linkage between SARS and airline stocks performance in Canada, China, Hong Kong, Singapore, and Thailand and illustrated that the stocks of the aviation sector are more sensitive than non-aviation stocks. MckKibbin and Sidorenko (2006) investigated the influenza epidemic's impact on the global economy's growth by considering its diverse magnitudes like slight, moderate and intense. Moreover, Chen et al. (2007) noticed the negative effects of SARS on the hotel industry's stock prices in Taiwan. They also investigated the significant influence of SARS on the four major stock markets of Asia and China. Nikkinen et al. (2008) discovered the impact of the 9/11 incident on the global stock prices; however, the markets recovered rapidly. Al Rjoub (2009) also studied the influence of financial crisis on stock market.

Besides, Kaplanski and Levy (2010) studied the effect of aviation accidents on stock returns and established that price fluctuations are sensitive to such incidents. Al Rjoub (2011) and Al Rjoub and Azzam (2012) investigated the impact of the Mexican tequila crisis (1994), Asian-Russian financial crisis (1997–98), 9/11 incident, Iraq war (2004), financial crisis (2005), and global financial crisis (2008–09) on the stock compensation behavior in Jordan's Stock Exchange. Righi and Ceretta (2011) established the positive effect of the European debt crisis (2010) on European markets' risk aptitude, especially the German, French, and British markets. Schwert (2011) explored the variabilities in the prices of US stocks during the financial crisis. Mctier et al. (2011) found the negative impact of Flu on the intensity of trading activities and stock returns in the USA. Besides, Rengasamy (2012) examined the effect of Eurozone sovereign debt-related policy announcements, development rewards, and stock market volatility on Brazil, Russia, India, China, and South Africa. Karlsson and Nilsson (2014) found the negative impact of the 1918 Spanish flu epidemic on capital returns. Lanfear et al. (2018) conducted a study to explore the effect of cyclones on stock returns, and they observed the effect of emergencies on stock returns. Chen et al. (2018) examined the influence of SARS on Asian financial markets.

Brief Overview of Literature

Studies have elaborated on the performance of global stock markets affecting the COVID-19 outbreak ( Ahmar and del Val, 2020 ; Al-Awadhi et al., 2020 ; Liu et al., 2020 ; Zhang et al., 2020 ). The pandemic has decreased investors' confidence level in the stock market as the market uncertainty was very high ( Liu et al., 2020 ). Iyke (2020) explained that COVID-19 has robust and continual negative effects on the global economy. Ahmar and del Val (2020) used ARIMA and SutteARIMA and forecasted the short-term impact of COVID-19 on Spain's IBEX index. They further explained that SutteARIMA is the better statistical measure in forecasting such impact.

Moreover, Alam et al. (2020) explained that pandemic has greatly hit Australia's capital market right from the start of 2020. The stock market has shown a bearish trend, though some sectors were at high risk and others have performed well. The researchers have focused on initial volatility and sectoral returns in eight different sectors. They have analyzed the data using the event study method and 10-days window for the official announcements of COVID-19 events in Australia. The findings revealed that some sectors performed well on the day of the announcement. Simultaneously, some others also showed good performance after the announcement except the transportation sector, which performed poorly.

The pandemic has posed severe challenges to the global economies ( Wang et al., 2021 ) and it has also created mental health issues ( Abbas et al., 2021 ). Chowdhury et al. (2020) examined the impact of COVID-19 on economic activities and stock markets worldwide. The study has targeted 12 countries from four continents from January-April 2020 by using the panel data. The stock market impact was measured using the event study method, and economic impact was measured using the panel vector autoregressive model. The results showed the extremely negative effects of pandemic variables on stock returns. Singh et al. (2020) investigated the influence of COVID-19 on the stock markets of G-20 states. The study used an event study for measuring abnormal returns and panel data to describe the causes of abnormal returns. The data consisted of 58 days of post-COVID period news provided by international media and 120 days before the event. The findings exhibited the significant negative abnormal returns during the event days. Liu et al. (2020) also examined the pandemic's effect on the most affected countries' stock markets by using the event study. The researchers revealed the negative effects of COVID-19 on the stock markets' performance.

He P. et al. (2020) and He Q. et al. (2020) also used the event study method to explore the impact of COVID-19 on Chinese industries and stock market performance. It has been observed that some industries were severely affected by the pandemic (mining, environment etc.). However, some other industries have faced limited effects of an outbreak (manufacturing, education etc.). Machmuddah et al. (2020) used the event study method to observe consumer goods' share prices before and after COVID-19. The data about daily stock prices and stock trade volume has been collected before and after the pandemic. Significant differences have been observed between daily closing prices and stock trade volume before and after the pandemic. Liu et al. (2020) used an event study method to study the short term impact of the outbreak on the stock market indices of 21 countries strongly affected by pandemic (Italy, UK, Germany etc.). Asian countries have taken the severe negative effect of the pandemic as compared to other states. Khatatbeh et al. (2020) also applied the event study method to discover the impact of COVID-19 on some targeted countries' stock indices by employing the daily stock prices and found a significant negative impact on returns.

Al-Awadhi et al. (2020) investigated the association of pandemic and stock market outcomes in the Chinese stock market. The findings showed the effect of pandemic cases and deaths on the stock returns of different organizations. Baker et al. (2020) claimed that COVID-19 strongly affects the US stock market compared to previous epidemics, including the Spanish Flu. Eighteen market jumps were observed from February-March 2020. The market jumps were considered to be the largest ones since 1990. The causes behind such jumps were the lockdowns and production cut. Ozili and Arun (2020) described that COVID-19 uncertainty and the fear of losing profit have resulted in 6 trillion USD in the global stock market on 24th February 2020. Similarly, the S&P 500 index has faced a loss of 5 trillion US dollar. The research also demonstrated the significant influence the pandemic on the opening, highest, and lowest stock indices in the US. Ngwakwe (2020) illustrated the influence of COVID-19 outbreak on some targeted stock indices (SSE, Euronext, and DJIA) by collecting the data for 50 days before and 50 days within the pandemic. The differential effects of the pandemic were observed in different stock markets. DJIA stock returns were decreased, SSE increased, however, S&P 500 index and Euronext 100 revealed insignificant effects.

He P. et al. (2020) and He Q. et al. (2020) examined the direct effects of COVID-19 spillovers on the stock market. The daily return data has collected from China, Italy, South Korea, France, Spain, Germany, Japan and the USA. The findings showed the negative short term effects of COVID-19 on the stock indices. Zhang et al. (2020) elaborated the impact of pandemic fear on the pattern of systematic risk and country-specific risk in the global financial markets. They explained the volatile nature of financial markets and the huge impact of uncertain market conditions on financial market risk. Sobieralski (2020) evaluated the effect of COVID-19 on employment and the aviation industry. The stock returns of China and US stocks have declined at a record level. Qin et al. (2020) investigated the influence of outbreak on oil markets.

Sansa (2020) explained the association between COVID-19 recorded cases and financial markets systems of SSE and DJIA during March 2020. Aslam et al. (2020) studied the impact of COVID-19 on 56 global stock market (developed, developing, emerging, and frontier) indices by using the network method. Topcu and Gulal (2020) have discovered a huge impact on Asian markets as compared to European markets. Ashraf (2020) explained that confirmed cases more strongly affect the stock market than deaths. Czech et al. (2020) used the TGARCH model and found the negative impact of COVID-19 on Visegrad stock market indices. They discovered that stock markets were seriously affected when the disease's nature was changed from epidemic to pandemic.

Zhang et al. (2020) also investigated the influence of COVID-19 on the stock markets of 10 countries. It was concluded that European stock markets showed connectivity during the outbreak; however, US markets could not show a leading role before and during the pandemic. Okorie and Lin (2021) discovered the occurrence of financial contagion during the pandemic. Corbet et al. (2020) presented some interesting insights. They illustrated that pandemic greatly affected the companies having names related to the virus, although these companies were not related to the virus.

The current research work basically pertains to the comprehensive discussion about the past present and future of world stock markets. For the sake of achieving the research aims, it has also presented a somehow brief yet inclusive debate about the happenings in the renowned stock markets. It has focused on the major market indices belong to different regions and also it has attempted to explain the actual position of some famous indices with the help of underlying real time data based graphs. Its major contribution is presenting the diverse opinions of traditional and behavioral finance regarding the behavior of stock market participants.

A General Debate About Stock Markets Performance

The global stock markets have been reported for their record decline. On 23 March 2020 the S&P 500 Index witnessed an usual drop of 35% compared to the record high on 18 February 2020. In no time at all, the intensity of this record fall became comparable with the financial crisis of 2008, black Monday of 1987, and the great depression of October-November, 1929 ( Helppie McFall, 2011 ). Fernandes (2020) also explained that the US S&P 500 index went down to 30% during March 2020. He further described that the UK and Germany's stock markets were noticed for their worst performance than the US market. The returns of these two markets were fallen by 37 and 33%, respectively. However, the worst performers in the global stock markets were Brazil (−48%) and Columbia (−47%).

Japan's market index dropped more than 20% compared to the record high values of December 2019. S&P 500 Index and Dow Jones share points were declined by 20% in March 2020. The Nikkei Index also reported the same downfall. The Colombo Stock Exchange witnessed a 9% drop in share value and experienced three market halts during mid-March 2020. The Indonesian stock market followed a similar decline. In April 2020, the index was opened with a 64.06 points decline. The UK-FTSE index plunged by 29.72%. The DAX (Germany) index was dropped by 33.37%, CAC (France) by 33.63%, NIKKEI (Japan) by 26.85%, and SUNSEX (India) want down by 17.74% ( Machmuddah et al., 2020 ). Shanghai Composite went down to 2,660.17 points on 23rd March 2020, showing a decline of 12.49% compared to December 2019. KOSPI touched the peak level of 2,204.21 points on 27th December 2019 and dropped to the lowest point of 1,457.64 on 19th March 2020, showing a drop of 33.87%. The BSE SENSEX reported the highest points of 41,681.54 on 20th December 2019. BSE SENSEX plunged to 25,981 points on 23rd March 2020 due to the COVID-19 outbreak, demonstrating a decline of 37.66%. FTSE 100 showed an upward trend on 27th December 2019 with a record index of 7,644.90 points, but it reflected the downward trend followed by a pandemic with an index value of 4,993.89 34.67% decline. The NASDAQ 100 Index reached 8,778.31 points on 26th December 2019 and observed the negative effects of the COVID outbreak by touching 7006.92 points with a declining trend of 20.17%. Moreover, MOEX revealed a bullish trend on 27th December 2019 with an index value of 3,050.47 points and reflected the effects of COVID-19 by reaching 2,112.64 points with the corresponding decline of 30.74%.

Besides, FTSE MIB reached the record level of 24,003.64 points on 20th December 2019 and then touched 14,894.44 points due to pandemic on 12th March 2020 with a declining rate of 37.94%. Nikkei 225 demonstrated an upward trend with the peak value of 24,066.12 on 17th December 2019 and represented the lowest range of 16,552.83 points following the pandemic on 19th March 2020 with the corresponding decline of 31.21%. CAC 40 represented 6,037.39 points on 27th December 2019, consequently faced the sharp jerk of 37.80% on 18th March 2020. DAX exhibited an ascending trend on 16th December 2020 with a peak value of 13,407.66, with the corresponding decline of 8,441.71 on 18th March 2020, signifying an increase of 37.04%. Moving forward, S&P/TSX jumped to 17,180.15 on 24th December 2019 and showed the devastating effects of COVID-19 with the sharp decline of 34.64% on 23rd March 2020. Besides, FTS/JSE reflected 3,513.21 points on 20th November 2020 and affected by the outbreak with a decline of 36.37% on 23rd March 2020 (Investopedia).

However, the global stock markets regained and demonstrated a bullish trend during the days of April 2020. The S&P 500 index increased by 29% and regained the strong position it had held in August 2019 ( Cox et al., 2020 ). Shanghai Composite index further increased by 8.22% in May 2020. KOSPI index showed a bullish trend and the index increased by 27.05%. Similarly, BSE SENSEX recaptured its position and touched 33,717.62 points on 30th April 2020, representing the rise of 22.94%. FTSE 100 secured an 18.33% increase, and the index targeted 6,115.25 points on 29th April 2020. NASDAQ 100 touched 9,485.02 points on 20th May 2020 with the respective rise of 26.12%. MOEX showed an upward trend with a 74.64% increase on 13th April 2020. Also, BOVESPA regained by 23.56% on 29th April 2020 and touched 83.170.80 points. FTSE MIB upbeat and reached 18,067.29 on 29th April 2020. On 20th May 2020, NIKKEI Index climbed at 20,595.15 points, reflecting an increase of 19.62%. Moreover, CAC 40 revived by 19.61% on 29th April 2020. DAX invigorated with the 24.79% increase on 20th May 2020. S&P/TSX touched 15,228 points on 29th April 2020, FTSE/JSE recovered by 27.09% on 20th May 2020, beating the outbreak's negative effect (Investopedia).

The stock market indices worldwide have been categorized in terms of Major Stock Indices, Global Stock Indices, and World Stock Indices etc. The Major World Stock market indices as well as their respective countries have been presented in the Table 1 .

Table 1 . Major world market indices.

Graphical Representation of Some Leading Indices

Source of all figures: tradingeconomics.com .

Figure 1 represents the stock market performance of the S&P ASX 50 index of Australia. It can be seen that the index was performing well-during January 2020, when COVID-19 was at its initial phase. However, March seemed to be a nightmare, when the index plunged and reached the lowest level as COVID-19 spread rapidly and hit a majority of the nations. But the index revived during April 2020, and a gradually limited bullish trend was observed. In-spite of such revival, the index could not reach its peak as the world is still facing the 3rd wave of the pandemic.

Figure 1 . S&P ASX 50 (Australia). Source: tradingeconomics.com . Reproduced with permission.

Figure 2 exhibits the stock market conditions of DAX Germany. The stock market did perform well-until February 2020, it showed a bearish trend in March 2020, followed by a gradual increase, and finally, it realized the position as it was before the pandemic.

Figure 2 . DAX (Germany). Source: tradingeconomics.com . Reproduced with permission.

Figure 3 demonstrates the stock market situation of Dow Jones Industrial Averages, one of the USA's leading indices. The same situation was observed just like previous indices. The bullish trend was observed before March 2020, followed by the bearish trend during March-April, 2020. Index regained slowly, and revival leads to the extreme upward movements.

Figure 3 . Dow Jones industrial averages (USA). Source: tradingeconomics.com . Reproduced with permission.

Figure 4 illustrates the stock market trend of CAC 40, the index of France. The index was at its peak during February 2020. However, a sudden jerk was observed during March 2020, and the index touched the lowest points. The index recovered quite slowly, and to date, it could not recover its previous position. The fluctuations in the index can still be noticed.

Figure 4 . CAC40 (France). Source: tradingeconomics.com . Reproduced with permission.

The variations in the FTSE 100 index of Europe's market conditions can be seen in Figure 5 . The bullish trend can be observed before March 2020, followed by the extreme bearish trend. The index went to the historical lowest points during March 2020. The upward movements were started during April 2020; however, slow movements were there, and the index is still in a slow recovery phase.

Figure 5 . FTSE-100 (Europe). Source: tradingeconomics.com . Reproduced with permission.

SENSEX index is a famous stock market index of India. Figure 6 is representing its performance. In January 2020, though the index was not performing very well, it faced the effects of COVID-19 during March 2020. The extreme slow revival was observed after March, and the index remains at the same pace. However, the gradual upward trends lead the index to its highest peak in 2021, as shown in the figure.

Figure 6 . SENSEX (India). Source: tradingeconomics.com . Reproduced with permission.

Figure 7 depicts Japan's famous index, i.e., the Nikkei 225. The index was in the recovery phase during January 2020; however, a bearish trend was observed from the outbreak. After March 2020, the recovery phase was there, but static movements were observed. Nevertheless, these slow recoveries finally touched the highest peak in 2021.

Figure 7 . Nikkei-225 (Japan). Source: tradingeconomics.com . Reproduced with permission.

Figure 8 deals with the NASDAQ stock market performance, one of the USA's leading indices. During the start of 2020, its performance was below average, ultimately reaching the lowest points in March 2020 as per the COVID-19 effects. The index escalates gradually, and to date, it jumped and touched the peak level.

Figure 8 . NASDAQ (USA). Source: tradingeconomics.com . Reproduced with permission.

Referring to Figure 9 , the PSX-100 of Pakistan was performing well-before the sharp rise of COVID-19 in Pakistan. However, the month of March 2020 proved to be a terrible one; the index plunged and touched the lowest level. A slow revival was observed, which ultimately hit the highest points during 2021, as showing in the Figure 9 .

Figure 9 . PSX-100 (Pakistan). Source: tradingeconomics.com . Reproduced with permission.

The performance of the S&P 500 index, a prominent index of the USA, seems to be similar to the NASDAQ stock market index. However, before COVID and the recovery phase after March 2020 is better than the NASDAQ index. Currently, the index has reached the highest level as shown in Figure 10 .

Figure 10 . S&P 500 (USA). Source: tradingeconomics.com . Reproduced with permission.

Figure 11 exhibits the Shanghai Stock Exchange Composite index of China, the origin of the COVID-19 pandemic. The SSE index is the outperformer index of China; however, it was severely affected by the pandemic. The index plunged from the start of the outbreak up to June 2020, followed by a sharp rise and now, with the gradual increase, the index has reached the maximum points.

Figure 11 . SSE composite (China). Source: tradingeconomics.com . Reproduced with permission.

Implications for Stock Market Participants

The current study has some implications for market participants and policymakers, i.e., investors, managers, corporations, and governments. The investors must have market know how to invest their resources in favorable avenues even during the contingent market conditions, which have just happened during COVID-19. The investors can take guidance from the mangers and policymakers in this regard. In this way, investors can take rational decision making for their investments. Moreover, investors can generate their portfolios and risk management strategies. Besides, investors must focus on diversification to avoid losses during the pandemic situation.

The managers are the key stakeholders of financial markets; they have experience with stocks' risky nature during the pandemic and can take preventive measures accordingly. The mangers can increase the confidence level of investors, which lead them to make long term investments.

Governments can also play a vital role in assisting with the outbreak in tax rebates and interest-free loans. Governments can even facilitate the national markets by relaxing the lending policies and providing short-term loans on relaxing terms. Governments can conduct surveys and can assist investors in reducing their uncertainty.

Policymakers can develop successful methodologies for balancing financial investments during the outbreak. For this, they can focus on understanding the dynamics of stock markets in devising effective strategies. Besides, policymakers can integrate policies to cope-up with the financial and economic impacts of the COVID-19 outbreak. The emphasis must be on the improvement of stock market stability.

Unlocking the Future in Post-COVID-19 World

The aim of realizing sustainable growth, a big challenge for all economies, has been underscored by the novel virus. The pandemic has directed that economies are not goal-oriented in terms of their aspiration; they are required to achieve the milestones of a robust global economy. The greatest accomplishments are always achieved through the heights of determination. History is always there to provide lessons for the future. Nearly 75 years ago, amid World War II and one of Britain's most difficult hours, Winston Churchill inspired the whole nation not with the slogans to “reconsider what is achievable” but with a firm determination to “never surrender.” Now at the most difficult time of the century, we are required to continue our fight for what the world needs instead of reconsidering the sustainable development goals. This crisis requires a determined global effort to “build back better” by making a big reset to reach where we were before ( Kharas and and McArthur, 2020 ). Moreover, the leaders of the world must draw a new course of action for improving the functioning of international financial and monetary system to make it strong enough to cope with any such crisis in future ( Coulibaly and Prasad, 2020 ). The stock markets had to face the worst situation in the last 30 years, business operations have abruptly failed, and various economic sectors have been critically affected. However, the best point that came out of the COVID-19 pandemic is the businesses' pressure to be innovative and redefine their operations. One example is the tech community, which has been progressing to facilitate the community in adopting the technology to deal with the pandemic's challenges. Such technological innovations assist specific divisions of organizations or even the whole organizations to carry on their operations irrespective of the current contingent situation. Certainly, the world and the multinational business models will face diverse post-virus issues. Following the COVID-19 pandemic, the nations will observe new policies relating to restructuring and operational strategies, i.e., strategic workforce planning including remote staff planning, flexible conventions, workers proficiency, best practices and HR strategies; Crisis response and business continuity planning, risk control strategies and measures; Financial resources to weather future unforeseen events; Cloud-enabled IT infrastructure (and the attendant improved cybersecurity procedures); and the Redundant sourcing of necessities (inventory, materials and individuals), ( David, 2020 ).

The prospects of the stock markets and the economies are based on the availability and accessibility of the vaccine. The optimism about the vaccine has revitalized the investors' appetite regarding hotels, energy firms, and airlines. However, some others have been brutally affected by the pandemic and are forced to sell their respective market shares. Stock markets are largely dealing with the sentiment that tomorrow may be better than today, leading to a fundamental and perhaps enduring sea change. The development of more vaccines would pave the way for more optimism. What this result demonstrates is that while the virus is not yet beaten, it is beatable. That ray of light has lit up stock markets around the world. As usual, some stock market participants are there to look for something else to worry about ( Jack, 2020 ).

The current study deals with the impact of the COVID-19 pandemic on the global stock markets. It has focused on the contingent effects of previous and current pandemics on the financial markets. It has also elaborated on the impact of the pandemic on diverse pillars of the economy. The pandemic has severely hit the worldwide markets and posited challenges for economists, policymakers, head of states, international financial institutions, regulatory authorities, and health institutions to deal with the long-lasting effects of the outbreak. It has opened our eyes to concentrate our efforts to protect the future health of citizens and the also financial issues. In the current pandemic situation, the stock markets faced the effects of Covid-19, and this back-and-forth is ongoing. The majority of the world stock markets have suffered trillion-dollar losses ( Lyócsa et al., 2020 ). International financial institutions like IMP and World Bank have been forced to reduce their forecasted growth for 2020 and the years to come ( Boone et al., 2020 ). The global stock markets have been reported for their record decline. The month of March 2020 saw an unusual drop in most worldwide indices like the S&P 500 Index, NASDAQ, NIKKEI, SSE composite, CAC-40; DAX etc. However, the global stock markets regained and demonstrated the bullish trend during the days of April 2020. Irrespective of all these cyclical effects of the pandemic, still hopes are there for the sharp rise and speedy improvements in global stock markets' performance. Moreover, these past events have become a key for mankind to get insights for better future planning ( Su et al., 2021 ).

Behavioral vs. Conventional Finance

The two polar aspects of finance i.e., traditional finance and behavioral finance have also shed light on the psychology of investors during the COVID-19 pandemic. As far as traditional finance is concerned, investors behave rationally. The rational attitude of investors restricts them from imitating the decisions of others. Investors get the basic facts and figures about the stock markets through their own efforts, resultantly the fear of avoiding future losses compel the investors to sell their stocks and the market shows bearish trend ( Jabeen and Rizavi, 2021 ). The same has happened in the world's stock markets during the peak of pandemic. There have been sudden jerks observed around the global stock markets ( Jabeen and Farhan, 2020 ).

On the other hand, behavioral finance is supposed to consist of a set of theories which focus on the irrationality of investors. The viewpoint of irrationality of investors is the foundation of behavioral finance. The irrational aspect of investors forces them to follow the decision of other investors by setting aside their own information. In such context, investors have confidence on the decision of other investors as they feel that others may possess better information skills ( Jabeen and Rizavi, 2021 ). As a result the panic market conditions lead investors to blindly follow the others to protect their investment and market also depicts the bearish trend, the one which has been seen during the COVID-19 outbreak.

This debate has proven that both the traditional finance and behavioral finance have provided the same mechanism during the COVID-19 pandemic, irrespective of the fact that these pillars of finance deal with the opposing behaviors of investors i.e., rational and irrational. In both of the scenarios, the investors have sale their shares and resultantly the bearish trend has been observed.

Data Availability Statement

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

Author Contributions

All authors listed have made a substantial, direct and intellectual contribution to the work, and approved it for publication.

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher's Note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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Keywords: COVID-19, stock markets, market indices, behavioral finance, SARS

Citation: Jabeen S, Farhan M, Zaka MA, Fiaz M and Farasat M (2022) COVID and World Stock Markets: A Comprehensive Discussion. Front. Psychol. 12:763346. doi: 10.3389/fpsyg.2021.763346

Received: 23 August 2021; Accepted: 30 September 2021; Published: 28 February 2022.

Reviewed by:

Copyright © 2022 Jabeen, Farhan, Zaka, Fiaz and Farasat. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Muhammad Farhan, muhammad.farhan@numl.edu.pk

Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.

• Open access
• Published: 28 August 2020

Short-term stock market price trend prediction using a comprehensive deep learning system

• Jingyi Shen 1 &
• M. Omair Shafiq   ORCID: orcid.org/0000-0002-1859-8296 1  

Journal of Big Data volume  7 , Article number:  66 ( 2020 ) Cite this article

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In the era of big data, deep learning for predicting stock market prices and trends has become even more popular than before. We collected 2 years of data from Chinese stock market and proposed a comprehensive customization of feature engineering and deep learning-based model for predicting price trend of stock markets. The proposed solution is comprehensive as it includes pre-processing of the stock market dataset, utilization of multiple feature engineering techniques, combined with a customized deep learning based system for stock market price trend prediction. We conducted comprehensive evaluations on frequently used machine learning models and conclude that our proposed solution outperforms due to the comprehensive feature engineering that we built. The system achieves overall high accuracy for stock market trend prediction. With the detailed design and evaluation of prediction term lengths, feature engineering, and data pre-processing methods, this work contributes to the stock analysis research community both in the financial and technical domains.

Introduction

Stock market is one of the major fields that investors are dedicated to, thus stock market price trend prediction is always a hot topic for researchers from both financial and technical domains. In this research, our objective is to build a state-of-art prediction model for price trend prediction, which focuses on short-term price trend prediction.

As concluded by Fama in [ 26 ], financial time series prediction is known to be a notoriously difficult task due to the generally accepted, semi-strong form of market efficiency and the high level of noise. Back in 2003, Wang et al. in [ 44 ] already applied artificial neural networks on stock market price prediction and focused on volume, as a specific feature of stock market. One of the key findings by them was that the volume was not found to be effective in improving the forecasting performance on the datasets they used, which was S&P 500 and DJI. Ince and Trafalis in [ 15 ] targeted short-term forecasting and applied support vector machine (SVM) model on the stock price prediction. Their main contribution is performing a comparison between multi-layer perceptron (MLP) and SVM then found that most of the scenarios SVM outperformed MLP, while the result was also affected by different trading strategies. In the meantime, researchers from financial domains were applying conventional statistical methods and signal processing techniques on analyzing stock market data.

The optimization techniques, such as principal component analysis (PCA) were also applied in short-term stock price prediction [ 22 ]. During the years, researchers are not only focused on stock price-related analysis but also tried to analyze stock market transactions such as volume burst risks, which expands the stock market analysis research domain broader and indicates this research domain still has high potential [ 39 ]. As the artificial intelligence techniques evolved in recent years, many proposed solutions attempted to combine machine learning and deep learning techniques based on previous approaches, and then proposed new metrics that serve as training features such as Liu and Wang [ 23 ]. This type of previous works belongs to the feature engineering domain and can be considered as the inspiration of feature extension ideas in our research. Liu et al. in [ 24 ] proposed a convolutional neural network (CNN) as well as a long short-term memory (LSTM) neural network based model to analyze different quantitative strategies in stock markets. The CNN serves for the stock selection strategy, automatically extracts features based on quantitative data, then follows an LSTM to preserve the time-series features for improving profits.

The latest work also proposes a similar hybrid neural network architecture, integrating a convolutional neural network with a bidirectional long short-term memory to predict the stock market index [ 4 ]. While the researchers frequently proposed different neural network solution architectures, it brought further discussions about the topic if the high cost of training such models is worth the result or not.

There are three key contributions of our work (1) a new dataset extracted and cleansed (2) a comprehensive feature engineering, and (3) a customized long short-term memory (LSTM) based deep learning model.

We have built the dataset by ourselves from the data source as an open-sourced data API called Tushare [ 43 ]. The novelty of our proposed solution is that we proposed a feature engineering along with a fine-tuned system instead of just an LSTM model only. We observe from the previous works and find the gaps and proposed a solution architecture with a comprehensive feature engineering procedure before training the prediction model. With the success of feature extension method collaborating with recursive feature elimination algorithms, it opens doors for many other machine learning algorithms to achieve high accuracy scores for short-term price trend prediction. It proved the effectiveness of our proposed feature extension as feature engineering. We further introduced our customized LSTM model and further improved the prediction scores in all the evaluation metrics. The proposed solution outperformed the machine learning and deep learning-based models in similar previous works.

The remainder of this paper is organized as follows. “ Survey of related works ” section describes the survey of related works. “ The dataset ” section provides details on the data that we extracted from the public data sources and the dataset prepared. “ Methods ” section presents the research problems, methods, and design of the proposed solution. Detailed technical design with algorithms and how the model implemented are also included in this section. “ Results ” section presents comprehensive results and evaluation of our proposed model, and by comparing it with the models used in most of the related works. “ Discussion ” section provides a discussion and comparison of the results. “ Conclusion ” section presents the conclusion. This research paper has been built based on Shen [ 36 ].

Survey of related works

In this section, we discuss related works. We reviewed the related work in two different domains: technical and financial, respectively.

Kim and Han in [ 19 ] built a model as a combination of artificial neural networks (ANN) and genetic algorithms (GAs) with discretization of features for predicting stock price index. The data used in their study include the technical indicators as well as the direction of change in the daily Korea stock price index (KOSPI). They used the data containing samples of 2928 trading days, ranging from January 1989 to December 1998, and give their selected features and formulas. They also applied optimization of feature discretization, as a technique that is similar to dimensionality reduction. The strengths of their work are that they introduced GA to optimize the ANN. First, the amount of input features and processing elements in the hidden layer are 12 and not adjustable. Another limitation is in the learning process of ANN, and the authors only focused on two factors in optimization. While they still believed that GA has great potential for feature discretization optimization. Our initialized feature pool refers to the selected features. Qiu and Song in [ 34 ] also presented a solution to predict the direction of the Japanese stock market based on an optimized artificial neural network model. In this work, authors utilize genetic algorithms together with artificial neural network based models, and name it as a hybrid GA-ANN model.

Piramuthu in [ 33 ] conducted a thorough evaluation of different feature selection methods for data mining applications. He used for datasets, which were credit approval data, loan defaults data, web traffic data, tam, and kiang data, and compared how different feature selection methods optimized decision tree performance. The feature selection methods he compared included probabilistic distance measure: the Bhattacharyya measure, the Matusita measure, the divergence measure, the Mahalanobis distance measure, and the Patrick-Fisher measure. For inter-class distance measures: the Minkowski distance measure, city block distance measure, Euclidean distance measure, the Chebychev distance measure, and the nonlinear (Parzen and hyper-spherical kernel) distance measure. The strength of this paper is that the author evaluated both probabilistic distance-based and several inter-class feature selection methods. Besides, the author performed the evaluation based on different datasets, which reinforced the strength of this paper. However, the evaluation algorithm was a decision tree only. We cannot conclude if the feature selection methods will still perform the same on a larger dataset or a more complex model.

Hassan and Nath in [ 9 ] applied the Hidden Markov Model (HMM) on the stock market forecasting on stock prices of four different Airlines. They reduce states of the model into four states: the opening price, closing price, the highest price, and the lowest price. The strong point of this paper is that the approach does not need expert knowledge to build a prediction model. While this work is limited within the industry of Airlines and evaluated on a very small dataset, it may not lead to a prediction model with generality. One of the approaches in stock market prediction related works could be exploited to do the comparison work. The authors selected a maximum 2 years as the date range of training and testing dataset, which provided us a date range reference for our evaluation part.

Lei in [ 21 ] exploited Wavelet Neural Network (WNN) to predict stock price trends. The author also applied Rough Set (RS) for attribute reduction as an optimization. Rough Set was utilized to reduce the stock price trend feature dimensions. It was also used to determine the structure of the Wavelet Neural Network. The dataset of this work consists of five well-known stock market indices, i.e., (1) SSE Composite Index (China), (2) CSI 300 Index (China), (3) All Ordinaries Index (Australian), (4) Nikkei 225 Index (Japan), and (5) Dow Jones Index (USA). Evaluation of the model was based on different stock market indices, and the result was convincing with generality. By using Rough Set for optimizing the feature dimension before processing reduces the computational complexity. However, the author only stressed the parameter adjustment in the discussion part but did not specify the weakness of the model itself. Meanwhile, we also found that the evaluations were performed on indices, the same model may not have the same performance if applied on a specific stock.

Lee in [ 20 ] used the support vector machine (SVM) along with a hybrid feature selection method to carry out prediction of stock trends. The dataset in this research is a sub dataset of NASDAQ Index in Taiwan Economic Journal Database (TEJD) in 2008. The feature selection part was using a hybrid method, supported sequential forward search (SSFS) played the role of the wrapper. Another advantage of this work is that they designed a detailed procedure of parameter adjustment with performance under different parameter values. The clear structure of the feature selection model is also heuristic to the primary stage of model structuring. One of the limitations was that the performance of SVM was compared to back-propagation neural network (BPNN) only and did not compare to the other machine learning algorithms.

Sirignano and Cont leveraged a deep learning solution trained on a universal feature set of financial markets in [ 40 ]. The dataset used included buy and sell records of all transactions, and cancellations of orders for approximately 1000 NASDAQ stocks through the order book of the stock exchange. The NN consists of three layers with LSTM units and a feed-forward layer with rectified linear units (ReLUs) at last, with stochastic gradient descent (SGD) algorithm as an optimization. Their universal model was able to generalize and cover the stocks other than the ones in the training data. Though they mentioned the advantages of a universal model, the training cost was still expensive. Meanwhile, due to the inexplicit programming of the deep learning algorithm, it is unclear that if there are useless features contaminated when feeding the data into the model. Authors found out that it would have been better if they performed feature selection part before training the model and found it as an effective way to reduce the computational complexity.

Ni et al. in [ 30 ] predicted stock price trends by exploiting SVM and performed fractal feature selection for optimization. The dataset they used is the Shanghai Stock Exchange Composite Index (SSECI), with 19 technical indicators as features. Before processing the data, they optimized the input data by performing feature selection. When finding the best parameter combination, they also used a grid search method, which is k cross-validation. Besides, the evaluation of different feature selection methods is also comprehensive. As the authors mentioned in their conclusion part, they only considered the technical indicators but not macro and micro factors in the financial domain. The source of datasets that the authors used was similar to our dataset, which makes their evaluation results useful to our research. They also mentioned a method called k cross-validation when testing hyper-parameter combinations.

McNally et al. in [ 27 ] leveraged RNN and LSTM on predicting the price of Bitcoin, optimized by using the Boruta algorithm for feature engineering part, and it works similarly to the random forest classifier. Besides feature selection, they also used Bayesian optimization to select LSTM parameters. The Bitcoin dataset ranged from the 19th of August 2013 to 19th of July 2016. Used multiple optimization methods to improve the performance of deep learning methods. The primary problem of their work is overfitting. The research problem of predicting Bitcoin price trend has some similarities with stock market price prediction. Hidden features and noises embedded in the price data are threats of this work. The authors treated the research question as a time sequence problem. The best part of this paper is the feature engineering and optimization part; we could replicate the methods they exploited in our data pre-processing.

Weng et al. in [ 45 ] focused on short-term stock price prediction by using ensemble methods of four well-known machine learning models. The dataset for this research is five sets of data. They obtained these datasets from three open-sourced APIs and an R package named TTR. The machine learning models they used are (1) neural network regression ensemble (NNRE), (2) a Random Forest with unpruned regression trees as base learners (RFR), (3) AdaBoost with unpruned regression trees as base learners (BRT) and (4) a support vector regression ensemble (SVRE). A thorough study of ensemble methods specified for short-term stock price prediction. With background knowledge, the authors selected eight technical indicators in this study then performed a thoughtful evaluation of five datasets. The primary contribution of this paper is that they developed a platform for investors using R, which does not need users to input their own data but call API to fetch the data from online source straightforward. From the research perspective, they only evaluated the prediction of the price for 1 up to 10 days ahead but did not evaluate longer terms than two trading weeks or a shorter term than 1 day. The primary limitation of their research was that they only analyzed 20 U.S.-based stocks, the model might not be generalized to other stock market or need further revalidation to see if it suffered from overfitting problems.

Kara et al. in [ 17 ] also exploited ANN and SVM in predicting the movement of stock price index. The data set they used covers a time period from January 2, 1997, to December 31, 2007, of the Istanbul Stock Exchange. The primary strength of this work is its detailed record of parameter adjustment procedures. While the weaknesses of this work are that neither the technical indicator nor the model structure has novelty, and the authors did not explain how their model performed better than other models in previous works. Thus, more validation works on other datasets would help. They explained how ANN and SVM work with stock market features, also recorded the parameter adjustment. The implementation part of our research could benefit from this previous work.

Jeon et al. in [ 16 ] performed research on millisecond interval-based big dataset by using pattern graph tracking to complete stock price prediction tasks. The dataset they used is a millisecond interval-based big dataset of historical stock data from KOSCOM, from August 2014 to October 2014, 10G–15G capacity. The author applied Euclidean distance, Dynamic Time Warping (DTW) for pattern recognition. For feature selection, they used stepwise regression. The authors completed the prediction task by ANN and Hadoop and RHive for big data processing. The “ Results ” section is based on the result processed by a combination of SAX and Jaro–Winkler distance. Before processing the data, they generated aggregated data at 5-min intervals from discrete data. The primary strength of this work is the explicit structure of the whole implementation procedure. While they exploited a relatively old model, another weakness is the overall time span of the training dataset is extremely short. It is difficult to access the millisecond interval-based data in real life, so the model is not as practical as a daily based data model.

Huang et al. in [ 12 ] applied a fuzzy-GA model to complete the stock selection task. They used the key stocks of the 200 largest market capitalization listed as the investment universe in the Taiwan Stock Exchange. Besides, the yearly financial statement data and the stock returns were taken from the Taiwan Economic Journal (TEJ) database at www.tej.com.tw/ for the time period from year 1995 to year 2009. They conducted the fuzzy membership function with model parameters optimized with GA and extracted features for optimizing stock scoring. The authors proposed an optimized model for selection and scoring of stocks. Different from the prediction model, the authors more focused on stock rankings, selection, and performance evaluation. Their structure is more practical among investors. But in the model validation part, they did not compare the model with existed algorithms but the statistics of the benchmark, which made it challenging to identify if GA would outperform other algorithms.

Fischer and Krauss in [ 5 ] applied long short-term memory (LSTM) on financial market prediction. The dataset they used is S&P 500 index constituents from Thomson Reuters. They obtained all month-end constituent lists for the S&P 500 from Dec 1989 to Sep 2015, then consolidated the lists into a binary matrix to eliminate survivor bias. The authors also used RMSprop as an optimizer, which is a mini-batch version of rprop. The primary strength of this work is that the authors used the latest deep learning technique to perform predictions. They relied on the LSTM technique, lack of background knowledge in the financial domain. Although the LSTM outperformed the standard DNN and logistic regression algorithms, while the author did not mention the effort to train an LSTM with long-time dependencies.

Tsai and Hsiao in [ 42 ] proposed a solution as a combination of different feature selection methods for prediction of stocks. They used Taiwan Economic Journal (TEJ) database as data source. The data used in their analysis was from year 2000 to 2007. In their work, they used a sliding window method and combined it with multi layer perceptron (MLP) based artificial neural networks with back propagation, as their prediction model. In their work, they also applied principal component analysis (PCA) for dimensionality reduction, genetic algorithms (GA) and the classification and regression trees (CART) to select important features. They did not just rely on technical indices only. Instead, they also included both fundamental and macroeconomic indices in their analysis. The authors also reported a comparison on feature selection methods. The validation part was done by combining the model performance stats with statistical analysis.

Pimenta et al. in [ 32 ] leveraged an automated investing method by using multi-objective genetic programming and applied it in the stock market. The dataset was obtained from Brazilian stock exchange market (BOVESPA), and the primary techniques they exploited were a combination of multi-objective optimization, genetic programming, and technical trading rules. For optimization, they leveraged genetic programming (GP) to optimize decision rules. The novelty of this paper was in the evaluation part. They included a historical period, which was a critical moment of Brazilian politics and economics when performing validation. This approach reinforced the generalization strength of their proposed model. When selecting the sub-dataset for evaluation, they also set criteria to ensure more asset liquidity. While the baseline of the comparison was too basic and fundamental, and the authors did not perform any comparison with other existing models.

Huang and Tsai in [ 13 ] conducted a filter-based feature selection assembled with a hybrid self-organizing feature map (SOFM) support vector regression (SVR) model to forecast Taiwan index futures (FITX) trend. They divided the training samples into clusters to marginally improve the training efficiency. The authors proposed a comprehensive model, which was a combination of two novel machine learning techniques in stock market analysis. Besides, the optimizer of feature selection was also applied before the data processing to improve the prediction accuracy and reduce the computational complexity of processing daily stock index data. Though they optimized the feature selection part and split the sample data into small clusters, it was already strenuous to train daily stock index data of this model. It would be difficult for this model to predict trading activities in shorter time intervals since the data volume would be increased drastically. Moreover, the evaluation is not strong enough since they set a single SVR model as a baseline, but did not compare the performance with other previous works, which caused difficulty for future researchers to identify the advantages of SOFM-SVR model why it outperforms other algorithms.

Thakur and Kumar in [ 41 ] also developed a hybrid financial trading support system by exploiting multi-category classifiers and random forest (RAF). They conducted their research on stock indices from NASDAQ, DOW JONES, S&P 500, NIFTY 50, and NIFTY BANK. The authors proposed a hybrid model combined random forest (RF) algorithms with a weighted multicategory generalized eigenvalue support vector machine (WMGEPSVM) to generate “Buy/Hold/Sell” signals. Before processing the data, they used Random Forest (RF) for feature pruning. The authors proposed a practical model designed for real-life investment activities, which could generate three basic signals for investors to refer to. They also performed a thorough comparison of related algorithms. While they did not mention the time and computational complexity of their works. Meanwhile, the unignorable issue of their work was the lack of financial domain knowledge background. The investors regard the indices data as one of the attributes but could not take the signal from indices to operate a specific stock straightforward.

Hsu in [ 11 ] assembled feature selection with a back propagation neural network (BNN) combined with genetic programming to predict the stock/futures price. The dataset in this research was obtained from Taiwan Stock Exchange Corporation (TWSE). The authors have introduced the description of the background knowledge in detail. While the weakness of their work is that it is a lack of data set description. This is a combination of the model proposed by other previous works. Though we did not see the novelty of this work, we can still conclude that the genetic programming (GP) algorithm is admitted in stock market research domain. To reinforce the validation strengths, it would be good to consider adding GP models into evaluation if the model is predicting a specific price.

Hafezi et al. in [ 7 ] built a bat-neural network multi-agent system (BN-NMAS) to predict stock price. The dataset was obtained from the Deutsche bundes-bank. They also applied the Bat algorithm (BA) for optimizing neural network weights. The authors illustrated their overall structure and logic of system design in clear flowcharts. While there were very few previous works that had performed on DAX data, it would be difficult to recognize if the model they proposed still has the generality if migrated on other datasets. The system design and feature selection logic are fascinating, which worth referring to. Their findings in optimization algorithms are also valuable for the research in the stock market price prediction research domain. It is worth trying the Bat algorithm (BA) when constructing neural network models.

Long et al. in [ 25 ] conducted a deep learning approach to predict the stock price movement. The dataset they used is the Chinese stock market index CSI 300. For predicting the stock price movement, they constructed a multi-filter neural network (MFNN) with stochastic gradient descent (SGD) and back propagation optimizer for learning NN parameters. The strength of this paper is that the authors exploited a novel model with a hybrid model constructed by different kinds of neural networks, it provides an inspiration for constructing hybrid neural network structures.

Atsalakis and Valavanis in [ 1 ] proposed a solution of a neuro-fuzzy system, which is composed of controller named as Adaptive Neuro Fuzzy Inference System (ANFIS), to achieve short-term stock price trend prediction. The noticeable strength of this work is the evaluation part. Not only did they compare their proposed system with the popular data models, but also compared with investment strategies. While the weakness that we found from their proposed solution is that their solution architecture is lack of optimization part, which might limit their model performance. Since our proposed solution is also focusing on short-term stock price trend prediction, this work is heuristic for our system design. Meanwhile, by comparing with the popular trading strategies from investors, their work inspired us to compare the strategies used by investors with techniques used by researchers.

Nekoeiqachkanloo et al. in [ 29 ] proposed a system with two different approaches for stock investment. The strengths of their proposed solution are obvious. First, it is a comprehensive system that consists of data pre-processing and two different algorithms to suggest the best investment portions. Second, the system also embedded with a forecasting component, which also retains the features of the time series. Last but not least, their input features are a mix of fundamental features and technical indices that aim to fill in the gap between the financial domain and technical domain. However, their work has a weakness in the evaluation part. Instead of evaluating the proposed system on a large dataset, they chose 25 well-known stocks. There is a high possibility that the well-known stocks might potentially share some common hidden features.

As another related latest work, Idrees et al. [ 14 ] published a time series-based prediction approach for the volatility of the stock market. ARIMA is not a new approach in the time series prediction research domain. Their work is more focusing on the feature engineering side. Before feeding the features into ARIMA models, they designed three steps for feature engineering: Analyze the time series, identify if the time series is stationary or not, perform estimation by plot ACF and PACF charts and look for parameters. The only weakness of their proposed solution is that the authors did not perform any customization on the existing ARIMA model, which might limit the system performance to be improved.

One of the main weaknesses found in the related works is limited data-preprocessing mechanisms built and used. Technical works mostly tend to focus on building prediction models. When they select the features, they list all the features mentioned in previous works and go through the feature selection algorithm then select the best-voted features. Related works in the investment domain have shown more interest in behavior analysis, such as how herding behaviors affect the stock performance, or how the percentage of inside directors hold the firm’s common stock affects the performance of a certain stock. These behaviors often need a pre-processing procedure of standard technical indices and investment experience to recognize.

In the related works, often a thorough statistical analysis is performed based on a special dataset and conclude new features rather than performing feature selections. Some data, such as the percentage of a certain index fluctuation has been proven to be effective on stock performance. We believe that by extracting new features from data, then combining such features with existed common technical indices will significantly benefit the existing and well-tested prediction models.

The dataset

This section details the data that was extracted from the public data sources, and the final dataset that was prepared. Stock market-related data are diverse, so we first compared the related works from the survey of financial research works in stock market data analysis to specify the data collection directions. After collecting the data, we defined a data structure of the dataset. Given below, we describe the dataset in detail, including the data structure, and data tables in each category of data with the segment definitions.

Description of our dataset

In this section, we will describe the dataset in detail. This dataset consists of 3558 stocks from the Chinese stock market. Besides the daily price data, daily fundamental data of each stock ID, we also collected the suspending and resuming history, top 10 shareholders, etc. We list two reasons that we choose 2 years as the time span of this dataset: (1) most of the investors perform stock market price trend analysis using the data within the latest 2 years, (2) using more recent data would benefit the analysis result. We collected data through the open-sourced API, namely Tushare [ 43 ], mean-while we also leveraged a web-scraping technique to collect data from Sina Finance web pages, SWS Research website.

Data structure

Figure  1 illustrates all the data tables in the dataset. We collected four categories of data in this dataset: (1) basic data, (2) trading data, (3) finance data, and (4) other reference data. All the data tables can be linked to each other by a common field called “Stock ID” It is a unique stock identifier registered in the Chinese Stock market. Table  1 shows an overview of the dataset.

Data structure for the extracted dataset

The Table  1 lists the field information of each data table as well as which category the data table belongs to.

In this section, we present the proposed methods and the design of the proposed solution. Moreover, we also introduce the architecture design as well as algorithmic and implementation details.

Problem statement

We analyzed the best possible approach for predicting short-term price trends from different aspects: feature engineering, financial domain knowledge, and prediction algorithm. Then we addressed three research questions in each aspect, respectively: How can feature engineering benefit model prediction accuracy? How do findings from the financial domain benefit prediction model design? And what is the best algorithm for predicting short-term price trends?

The first research question is about feature engineering. We would like to know how the feature selection method benefits the performance of prediction models. From the abundance of the previous works, we can conclude that stock price data embedded with a high level of noise, and there are also correlations between features, which makes the price prediction notoriously difficult. That is also the primary reason for most of the previous works introduced the feature engineering part as an optimization module.

The second research question is evaluating the effectiveness of findings we extracted from the financial domain. Different from the previous works, besides the common evaluation of data models such as the training costs and scores, our evaluation will emphasize the effectiveness of newly added features that we extracted from the financial domain. We introduce some features from the financial domain. While we only obtained some specific findings from previous works, and the related raw data needs to be processed into usable features. After extracting related features from the financial domain, we combine the features with other common technical indices for voting out the features with a higher impact. There are numerous features said to be effective from the financial domain, and it would be impossible for us to cover all of them. Thus, how to appropriately convert the findings from the financial domain to a data processing module of our system design is a hidden research question that we attempt to answer.

The third research question is that which algorithms are we going to model our data? From the previous works, researchers have been putting efforts into the exact price prediction. We decompose the problem into predicting the trend and then the exact number. This paper focuses on the first step. Hence, the objective has been converted to resolve a binary classification problem, meanwhile, finding an effective way to eliminate the negative effect brought by the high level of noise. Our approach is to decompose the complex problem into sub-problems which have fewer dependencies and resolve them one by one, and then compile the resolutions into an ensemble model as an aiding system for investing behavior reference.

In the previous works, researchers have been using a variety of models for predicting stock price trends. While most of the best-performed models are based on machine learning techniques, in this work, we will compare our approach with the outperformed machine learning models in the evaluation part and find the solution for this research question.

Proposed solution

The high-level architecture of our proposed solution could be separated into three parts. First is the feature selection part, to guarantee the selected features are highly effective. Second, we look into the data and perform the dimensionality reduction. And the last part, which is the main contribution of our work is to build a prediction model of target stocks. Figure  2 depicts a high-level architecture of the proposed solution.

High-level architecture of the proposed solution

There are ways to classify different categories of stocks. Some investors prefer long-term investments, while others show more interest in short-term investments. It is common to see the stock-related reports showing an average performance, while the stock price is increasing drastically; this is one of the phenomena that indicate the stock price prediction has no fixed rules, thus finding effective features before training a model on data is necessary.

In this research, we focus on the short-term price trend prediction. Currently, we only have the raw data with no labels. So, the very first step is to label the data. We mark the price trend by comparing the current closing price with the closing price of n trading days ago, the range of n is from 1 to 10 since our research is focusing on the short-term. If the price trend goes up, we mark it as 1 or mark as 0 in the opposite case. To be more specified, we use the indices from the indices of n  −  1 th day to predict the price trend of the n th day.

According to the previous works, some researchers who applied both financial domain knowledge and technical methods on stock data were using rules to filter the high-quality stocks. We referred to their works and exploited their rules to contribute to our feature extension design.

However, to ensure the best performance of the prediction model, we will look into the data first. There are a large number of features in the raw data; if we involve all the features into our consideration, it will not only drastically increase the computational complexity but will also cause side effects if we would like to perform unsupervised learning in further research. So, we leverage the recursive feature elimination (RFE) to ensure all the selected features are effective.

We found most of the previous works in the technical domain were analyzing all the stocks, while in the financial domain, researchers prefer to analyze the specific scenario of investment, to fill the gap between the two domains, we decide to apply a feature extension based on the findings we gathered from the financial domain before we start the RFE procedure.

Since we plan to model the data into time series, the number of the features, the more complex the training procedure will be. So, we will leverage the dimensionality reduction by using randomized PCA at the beginning of our proposed solution architecture.

Detailed technical design elaboration

This section provides an elaboration of the detailed technical design as being a comprehensive solution based on utilizing, combining, and customizing several existing data preprocessing, feature engineering, and deep learning techniques. Figure  3 provides the detailed technical design from data processing to prediction, including the data exploration. We split the content by main procedures, and each procedure contains algorithmic steps. Algorithmic details are elaborated in the next section. The contents of this section will focus on illustrating the data workflow.

Detailed technical design of the proposed solution

Based on the literature review, we select the most commonly used technical indices and then feed them into the feature extension procedure to get the expanded feature set. We will select the most effective i features from the expanded feature set. Then we will feed the data with i selected features into the PCA algorithm to reduce the dimension into j features. After we get the best combination of i and j , we process the data into finalized the feature set and feed them into the LSTM [ 10 ] model to get the price trend prediction result.

The novelty of our proposed solution is that we will not only apply the technical method on raw data but also carry out the feature extensions that are used among stock market investors. Details on feature extension are given in the next subsection. Experiences gained from applying and optimizing deep learning based solutions in [ 37 , 38 ] were taken into account while designing and customizing feature engineering and deep learning solution in this work.

Applying feature extension

The first main procedure in Fig.  3 is the feature extension. In this block, the input data is the most commonly used technical indices concluded from related works. The three feature extension methods are max–min scaling, polarizing, and calculating fluctuation percentage. Not all the technical indices are applicable for all three of the feature extension methods; this procedure only applies the meaningful extension methods on technical indices. We choose meaningful extension methods while looking at how the indices are calculated. The technical indices and the corresponding feature extension methods are illustrated in Table  2 .

After the feature extension procedure, the expanded features will be combined with the most commonly used technical indices, i.e., input data with output data, and feed into RFE block as input data in the next step.

Applying recursive feature elimination

After the feature extension above, we explore the most effective i features by using the Recursive Feature Elimination (RFE) algorithm [ 6 ]. We estimate all the features by two attributes, coefficient, and feature importance. We also limit the features that remove from the pool by one, which means we will remove one feature at each step and retain all the relevant features. Then the output of the RFE block will be the input of the next step, which refers to PCA.

Applying principal component analysis (PCA)

The very first step before leveraging PCA is feature pre-processing. Because some of the features after RFE are percentage data, while others are very large numbers, i.e., the output from RFE are in different units. It will affect the principal component extraction result. Thus, before feeding the data into the PCA algorithm [ 8 ], a feature pre-processing is necessary. We also illustrate the effectiveness and methods comparison in “ Results ” section.

After performing feature pre-processing, the next step is to feed the processed data with selected i features into the PCA algorithm to reduce the feature matrix scale into j features. This step is to retain as many effective features as possible and meanwhile eliminate the computational complexity of training the model. This research work also evaluates the best combination of i and j, which has relatively better prediction accuracy, meanwhile, cuts the computational consumption. The result can be found in the “ Results ” section, as well. After the PCA step, the system will get a reshaped matrix with j columns.

Fitting long short-term memory (LSTM) model

PCA reduced the dimensions of the input data, while the data pre-processing is mandatory before feeding the data into the LSTM layer. The reason for adding the data pre-processing step before the LSTM model is that the input matrix formed by principal components has no time steps. While one of the most important parameters of training an LSTM is the number of time steps. Hence, we have to model the matrix into corresponding time steps for both training and testing dataset.

After performing the data pre-processing part, the last step is to feed the training data into LSTM and evaluate the performance using testing data. As a variant neural network of RNN, even with one LSTM layer, the NN structure is still a deep neural network since it can process sequential data and memorizes its hidden states through time. An LSTM layer is composed of one or more LSTM units, and an LSTM unit consists of cells and gates to perform classification and prediction based on time series data.

The LSTM structure is formed by two layers. The input dimension is determined by j after the PCA algorithm. The first layer is the input LSTM layer, and the second layer is the output layer. The final output will be 0 or 1 indicates if the stock price trend prediction result is going down or going up, as a supporting suggestion for the investors to perform the next investment decision.

Design discussion

Feature extension is one of the novelties of our proposed price trend predicting system. In the feature extension procedure, we use technical indices to collaborate with the heuristic processing methods learned from investors, which fills the gap between the financial research area and technical research area.

Since we proposed a system of price trend prediction, feature engineering is extremely important to the final prediction result. Not only the feature extension method is helpful to guarantee we do not miss the potentially correlated feature, but also feature selection method is necessary for pooling the effective features. The more irrelevant features are fed into the model, the more noise would be introduced. Each main procedure is carefully considered contributing to the whole system design.

Besides the feature engineering part, we also leverage LSTM, the state-of-the-art deep learning method for time-series prediction, which guarantees the prediction model can capture both complex hidden pattern and the time-series related pattern.

It is known that the training cost of deep learning models is expansive in both time and hardware aspects; another advantage of our system design is the optimization procedure—PCA. It can retain the principal components of the features while reducing the scale of the feature matrix, thus help the system to save the training cost of processing the large time-series feature matrix.

Algorithm elaboration

This section provides comprehensive details on the algorithms we built while utilizing and customizing different existing techniques. Details about the terminologies, parameters, as well as optimizers. From the legend on the right side of Fig.  3 , we note the algorithm steps as octagons, all of them can be found in this “ Algorithm elaboration ” section.

Before dive deep into the algorithm steps, here is the brief introduction of data pre-processing: since we will go through the supervised learning algorithms, we also need to program the ground truth. The ground truth of this research is programmed by comparing the closing price of the current trading date with the closing price of the previous trading date the users want to compare with. Label the price increase as 1, else the ground truth will be labeled as 0. Because this research work is not only focused on predicting the price trend of a specific period of time but short-term in general, the ground truth processing is according to a range of trading days. While the algorithms will not change with the prediction term length, we can regard the term length as a parameter.

The algorithmic detail is elaborated, respectively, the first algorithm is the hybrid feature engineering part for preparing high-quality training and testing data. It corresponds to the Feature extension, RFE, and PCA blocks in Fig.  3 . The second algorithm is the LSTM procedure block, including time-series data pre-processing, NN constructing, training, and testing.

Algorithm 1: Short-term stock market price trend prediction—applying feature engineering using FE + RFE + PCA

The function FE is corresponding to the feature extension block. For the feature extension procedure, we apply three different processing methods to translate the findings from the financial domain to a technical module in our system design. While not all the indices are applicable for expanding, we only choose the proper method(s) for certain features to perform the feature extension (FE), according to Table  2 .

Normalize method preserves the relative frequencies of the terms, and transform the technical indices into the range of [0, 1]. Polarize is a well-known method often used by real-world investors, sometimes they prefer to consider if the technical index value is above or below zero, we program some of the features using polarize method and prepare for RFE. Max-min (or min-max) [ 35 ] scaling is a transformation method often used as an alternative to zero mean and unit variance scaling. Another well-known method used is fluctuation percentage, and we transform the technical indices fluctuation percentage into the range of [− 1, 1].

The function RFE () in the first algorithm refers to recursive feature elimination. Before we perform the training data scale reduction, we will have to make sure that the features we selected are effective. Ineffective features will not only drag down the classification precision but also add more computational complexity. For the feature selection part, we choose recursive feature elimination (RFE). As [ 45 ] explained, the process of recursive feature elimination can be split into the ranking algorithm, resampling, and external validation.

For the ranking algorithm, it fits the model to the features and ranks by the importance to the model. We set the parameter to retain i numbers of features, and at each iteration of feature selection retains Si top-ranked features, then refit the model and assess the performance again to begin another iteration. The ranking algorithm will eventually determine the top Si features.

The RFE algorithm is known to have suffered from the over-fitting problem. To eliminate the over-fitting issue, we will run the RFE algorithm multiple times on randomly selected stocks as the training set and ensure all the features we select are high-weighted. This procedure is called data resampling. Resampling can be built as an optimization step as an outer layer of the RFE algorithm.

The last part of our hybrid feature engineering algorithm is for optimization purposes. For the training data matrix scale reduction, we apply Randomized principal component analysis (PCA) [ 31 ], before we decide the features of the classification model.

Financial ratios of a listed company are used to present the growth ability, earning ability, solvency ability, etc. Each financial ratio consists of a set of technical indices, each time we add a technical index (or feature) will add another column of data into the data matrix and will result in low training efficiency and redundancy. If non-relevant or less relevant features are included in training data, it will also decrease the precision of classification.

The above equation represents the explanation power of principal components extracted by PCA method for original data. If an ACR is below 85%, the PCA method would be unsuitable due to a loss of original information. Because the covariance matrix is sensitive to the order of magnitudes of data, there should be a data standardize procedure before performing the PCA. The commonly used standardized methods are mean-standardization and normal-standardization and are noted as given below:

Mean-standardization: \(X_{ij}^{*} = X_{ij} /\overline{{X_{j} }}\) , which \(\overline{{X_{j} }}\) represents the mean value.

Normal-standardization: \(X_{ij}^{*} = (X_{ij} - \overline{{X_{j} }} )/s_{j}\) , which \(\overline{{X_{j} }}\) represents the mean value, and \(s_{j}\) is the standard deviation.

The array fe_array is defined according to Table  2 , row number maps to the features, columns 0, 1, 2, 3 note for the extension methods of normalize, polarize, max–min scale, and fluctuation percentage, respectively. Then we fill in the values for the array by the rule where 0 stands for no necessity to expand and 1 for features need to apply the corresponding extension methods. The final algorithm of data preprocessing using RFE and PCA can be illustrated as Algorithm 1.

Algorithm 2: Price trend prediction model using LSTM

After the principal component extraction, we will get the scale-reduced matrix, which means i most effective features are converted into j principal components for training the prediction model. We utilized an LSTM model and added a conversion procedure for our stock price dataset. The detailed algorithm design is illustrated in Alg 2. The function TimeSeriesConversion () converts the principal components matrix into time series by shifting the input data frame according to the number of time steps [ 3 ], i.e., term length in this research. The processed dataset consists of the input sequence and forecast sequence. In this research, the parameter of LAG is 1, because the model is detecting the pattern of features fluctuation on a daily basis. Meanwhile, the N_TIME_STEPS is varied from 1 trading day to 10 trading days. The functions DataPartition (), FitModel (), EvaluateModel () are regular steps without customization. The NN structure design, optimizer decision, and other parameters are illustrated in function ModelCompile () .

Some procedures impact the efficiency but do not affect the accuracy or precision and vice versa, while other procedures may affect both efficiency and prediction result. To fully evaluate our algorithm design, we structure the evaluation part by main procedures and evaluate how each procedure affects the algorithm performance. First, we evaluated our solution on a machine with 2.2 GHz i7 processor, with 16 GB of RAM. Furthermore, we also evaluated our solution on Amazon EC2 instance, 3.1 GHz Processor with 16 vCPUs, and 64 GB RAM.

In the implementation part, we expanded 20 features into 54 features, while we retain 30 features that are the most effective. In this section, we discuss the evaluation of feature selection. The dataset was divided into two different subsets, i.e., training and testing datasets. Test procedure included two parts, one testing dataset is for feature selection, and another one is for model testing. We note the feature selection dataset and model testing dataset as DS_test_f and DS_test_m, respectively.

We randomly selected two-thirds of the stock data by stock ID for RFE training and note the dataset as DS_train_f; all the data consist of full technical indices and expanded features throughout 2018. The estimator of the RFE algorithm is SVR with linear kernels. We rank the 54 features by voting and get 30 effective features then process them using the PCA algorithm to perform dimension reduction and reduce the features into 20 principal components. The rest of the stock data forms the testing dataset DS_test_f to validate the effectiveness of principal components we extracted from selected features. We reformed all the data from 2018 as the training dataset of the data model and noted as DS_train_m. The model testing dataset DS_test_m consists of the first 3 months of data in 2019, which has no overlap with the dataset we utilized in the previous steps. This approach is to prevent the hidden problem caused by overfitting.

Term length

To build an efficient prediction model, instead of the approach of modeling the data to time series, we determined to use 1 day ahead indices data to predict the price trend of the next day. We tested the RFE algorithm on a range of short-term from 1 day to 2 weeks (ten trading days), to evaluate how the commonly used technical indices correlated to price trends. For evaluating the prediction term length, we fully expanded the features as Table  2 , and feed them to RFE. During the test, we found that different length of the term has a different level of sensitive-ness to the same indices set.

We get the close price of the first trading date and compare it with the close price of the n _ th trading date. Since we are predicting the price trend, we do not consider the term lengths if the cross-validation score is below 0.5. And after the test, as we can see from Fig.  4 , there are three-term lengths that are most sensitive to the indices we selected from the related works. They are n  = {2, 5, 10}, which indicates that price trend prediction of every other day, 1 week, and 2 weeks using the indices set are likely to be more reliable.

How do term lengths affect the cross-validation score of RFE

While these curves have different patterns, for the length of 2 weeks, the cross-validation score increases with the number of features selected. If the prediction term length is 1 week, the cross-validation score will decrease if selected over 8 features. For every other day price trend prediction, the best cross-validation score is achieved by selecting 48 features. Biweekly prediction requires 29 features to achieve the best score. In Table  3 , we listed the top 15 effective features for these three-period lengths. If we predict the price trend of every other day, the cross-validation score merely fluctuates with the number of features selected. So, in the next step, we will evaluate the RFE result for these three-term lengths, as shown in Fig.  4 .

We compare the output feature set of RFE with the all-original feature set as a baseline, the all-original feature set consists of n features and we choose n most effective features from RFE output features to evaluate the result using linear SVR. We used two different approaches to evaluate feature effectiveness. The first method is to combine all the data into one large matrix and evaluate them by running the RFE algorithm once. Another method is to run RFE for each individual stock and calculate the most effective features by voting.

Feature extension and RFE

From the result of the previous subsection, we can see that when predicting the price trend for every other day or biweekly, the best result is achieved by selecting a large number of features. Within the selected features, some features processed from extension methods have better ranks than original features, which proves that the feature extension method is useful for optimizing the model. The feature extension affects both precision and efficiency, while in this part, we only discuss the precision aspect and leave efficiency part in the next step since PCA is the most effective method for training efficiency optimization in our design. We involved an evaluation of how feature extension affects RFE and use the test result to measure the improvement of involving feature extension.

We further test the effectiveness of feature extension, i.e., if polarize, max–min scale, and calculate fluctuation percentage works better than original technical indices. The best case to leverage this test is the weekly prediction since it has the least effective feature selected. From the result we got from the last section, we know the best cross-validation score appears when selecting 8 features. The test consists of two steps, and the first step is to test the feature set formed by original features only, in this case, only SLOWK, SLOWD, and RSI_5 are included. The next step is to test the feature set of all 8 features we selected in the previous subsection. We leveraged the test by defining the simplest DNN model with three layers.

The normalized confusion matrix of testing the two feature sets are illustrated in Fig.  5 . The left one is the confusion matrix of the feature set with expanded features, and the right one besides is the test result of using original features only. Both precisions of true positive and true negative have been improved by 7% and 10%, respectively, which proves that our feature extension method design is reasonably effective.

Confusion matrix of validating feature extension effectiveness

Feature reduction using principal component analysis

PCA will affect the algorithm performance on both prediction accuracy and training efficiency, while this part should be evaluated with the NN model, so we also defined the simplest DNN model with three layers as we used in the previous step to perform the evaluation. This part introduces the evaluation method and result of the optimization part of the model from computational efficiency and accuracy impact perspectives.

In this section, we will choose bi-weekly prediction to perform a use case analysis, since it has a smoothly increasing cross-validation score curve, moreover, unlike every other day prediction, it has excluded more than 20 ineffective features already. In the first step, we select all 29 effective features and train the NN model without performing PCA. It creates a baseline of the accuracy and training time for comparison. To evaluate the accuracy and efficiency, we keep the number of the principal component as 5, 10, 15, 20, 25. Table  4 recorded how the number of features affects the model training efficiency, then uses the stack bar chart in Fig.  6 to illustrate how PCA affects training efficiency. Table  6 shows accuracy and efficiency analysis on different procedures for the pre-processing of features. The times taken shown in Tables  4 , 6 are based on experiments conducted in a standard user machine to show the viability of our solution with limited or average resource availability.

Relationship between feature number and training time

We also listed the confusion matrix of each test in Fig.  7 . The stack bar chart shows that the overall time spends on training the model is decreasing by the number of selected features, while the PCA method is significantly effective in optimizing training dataset preparation. For the time spent on the training stage, PCA is not as effective as the data preparation stage. While there is the possibility that the optimization effect of PCA is not drastic enough because of the simple structure of the NN model.

How does the number of principal components affect evaluation results

Table  5 indicates that the overall prediction accuracy is not drastically affected by reducing the dimension. However, the accuracy could not fully support if the PCA has no side effect to model prediction, so we looked into the confusion matrices of test results.

From Fig.  7 we can conclude that PCA does not have a severe negative impact on prediction precision. The true positive rate and false positive rate are barely be affected, while the false negative and true negative rates are influenced by 2% to 4%. Besides evaluating how the number of selected features affects the training efficiency and model performance, we also leveraged a test upon how data pre-processing procedures affect the training procedure and predicting result. Normalizing and max–min scaling is the most commonly seen data pre-procedure performed before PCA, since the measure units of features are varied, and it is said that it could increase the training efficiency afterward.

We leveraged another test on adding pre-procedures before extracting 20 principal components from the original dataset and make the comparison in the aspects of time elapse of training stage and prediction precision. However, the test results lead to different conclusions. In Table  6 we can conclude that feature pre-processing does not have a significant impact on training efficiency, but it does influence the model prediction accuracy. Moreover, the first confusion matrix in Fig.  8 indicates that without any feature pre-processing procedure, the false-negative rate and true negative rate are severely affected, while the true positive rate and false positive rate are not affected. If it performs the normalization before PCA, both true positive rate and true negative rate are decreasing by approximately 10%. This test also proved that the best feature pre-processing method for our feature set is exploiting the max–min scale.

Confusion matrices of different feature pre-processing methods

In this section, we discuss and compare the results of our proposed model, other approaches, and the most related works.

Comparison with related works

From the previous works, we found the most commonly exploited models for short-term stock market price trend prediction are support vector machine (SVM), multilayer perceptron artificial neural network (MLP), Naive Bayes classifier (NB), random forest classifier (RAF) and logistic regression classifier (LR). The test case of comparison is also bi-weekly price trend prediction, to evaluate the best result of all models, we keep all 29 features selected by the RFE algorithm. For MLP evaluation, to test if the number of hidden layers would affect the metric scores, we noted layer number as n and tested n  = {1, 3, 5}, 150 training epochs for all the tests, found slight differences in the model performance, which indicates that the variable of MLP layer number hardly affects the metric scores.

From the confusion matrices in Fig.  9 , we can see all the machine learning models perform well when training with the full feature set we selected by RFE. From the perspective of training time, training the NB model got the best efficiency. LR algorithm cost less training time than other algorithms while it can achieve a similar prediction result with other costly models such as SVM and MLP. RAF algorithm achieved a relatively high true-positive rate while the poor performance in predicting negative labels. For our proposed LSTM model, it achieves a binary accuracy of 93.25%, which is a significantly high precision of predicting the bi-weekly price trend. We also pre-processed data through PCA and got five principal components, then trained for 150 epochs. The learning curve of our proposed solution, based on feature engineering and the LSTM model, is illustrated in Fig.  10 . The confusion matrix is the figure on the right in Fig.  11 , and detailed metrics scores can be found in Table  9 .

Model prediction comparison—confusion matrices

Learning curve of proposed solution

Proposed model prediction precision comparison—confusion matrices

The detailed evaluate results are recorded in Table  7 . We will also initiate a discussion upon the evaluation result in the next section.

Because the resulting structure of our proposed solution is different from most of the related works, it would be difficult to make naïve comparison with previous works. For example, it is hard to find the exact accuracy number of price trend prediction in most of the related works since the authors prefer to show the gain rate of simulated investment. Gain rate is a processed number based on simulated investment tests, sometimes one correct investment decision with a large trading volume can achieve a high gain rate regardless of the price trend prediction accuracy. Besides, it is also a unique and heuristic innovation in our proposed solution, we transform the problem of predicting an exact price straight forward to two sequential problems, i.e., predicting the price trend first, focus on building an accurate binary classification model, construct a solid foundation for predicting the exact price change in future works. Besides the different result structure, the datasets that previous works researched on are also different from our work. Some of the previous works involve news data to perform sentiment analysis and exploit the SE part as another system component to support their prediction model.

The latest related work that can compare is Zubair et al. [ 47 ], the authors take multiple r-square for model accuracy measurement. Multiple r-square is also called the coefficient of determination, and it shows the strength of predictor variables explaining the variation in stock return [ 28 ]. They used three datasets (KSE 100 Index, Lucky Cement Stock, Engro Fertilizer Limited) to evaluate the proposed multiple regression model and achieved 95%, 89%, and 97%, respectively. Except for the KSE 100 Index, the dataset choice in this related work is individual stocks; thus, we choose the evaluation result of the first dataset of their proposed model.

We listed the leading stock price trend prediction model performance in Table  8 , from the comparable metrics, the metric scores of our proposed solution are generally better than other related works. Instead of concluding arbitrarily that our proposed model outperformed other models in related works, we first look into the dataset column of Table  8 . By looking into the dataset used by each work [ 18 ], only trained and tested their proposed solution on three individual stocks, which is difficult to prove the generalization of their proposed model. Ayo [ 2 ] leveraged analysis on the stock data from the New York Stock Exchange (NYSE), while the weakness is they only performed analysis on closing price, which is a feature embedded with high noise. Zubair et al. [ 47 ] trained their proposed model on both individual stocks and index price, but as we have mentioned in the previous section, index price only consists of the limited number of features and stock IDs, which will further affect the model training quality. For our proposed solution, we collected sufficient data from the Chinese stock market, and applied FE + RFE algorithm on the original indices to get more effective features, the comprehensive evaluation result of 3558 stock IDs can reasonably explain the generalization and effectiveness of our proposed solution in Chinese stock market. However, the authors of Khaidem and Dey [ 18 ] and Ayo [ 2 ] chose to analyze the stock market in the United States, Zubair et al. [ 47 ] performed analysis on Pakistani stock market price, and we obtained the dataset from Chinese stock market, the policies of different countries might impact the model performance, which needs further research to validate.

Proposed model evaluation—PCA effectiveness

Besides comparing the performance across popular machine learning models, we also evaluated how the PCA algorithm optimizes the training procedure of the proposed LSTM model. We recorded the confusion matrices comparison between training the model by 29 features and by five principal components in Fig.  11 . The model training using the full 29 features takes 28.5 s per epoch on average. While it only takes 18 s on average per epoch training on the feature set of five principal components. PCA has significantly improved the training efficiency of the LSTM model by 36.8%. The detailed metrics data are listed in Table  9 . We will leverage a discussion in the next section about complexity analysis.

Complexity analysis of proposed solution

This section analyzes the complexity of our proposed solution. The Long Short-term Memory is different from other NNs, and it is a variant of standard RNN, which also has time steps with memory and gate architecture. In the previous work [ 46 ], the author performed an analysis of the RNN architecture complexity. They introduced a method to regard RNN as a directed acyclic graph and proposed a concept of recurrent depth, which helps perform the analysis on the intricacy of RNN.

The recurrent depth is a positive rational number, and we denote it as \(d_{rc}\) . As the growth of \(n\) \(d_{rc}\) measures, the nonlinear transformation average maximum number of each time step. We then unfold the directed acyclic graph of RNN and denote the processed graph as \(g_{c}\) , meanwhile, denote \(C(g_{c} )\) as the set of directed cycles in this graph. For the vertex \(v\) , we note \(\sigma_{s} (v)\) as the sum of edge weights and \(l(v)\) as the length. The equation below is proved under a mild assumption, which could be found in [ 46 ].

They also found that another crucial factor that impacts the performance of LSTM, which is the recurrent skip coefficients. We note \(s_{rc}\) as the reciprocal of the recurrent skip coefficient. Please be aware that \(s_{rc}\) is also a positive rational number.

According to the above definition, our proposed model is a 2-layers stacked LSTM, which \(d_{rc} = 2\) and \(s_{rc} = 1\) . From the experiments performed in previous work, the authors also found that when facing the problems of long-term dependency, LSTMs may benefit from decreasing the reciprocal of recurrent skip coefficients and from increasing recurrent depth. The empirical findings above mentioned are useful to enhance the performance of our proposed model further.

This work consists of three parts: data extraction and pre-processing of the Chinese stock market dataset, carrying out feature engineering, and stock price trend prediction model based on the long short-term memory (LSTM). We collected, cleaned-up, and structured 2 years of Chinese stock market data. We reviewed different techniques often used by real-world investors, developed a new algorithm component, and named it as feature extension, which is proved to be effective. We applied the feature expansion (FE) approaches with recursive feature elimination (RFE), followed by principal component analysis (PCA), to build a feature engineering procedure that is both effective and efficient. The system is customized by assembling the feature engineering procedure with an LSTM prediction model, achieved high prediction accuracy that outperforms the leading models in most related works. We also carried out a comprehensive evaluation of this work. By comparing the most frequently used machine learning models with our proposed LSTM model under the feature engineering part of our proposed system, we conclude many heuristic findings that could be future research questions in both technical and financial research domains.

Our proposed solution is a unique customization as compared to the previous works because rather than just proposing yet another state-of-the-art LSTM model, we proposed a fine-tuned and customized deep learning prediction system along with utilization of comprehensive feature engineering and combined it with LSTM to perform prediction. By researching into the observations from previous works, we fill in the gaps between investors and researchers by proposing a feature extension algorithm before recursive feature elimination and get a noticeable improvement in the model performance.

Though we have achieved a decent outcome from our proposed solution, this research has more potential towards research in future. During the evaluation procedure, we also found that the RFE algorithm is not sensitive to the term lengths other than 2-day, weekly, biweekly. Getting more in-depth research into what technical indices would influence the irregular term lengths would be a possible future research direction. Moreover, by combining latest sentiment analysis techniques with feature engineering and deep learning model, there is also a high potential to develop a more comprehensive prediction system which is trained by diverse types of information such as tweets, news, and other text-based data.

Abbreviations

Long short term memory

Principal component analysis

Recurrent neural networks

Artificial neural network

Deep neural network

Dynamic Time Warping

Recursive feature elimination

Support vector machine

Convolutional neural network

Stochastic gradient descent

Rectified linear unit

Multi layer perceptron

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Acknowledgements

This research is supported by Carleton University, in Ottawa, ON, Canada. This research paper has been built based on the thesis [ 36 ] of Jingyi Shen, supervised by M. Omair Shafiq at Carleton University, Canada, available at https://curve.carleton.ca/52e9187a-7f71-48ce-bdfe-e3f6a420e31a .

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Shen, J., Shafiq, M.O. Short-term stock market price trend prediction using a comprehensive deep learning system. J Big Data 7 , 66 (2020). https://doi.org/10.1186/s40537-020-00333-6

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The Impact of Green Investors on Stock Prices

We study the impact of green investors on stock prices in a dynamic equilibrium model where investors are green, passive or active. Green investors track an index that progressively excludes the stocks of the brownest firms; passive investors hold a value-weighted index of all stocks; and active investors hold a mean-variance efficient portfolio of all stocks. Contrary to the literature, we find large drops in the stock prices of the brownest firms and moderate increases for greener firms. These effects occur primarily upon the announcement of the green index's formation and continue during the exclusion phase. The announcement effects imply a first-mover advantage to early adopters of decarbonisation strategies.

We thank participants in the BIS Research Meeting and the NGFS Expert Network on Research webinar series for their constructive comments, and Jingtong Zhang for excellent research assistance. The project started when Gong Cheng was at the BIS. The views presented in this paper are those of the authors and do not necessarily reflect those of the BIS, nor those of the National Bureau of Economic Research.

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Stock Research: How to Do Your Due Diligence in 4 Steps

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The investing information provided on this page is for educational purposes only. NerdWallet, Inc. does not offer advisory or brokerage services, nor does it recommend or advise investors to buy or sell particular stocks, securities or other investments.

Stock research involves investigating a company's financials, leadership team and competition to figure out if you want to invest.

When doing stock research, it's helpful to know terms such as revenue, earnings per share and price-earnings ratio.

A good stock research site can help you find lots of information quickly and may even offer stock analysis.

Stock research is a lot like shopping for a car. You can base a decision solely on technical specs, but it’s also important to consider how the ride feels on the road, the manufacturer’s reputation and whether the color of the interior will camouflage dog hair.

What is stock research?

Stock research is a method of analyzing stocks based on factors such as the company’s financials, leadership team and competition. Stock research helps investors evaluate a stock and decide whether it deserves a spot in their portfolio.

» Looking for a lesson in how to buy stocks instead? We have a full guide to that here .

4 steps to research stocks

One note before we dive in: Stocks are considered long-term investments because they carry quite a bit of risk; you need time to weather any ups and downs and benefit from long-term gains. That means investing in stocks is best for money you won't need in at least the next five years. (Elsewhere we outline better options for short-term savings .)

1. Gather your stock research materials

Start by reviewing the company's financials. This is called quantitative research, and it begins with pulling together a few documents that companies are required to file with the U.S. Securities and Exchange Commission (SEC):

Form 10-K: An annual report that includes key financial statements that have been independently audited. Here you can review a company’s balance sheet, its sources of income and how it handles its cash, and its revenues and expenses.

Form 10-Q: A quarterly update on operations and financial results.

Best stock research websites

The SEC’s Electronic Data Gathering, Analysis and Retrieval (EDGAR) website provides a searchable database of the forms named above. It’s a valuable resource for learning how to research stocks.

Short on time? You’ll find highlights from the above filings and important financial ratios on your brokerage firm ’s website or on major financial news websites. (If you don't have a brokerage account, here's how to open one .) This information will help you compare a company’s performance against other candidates for your investment dollars.

» View our picks: The best online brokers for stock trading

2. Narrow your focus

These financial reports contain a ton of numbers and it's easy to get bogged down. Zero in on the following line items to become familiar with the measurable inner workings of a company:

Revenue: This is the amount of money a company brought in during the specified period. It’s the first thing you’ll see on the income statement, which is why it’s often referred to as the “top line.” Sometimes revenue is broken down into “operating revenue” and “nonoperating revenue.” Operating revenue is most telling because it’s generated from the company’s core business. Nonoperating revenue often comes from one-time business activities, such as selling an asset.

Net income: This “bottom line” figure — so called because it’s listed at the end of the income statement — is the total amount of money a company has made after operating expenses, taxes and depreciation are subtracted from revenue. Revenue is the equivalent of your gross salary, and net income is comparable to what’s left over after you’ve paid taxes and living expenses.

Earnings and earnings per share (EPS). When you divide earnings by the number of shares available to trade, you get earnings per share. This number shows a company’s profitability on a per-share basis, which makes it easier to compare with other companies. When you see earnings per share followed by “(ttm)” that refers to the “trailing twelve months.”

Earnings is far from a perfect financial measurement because it doesn’t tell you how — or how efficiently — the company uses its capital. Some companies take those earnings and reinvest them in the business. Others pay them out to shareholders in the form of dividends.

Price-earnings ratio (P/E): Dividing a company’s current stock price by its earnings per share — usually over the last 12 months — gives you a company’s trailing P/E ratio . Dividing the stock price by forecasted earnings from Wall Street analysts gives you the forward P/E. This measure of a stock’s value tells you how much investors are willing to pay to receive $1 of the company’s current earnings.

Keep in mind that the P/E ratio is derived from the potentially flawed earnings per share calculation, and analyst estimates are notoriously focused on the short term. Therefore it’s not a reliable stand-alone metric.

Return on equity (ROE) and return on assets (ROA): Return on equity reveals, in percentage terms, how much profit a company generates with each dollar shareholders have invested. The equity is shareholder equity. Return on assets shows what percentage of its profits the company generates with each dollar of its assets. Each is derived from dividing a company’s annual net income by one of those measures. These percentages also tell you something about how efficient the company is at generating profits.

Here again, beware of the gotchas. A company can artificially boost return on equity by buying back shares to reduce the shareholder equity denominator. Similarly, taking on more debt — say, loans to increase inventory or finance property — increases the amount in assets used to calculate return on assets.

» Want to make sense of stock charts? Learn how to read stock charts and interpret data

3. Turn to qualitative stock research

If quantitative stock research reveals the black-and-white financials of a company’s story, qualitative stock research provides the technicolor details that give you a truer picture of its operations and prospects.

Warren Buffett famously said: “Buy into a company because you want to own it, not because you want the stock to go up.” That’s because when you buy stocks, you purchase a personal stake in a business.

Here are some questions to help you screen your potential business partners:

How does the company make money? Sometimes it’s obvious, such as a clothing retailer whose main business is selling clothes. Sometimes it’s not, such as a fast-food company that derives most of its revenue from selling franchises or an electronics firm that relies on providing consumer financing for growth. A good rule of thumb that’s served Buffett well: Invest in common-sense companies that you truly understand.

Does this company have a competitive advantage? Look for something about the business that makes it difficult to imitate, equal or eclipse. This could be its brand, business model, ability to innovate, research capabilities, patent ownership, operational excellence or superior distribution capabilities, to name a few. The harder it is for competitors to breach the company’s moat, the stronger the competitive advantage.

How good is the management team? A company is only as good as its leaders’ ability to plot a course and steer the enterprise. You can find out a lot about management by reading their words in the transcripts of company conference calls and annual reports. Also research the company’s board of directors, the people representing shareholders in the boardroom. Be wary of boards comprised mainly of company insiders. You want to see a healthy number of independent thinkers who can objectively assess management’s actions.

What could go wrong ? We’re not talking about developments that might affect the company’s stock price in the short-term, but fundamental changes that affect a business’s ability to grow over many years. Identify potential red flags using “what if” scenarios: An important patent expires; the CEO’s successor starts taking the business in a different direction; a viable competitor emerges; new technology usurps the company’s product or service.

4. Put your stock research into context

As you can see, there are endless metrics and ratios investors can use to assess a company’s general financial health and calculate the intrinsic value of its stock. But looking solely at a company's revenue or income from a single year or the management team's most recent decisions paints an incomplete picture.

Before you buy any stock, you want to build a well-informed narrative about the company and what factors make it worthy of a long-term partnership. And to do that, context is key.

For long-term context, pull back the lens of your research to look at historical data. This will give you insight into the company's resilience during tough times, reactions to challenges, and ability to improve its performance and deliver shareholder value over time.

Then look at how the company fits into the big picture by comparing the numbers and key ratios above to industry averages and other companies in the same or similar business. Many brokers offer research tools on their websites. The easiest way to make these comparisons is by using your broker's educational tools, such as a stock screener. (Learn how to use a stock screener .) There are also several free stock screeners available online.

The bottom line on how to research stocks

Stock research is just a matter of gathering the right materials from the right websites, looking at some key numbers (quantitative stock research), asking some important questions (qualitative stock research) and looking at how a company compares to its industry peers — as well as how it compares to itself in years past.

Following these four steps can help you gain a deeper understanding of how to research stocks.

Colloquially, yes — "due diligence" or "DD" is a synonym for stock research.

Some professional investors, such as financial advisors, have a duty to act in their clients' best interest and are legally required take care, or exercise "due diligence," to not harm them financially — for example, by thoroughly researching an investment before buying it on behalf of a client.

Paid subscriptions and tools may streamline the research process, and may have more obscure types of stock data that aren't easy to find for free. But all of the types of data we've discussed in this article, such as SEC filings and valuation metrics, are available for free on websites such as EDGAR and Yahoo Finance .

Some professional investors, such as

financial advisors,

have a duty to act in their clients' best interest and are legally required take care, or exercise "due diligence," to not harm them financially — for example, by thoroughly researching an investment before buying it on behalf of a client.

Paid subscriptions and tools may streamline the research process, and may have more obscure types of stock data that aren't easy to find for free. But all of the types of data we've discussed in this article, such as SEC filings and valuation metrics, are available for free on websites such as

Yahoo Finance

More reading for active investors

Stock Market Outlook

Short Selling: 5 Steps to Shorting a Stock

» Who offers the best research? View our list of the best online brokers for beginners .

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AI infrastructure stocks are poised to be the next phase of investment

Interest in generative artificial intelligence is intensifying, as measured by internet search volumes, news stories, and more discussion of the topic than ever before on fourth-quarter earnings calls. The economic potential of the new technology has helped lift the stock market to new highs, led by Nvidia, the maker of specialized chips that are crucial to run generative AI models.

Now a key question for investors is: What happens next as the AI rally broadens to involve more companies? According to Goldman Sachs Research, if Nvidia represents the first phase of the AI trade, Phase 2 will be about other companies that are helping to build AI-related infrastructure. Phase 3 deals with companies incorporating AI into their products to boost revenue, while Phase 4 is about the AI-related productivity gains that should be possible across many businesses.

Are AI stocks in a bubble?

So far, investor optimism isn’t running as high as it was at prior peaks in 2000 and 2021, Goldman Sachs Research strategist Ryan Hammond writes in the team’s report. The implied level of long-term earnings growth that investors expect has climbed to 11% a year. That’s above the long-run average of 9% but still below the 16% percent growth that was expected at the height of the technology bubble in 2000 or the 13% growth implied by stock prices at the peak of the post-Covid rally in 2021. The analysis is based on the relationship between return-on-equity and price-to-book, to quantify the long-term growth in earnings implied by how the market is priced today.

As another way to measure optimism, analyst growth estimates are optimistic for the 10 largest technology companies but, again, are below what was seen during the technology bubble. The median large tech company is expected to deliver 15% earnings per share growth in three years, according to analysts’ consensus estimates. That compares with a median of 11% for the S&P 500 as a whole, but it’s well below the 24% earnings growth analysts foresaw in March 2000.

What’s more, current valuations of large tech stocks are not as stretched as they were in prior periods. The 10 largest are trading at 28 times earnings, which “pales in comparison to the peak of the tech bubble,” Hammond writes. Valuations for the 10 biggest tech companies reached 52 times earnings in 2000 and touched 43 times in late 2021.

What’s next for AI investment in the stock market?

Phase 1: Nvidia

Nvidia shares have returned more than 500% since the start of 2023. Remarkably, though, those gains have been entirely driven by earnings growth: The company’s price-to-earnings ratio is barely higher than it was at the start of last year, according to Goldman Sachs Research.

While Nvidia has dominated the initial phase of the AI trade, the companies in Goldman Sachs Research’s three subsequent phases have also outperformed relative to their industry groups over the past six months.

Phase 2: AI infrastructure

Companies beyond Nvidia that stand to benefit from the buildout of AI-related infrastructure include semiconductor designers and manufacturers, cloud providers, computer and network equipment makers, data center real estate investment trusts, utilities, and security software providers.

To date, the performance of stocks in this group has varied widely, Hammond writes. Companies that design chips and have intellectual property in this area, along with security companies, have had significant gains. On the other hand, utilities that might be expected to benefit from increased electricity demand from data centers have barely budged.

Phase 3: AI-enabled revenue

Companies that can incorporate generative AI advances into their product offerings make up the next phase of the AI trade. Software and IT services stocks may be best positioned, according to Goldman Sachs Research, and many of them have begun to describe for investors how their tools will enable other companies to use the new AI technology.

The research team identified stocks that fall into this group by screening for companies that made relevant mentions of AI product offerings during fourth-quarter earnings calls. They also screened for shares that trade with a statistically significant beta to Nvidia stock, suggesting they are reacting similarly to news and market developments.

“The outperformance of these stocks, while driven by many factors other than exclusively AI, suggests investors have begun to trade Phase 3 already,” Hammond writes.

Phase 4: AI-productivity gains

Eventually, emerging AI technology can be expected to benefit companies across a range of industries that can use it to boost productivity.

Software and services companies and commercial and professional services firms appear to have the biggest potential for earnings gains from AI, because they have a combination of relatively high labor costs overall and a high share of their labor bill that may be exposed to AI automation.

The report notes that 30% of all mentions of AI-related productivity gains on fourth-quarter earnings calls came from companies in these industries. Such mentions likely signal both strong opportunities for AI to boost productivity and the ready willingness by the management team to pursue and embrace the potential. 

Where are we now?

So far, few companies come close to reflecting AI optimism the way Nvidia has. But stocks in Phases 2 and 3 have shown more signs of investor optimism than companies in Phase 4, the report suggests. “Many companies in these two phases are necessary for every other company to use the technology to improve productivity,” the report notes. 

This article is being provided for educational purposes only. The information contained in this article does not constitute a recommendation from any Goldman Sachs entity to the recipient, and Goldman Sachs is not providing any financial, economic, legal, investment, accounting, or tax advice through this article or to its recipient. Neither Goldman Sachs nor any of its affiliates makes any representation or warranty, express or implied, as to the accuracy or completeness of the statements or any information contained in this article and any liability therefore (including in respect of direct, indirect, or consequential loss or damage) is expressly disclaimed.

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• Published: 17 April 2024

The economic commitment of climate change

• Maximilian Kotz   ORCID: orcid.org/0000-0003-2564-5043 1 , 2 ,
• Anders Levermann   ORCID: orcid.org/0000-0003-4432-4704 1 , 2 &
• Leonie Wenz   ORCID: orcid.org/0000-0002-8500-1568 1 , 3  

Nature volume  628 ,  pages 551–557 ( 2024 ) Cite this article

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• Environmental economics
• Environmental health
• Interdisciplinary studies
• Projection and prediction

Global projections of macroeconomic climate-change damages typically consider impacts from average annual and national temperatures over long time horizons 1 , 2 , 3 , 4 , 5 , 6 . Here we use recent empirical findings from more than 1,600 regions worldwide over the past 40 years to project sub-national damages from temperature and precipitation, including daily variability and extremes 7 , 8 . Using an empirical approach that provides a robust lower bound on the persistence of impacts on economic growth, we find that the world economy is committed to an income reduction of 19% within the next 26 years independent of future emission choices (relative to a baseline without climate impacts, likely range of 11–29% accounting for physical climate and empirical uncertainty). These damages already outweigh the mitigation costs required to limit global warming to 2 °C by sixfold over this near-term time frame and thereafter diverge strongly dependent on emission choices. Committed damages arise predominantly through changes in average temperature, but accounting for further climatic components raises estimates by approximately 50% and leads to stronger regional heterogeneity. Committed losses are projected for all regions except those at very high latitudes, at which reductions in temperature variability bring benefits. The largest losses are committed at lower latitudes in regions with lower cumulative historical emissions and lower present-day income.

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Projections of the macroeconomic damage caused by future climate change are crucial to informing public and policy debates about adaptation, mitigation and climate justice. On the one hand, adaptation against climate impacts must be justified and planned on the basis of an understanding of their future magnitude and spatial distribution 9 . This is also of importance in the context of climate justice 10 , as well as to key societal actors, including governments, central banks and private businesses, which increasingly require the inclusion of climate risks in their macroeconomic forecasts to aid adaptive decision-making 11 , 12 . On the other hand, climate mitigation policy such as the Paris Climate Agreement is often evaluated by balancing the costs of its implementation against the benefits of avoiding projected physical damages. This evaluation occurs both formally through cost–benefit analyses 1 , 4 , 5 , 6 , as well as informally through public perception of mitigation and damage costs 13 .

Projections of future damages meet challenges when informing these debates, in particular the human biases relating to uncertainty and remoteness that are raised by long-term perspectives 14 . Here we aim to overcome such challenges by assessing the extent of economic damages from climate change to which the world is already committed by historical emissions and socio-economic inertia (the range of future emission scenarios that are considered socio-economically plausible 15 ). Such a focus on the near term limits the large uncertainties about diverging future emission trajectories, the resulting long-term climate response and the validity of applying historically observed climate–economic relations over long timescales during which socio-technical conditions may change considerably. As such, this focus aims to simplify the communication and maximize the credibility of projected economic damages from future climate change.

In projecting the future economic damages from climate change, we make use of recent advances in climate econometrics that provide evidence for impacts on sub-national economic growth from numerous components of the distribution of daily temperature and precipitation 3 , 7 , 8 . Using fixed-effects panel regression models to control for potential confounders, these studies exploit within-region variation in local temperature and precipitation in a panel of more than 1,600 regions worldwide, comprising climate and income data over the past 40 years, to identify the plausibly causal effects of changes in several climate variables on economic productivity 16 , 17 . Specifically, macroeconomic impacts have been identified from changing daily temperature variability, total annual precipitation, the annual number of wet days and extreme daily rainfall that occur in addition to those already identified from changing average temperature 2 , 3 , 18 . Moreover, regional heterogeneity in these effects based on the prevailing local climatic conditions has been found using interactions terms. The selection of these climate variables follows micro-level evidence for mechanisms related to the impacts of average temperatures on labour and agricultural productivity 2 , of temperature variability on agricultural productivity and health 7 , as well as of precipitation on agricultural productivity, labour outcomes and flood damages 8 (see Extended Data Table 1 for an overview, including more detailed references). References  7 , 8 contain a more detailed motivation for the use of these particular climate variables and provide extensive empirical tests about the robustness and nature of their effects on economic output, which are summarized in Methods . By accounting for these extra climatic variables at the sub-national level, we aim for a more comprehensive description of climate impacts with greater detail across both time and space.

Constraining the persistence of impacts

A key determinant and source of discrepancy in estimates of the magnitude of future climate damages is the extent to which the impact of a climate variable on economic growth rates persists. The two extreme cases in which these impacts persist indefinitely or only instantaneously are commonly referred to as growth or level effects 19 , 20 (see Methods section ‘Empirical model specification: fixed-effects distributed lag models’ for mathematical definitions). Recent work shows that future damages from climate change depend strongly on whether growth or level effects are assumed 20 . Following refs.  2 , 18 , we provide constraints on this persistence by using distributed lag models to test the significance of delayed effects separately for each climate variable. Notably, and in contrast to refs.  2 , 18 , we use climate variables in their first-differenced form following ref.  3 , implying a dependence of the growth rate on a change in climate variables. This choice means that a baseline specification without any lags constitutes a model prior of purely level effects, in which a permanent change in the climate has only an instantaneous effect on the growth rate 3 , 19 , 21 . By including lags, one can then test whether any effects may persist further. This is in contrast to the specification used by refs.  2 , 18 , in which climate variables are used without taking the first difference, implying a dependence of the growth rate on the level of climate variables. In this alternative case, the baseline specification without any lags constitutes a model prior of pure growth effects, in which a change in climate has an infinitely persistent effect on the growth rate. Consequently, including further lags in this alternative case tests whether the initial growth impact is recovered 18 , 19 , 21 . Both of these specifications suffer from the limiting possibility that, if too few lags are included, one might falsely accept the model prior. The limitations of including a very large number of lags, including loss of data and increasing statistical uncertainty with an increasing number of parameters, mean that such a possibility is likely. By choosing a specification in which the model prior is one of level effects, our approach is therefore conservative by design, avoiding assumptions of infinite persistence of climate impacts on growth and instead providing a lower bound on this persistence based on what is observable empirically (see Methods section ‘Empirical model specification: fixed-effects distributed lag models’ for further exposition of this framework). The conservative nature of such a choice is probably the reason that ref.  19 finds much greater consistency between the impacts projected by models that use the first difference of climate variables, as opposed to their levels.

We begin our empirical analysis of the persistence of climate impacts on growth using ten lags of the first-differenced climate variables in fixed-effects distributed lag models. We detect substantial effects on economic growth at time lags of up to approximately 8–10 years for the temperature terms and up to approximately 4 years for the precipitation terms (Extended Data Fig. 1 and Extended Data Table 2 ). Furthermore, evaluation by means of information criteria indicates that the inclusion of all five climate variables and the use of these numbers of lags provide a preferable trade-off between best-fitting the data and including further terms that could cause overfitting, in comparison with model specifications excluding climate variables or including more or fewer lags (Extended Data Fig. 3 , Supplementary Methods Section  1 and Supplementary Table 1 ). We therefore remove statistically insignificant terms at later lags (Supplementary Figs. 1 – 3 and Supplementary Tables 2 – 4 ). Further tests using Monte Carlo simulations demonstrate that the empirical models are robust to autocorrelation in the lagged climate variables (Supplementary Methods Section  2 and Supplementary Figs. 4 and 5 ), that information criteria provide an effective indicator for lag selection (Supplementary Methods Section  2 and Supplementary Fig. 6 ), that the results are robust to concerns of imperfect multicollinearity between climate variables and that including several climate variables is actually necessary to isolate their separate effects (Supplementary Methods Section  3 and Supplementary Fig. 7 ). We provide a further robustness check using a restricted distributed lag model to limit oscillations in the lagged parameter estimates that may result from autocorrelation, finding that it provides similar estimates of cumulative marginal effects to the unrestricted model (Supplementary Methods Section 4 and Supplementary Figs. 8 and 9 ). Finally, to explicitly account for any outstanding uncertainty arising from the precise choice of the number of lags, we include empirical models with marginally different numbers of lags in the error-sampling procedure of our projection of future damages. On the basis of the lag-selection procedure (the significance of lagged terms in Extended Data Fig. 1 and Extended Data Table 2 , as well as information criteria in Extended Data Fig. 3 ), we sample from models with eight to ten lags for temperature and four for precipitation (models shown in Supplementary Figs. 1 – 3 and Supplementary Tables 2 – 4 ). In summary, this empirical approach to constrain the persistence of climate impacts on economic growth rates is conservative by design in avoiding assumptions of infinite persistence, but nevertheless provides a lower bound on the extent of impact persistence that is robust to the numerous tests outlined above.

Committed damages until mid-century

We combine these empirical economic response functions (Supplementary Figs. 1 – 3 and Supplementary Tables 2 – 4 ) with an ensemble of 21 climate models (see Supplementary Table 5 ) from the Coupled Model Intercomparison Project Phase 6 (CMIP-6) 22 to project the macroeconomic damages from these components of physical climate change (see Methods for further details). Bias-adjusted climate models that provide a highly accurate reproduction of observed climatological patterns with limited uncertainty (Supplementary Table 6 ) are used to avoid introducing biases in the projections. Following a well-developed literature 2 , 3 , 19 , these projections do not aim to provide a prediction of future economic growth. Instead, they are a projection of the exogenous impact of future climate conditions on the economy relative to the baselines specified by socio-economic projections, based on the plausibly causal relationships inferred by the empirical models and assuming ceteris paribus. Other exogenous factors relevant for the prediction of economic output are purposefully assumed constant.

A Monte Carlo procedure that samples from climate model projections, empirical models with different numbers of lags and model parameter estimates (obtained by 1,000 block-bootstrap resamples of each of the regressions in Supplementary Figs. 1 – 3 and Supplementary Tables 2 – 4 ) is used to estimate the combined uncertainty from these sources. Given these uncertainty distributions, we find that projected global damages are statistically indistinguishable across the two most extreme emission scenarios until 2049 (at the 5% significance level; Fig. 1 ). As such, the climate damages occurring before this time constitute those to which the world is already committed owing to the combination of past emissions and the range of future emission scenarios that are considered socio-economically plausible 15 . These committed damages comprise a permanent income reduction of 19% on average globally (population-weighted average) in comparison with a baseline without climate-change impacts (with a likely range of 11–29%, following the likelihood classification adopted by the Intergovernmental Panel on Climate Change (IPCC); see caption of Fig. 1 ). Even though levels of income per capita generally still increase relative to those of today, this constitutes a permanent income reduction for most regions, including North America and Europe (each with median income reductions of approximately 11%) and with South Asia and Africa being the most strongly affected (each with median income reductions of approximately 22%; Fig. 1 ). Under a middle-of-the road scenario of future income development (SSP2, in which SSP stands for Shared Socio-economic Pathway), this corresponds to global annual damages in 2049 of 38 trillion in 2005 international dollars (likely range of 19–59 trillion 2005 international dollars). Compared with empirical specifications that assume pure growth or pure level effects, our preferred specification that provides a robust lower bound on the extent of climate impact persistence produces damages between these two extreme assumptions (Extended Data Fig. 3 ).

Estimates of the projected reduction in income per capita from changes in all climate variables based on empirical models of climate impacts on economic output with a robust lower bound on their persistence (Extended Data Fig. 1 ) under a low-emission scenario compatible with the 2 °C warming target and a high-emission scenario (SSP2-RCP2.6 and SSP5-RCP8.5, respectively) are shown in purple and orange, respectively. Shading represents the 34% and 10% confidence intervals reflecting the likely and very likely ranges, respectively (following the likelihood classification adopted by the IPCC), having estimated uncertainty from a Monte Carlo procedure, which samples the uncertainty from the choice of physical climate models, empirical models with different numbers of lags and bootstrapped estimates of the regression parameters shown in Supplementary Figs. 1 – 3 . Vertical dashed lines show the time at which the climate damages of the two emission scenarios diverge at the 5% and 1% significance levels based on the distribution of differences between emission scenarios arising from the uncertainty sampling discussed above. Note that uncertainty in the difference of the two scenarios is smaller than the combined uncertainty of the two respective scenarios because samples of the uncertainty (climate model and empirical model choice, as well as model parameter bootstrap) are consistent across the two emission scenarios, hence the divergence of damages occurs while the uncertainty bounds of the two separate damage scenarios still overlap. Estimates of global mitigation costs from the three IAMs that provide results for the SSP2 baseline and SSP2-RCP2.6 scenario are shown in light green in the top panel, with the median of these estimates shown in bold.

Damages already outweigh mitigation costs

We compare the damages to which the world is committed over the next 25 years to estimates of the mitigation costs required to achieve the Paris Climate Agreement. Taking estimates of mitigation costs from the three integrated assessment models (IAMs) in the IPCC AR6 database 23 that provide results under comparable scenarios (SSP2 baseline and SSP2-RCP2.6, in which RCP stands for Representative Concentration Pathway), we find that the median committed climate damages are larger than the median mitigation costs in 2050 (six trillion in 2005 international dollars) by a factor of approximately six (note that estimates of mitigation costs are only provided every 10 years by the IAMs and so a comparison in 2049 is not possible). This comparison simply aims to compare the magnitude of future damages against mitigation costs, rather than to conduct a formal cost–benefit analysis of transitioning from one emission path to another. Formal cost–benefit analyses typically find that the net benefits of mitigation only emerge after 2050 (ref.  5 ), which may lead some to conclude that physical damages from climate change are simply not large enough to outweigh mitigation costs until the second half of the century. Our simple comparison of their magnitudes makes clear that damages are actually already considerably larger than mitigation costs and the delayed emergence of net mitigation benefits results primarily from the fact that damages across different emission paths are indistinguishable until mid-century (Fig. 1 ).

Although these near-term damages constitute those to which the world is already committed, we note that damage estimates diverge strongly across emission scenarios after 2049, conveying the clear benefits of mitigation from a purely economic point of view that have been emphasized in previous studies 4 , 24 . As well as the uncertainties assessed in Fig. 1 , these conclusions are robust to structural choices, such as the timescale with which changes in the moderating variables of the empirical models are estimated (Supplementary Figs. 10 and 11 ), as well as the order in which one accounts for the intertemporal and international components of currency comparison (Supplementary Fig. 12 ; see Methods for further details).

Damages from variability and extremes

Committed damages primarily arise through changes in average temperature (Fig. 2 ). This reflects the fact that projected changes in average temperature are larger than those in other climate variables when expressed as a function of their historical interannual variability (Extended Data Fig. 4 ). Because the historical variability is that on which the empirical models are estimated, larger projected changes in comparison with this variability probably lead to larger future impacts in a purely statistical sense. From a mechanistic perspective, one may plausibly interpret this result as implying that future changes in average temperature are the most unprecedented from the perspective of the historical fluctuations to which the economy is accustomed and therefore will cause the most damage. This insight may prove useful in terms of guiding adaptation measures to the sources of greatest damage.

Estimates of the median projected reduction in sub-national income per capita across emission scenarios (SSP2-RCP2.6 and SSP2-RCP8.5) as well as climate model, empirical model and model parameter uncertainty in the year in which climate damages diverge at the 5% level (2049, as identified in Fig. 1 ). a , Impacts arising from all climate variables. b – f , Impacts arising separately from changes in annual mean temperature ( b ), daily temperature variability ( c ), total annual precipitation ( d ), the annual number of wet days (>1 mm) ( e ) and extreme daily rainfall ( f ) (see Methods for further definitions). Data on national administrative boundaries are obtained from the GADM database version 3.6 and are freely available for academic use ( https://gadm.org/ ).

Nevertheless, future damages based on empirical models that consider changes in annual average temperature only and exclude the other climate variables constitute income reductions of only 13% in 2049 (Extended Data Fig. 5a , likely range 5–21%). This suggests that accounting for the other components of the distribution of temperature and precipitation raises net damages by nearly 50%. This increase arises through the further damages that these climatic components cause, but also because their inclusion reveals a stronger negative economic response to average temperatures (Extended Data Fig. 5b ). The latter finding is consistent with our Monte Carlo simulations, which suggest that the magnitude of the effect of average temperature on economic growth is underestimated unless accounting for the impacts of other correlated climate variables (Supplementary Fig. 7 ).

In terms of the relative contributions of the different climatic components to overall damages, we find that accounting for daily temperature variability causes the largest increase in overall damages relative to empirical frameworks that only consider changes in annual average temperature (4.9 percentage points, likely range 2.4–8.7 percentage points, equivalent to approximately 10 trillion international dollars). Accounting for precipitation causes smaller increases in overall damages, which are—nevertheless—equivalent to approximately 1.2 trillion international dollars: 0.01 percentage points (−0.37–0.33 percentage points), 0.34 percentage points (0.07–0.90 percentage points) and 0.36 percentage points (0.13–0.65 percentage points) from total annual precipitation, the number of wet days and extreme daily precipitation, respectively. Moreover, climate models seem to underestimate future changes in temperature variability 25 and extreme precipitation 26 , 27 in response to anthropogenic forcing as compared with that observed historically, suggesting that the true impacts from these variables may be larger.

The distribution of committed damages

The spatial distribution of committed damages (Fig. 2a ) reflects a complex interplay between the patterns of future change in several climatic components and those of historical economic vulnerability to changes in those variables. Damages resulting from increasing annual mean temperature (Fig. 2b ) are negative almost everywhere globally, and larger at lower latitudes in regions in which temperatures are already higher and economic vulnerability to temperature increases is greatest (see the response heterogeneity to mean temperature embodied in Extended Data Fig. 1a ). This occurs despite the amplified warming projected at higher latitudes 28 , suggesting that regional heterogeneity in economic vulnerability to temperature changes outweighs heterogeneity in the magnitude of future warming (Supplementary Fig. 13a ). Economic damages owing to daily temperature variability (Fig. 2c ) exhibit a strong latitudinal polarisation, primarily reflecting the physical response of daily variability to greenhouse forcing in which increases in variability across lower latitudes (and Europe) contrast decreases at high latitudes 25 (Supplementary Fig. 13b ). These two temperature terms are the dominant determinants of the pattern of overall damages (Fig. 2a ), which exhibits a strong polarity with damages across most of the globe except at the highest northern latitudes. Future changes in total annual precipitation mainly bring economic benefits except in regions of drying, such as the Mediterranean and central South America (Fig. 2d and Supplementary Fig. 13c ), but these benefits are opposed by changes in the number of wet days, which produce damages with a similar pattern of opposite sign (Fig. 2e and Supplementary Fig. 13d ). By contrast, changes in extreme daily rainfall produce damages in all regions, reflecting the intensification of daily rainfall extremes over global land areas 29 , 30 (Fig. 2f and Supplementary Fig. 13e ).

The spatial distribution of committed damages implies considerable injustice along two dimensions: culpability for the historical emissions that have caused climate change and pre-existing levels of socio-economic welfare. Spearman’s rank correlations indicate that committed damages are significantly larger in countries with smaller historical cumulative emissions, as well as in regions with lower current income per capita (Fig. 3 ). This implies that those countries that will suffer the most from the damages already committed are those that are least responsible for climate change and which also have the least resources to adapt to it.

Estimates of the median projected change in national income per capita across emission scenarios (RCP2.6 and RCP8.5) as well as climate model, empirical model and model parameter uncertainty in the year in which climate damages diverge at the 5% level (2049, as identified in Fig. 1 ) are plotted against cumulative national emissions per capita in 2020 (from the Global Carbon Project) and coloured by national income per capita in 2020 (from the World Bank) in a and vice versa in b . In each panel, the size of each scatter point is weighted by the national population in 2020 (from the World Bank). Inset numbers indicate the Spearman’s rank correlation ρ and P -values for a hypothesis test whose null hypothesis is of no correlation, as well as the Spearman’s rank correlation weighted by national population.

To further quantify this heterogeneity, we assess the difference in committed damages between the upper and lower quartiles of regions when ranked by present income levels and historical cumulative emissions (using a population weighting to both define the quartiles and estimate the group averages). On average, the quartile of countries with lower income are committed to an income loss that is 8.9 percentage points (or 61%) greater than the upper quartile (Extended Data Fig. 6 ), with a likely range of 3.8–14.7 percentage points across the uncertainty sampling of our damage projections (following the likelihood classification adopted by the IPCC). Similarly, the quartile of countries with lower historical cumulative emissions are committed to an income loss that is 6.9 percentage points (or 40%) greater than the upper quartile, with a likely range of 0.27–12 percentage points. These patterns reemphasize the prevalence of injustice in climate impacts 31 , 32 , 33 in the context of the damages to which the world is already committed by historical emissions and socio-economic inertia.

Contextualizing the magnitude of damages

The magnitude of projected economic damages exceeds previous literature estimates 2 , 3 , arising from several developments made on previous approaches. Our estimates are larger than those of ref.  2 (see first row of Extended Data Table 3 ), primarily because of the facts that sub-national estimates typically show a steeper temperature response (see also refs.  3 , 34 ) and that accounting for other climatic components raises damage estimates (Extended Data Fig. 5 ). However, we note that our empirical approach using first-differenced climate variables is conservative compared with that of ref.  2 in regard to the persistence of climate impacts on growth (see introduction and Methods section ‘Empirical model specification: fixed-effects distributed lag models’), an important determinant of the magnitude of long-term damages 19 , 21 . Using a similar empirical specification to ref.  2 , which assumes infinite persistence while maintaining the rest of our approach (sub-national data and further climate variables), produces considerably larger damages (purple curve of Extended Data Fig. 3 ). Compared with studies that do take the first difference of climate variables 3 , 35 , our estimates are also larger (see second and third rows of Extended Data Table 3 ). The inclusion of further climate variables (Extended Data Fig. 5 ) and a sufficient number of lags to more adequately capture the extent of impact persistence (Extended Data Figs. 1 and 2 ) are the main sources of this difference, as is the use of specifications that capture nonlinearities in the temperature response when compared with ref.  35 . In summary, our estimates develop on previous studies by incorporating the latest data and empirical insights 7 , 8 , as well as in providing a robust empirical lower bound on the persistence of impacts on economic growth, which constitutes a middle ground between the extremes of the growth-versus-levels debate 19 , 21 (Extended Data Fig. 3 ).

Compared with the fraction of variance explained by the empirical models historically (<5%), the projection of reductions in income of 19% may seem large. This arises owing to the fact that projected changes in climatic conditions are much larger than those that were experienced historically, particularly for changes in average temperature (Extended Data Fig. 4 ). As such, any assessment of future climate-change impacts necessarily requires an extrapolation outside the range of the historical data on which the empirical impact models were evaluated. Nevertheless, these models constitute the most state-of-the-art methods for inference of plausibly causal climate impacts based on observed data. Moreover, we take explicit steps to limit out-of-sample extrapolation by capping the moderating variables of the interaction terms at the 95th percentile of the historical distribution (see Methods ). This avoids extrapolating the marginal effects outside what was observed historically. Given the nonlinear response of economic output to annual mean temperature (Extended Data Fig. 1 and Extended Data Table 2 ), this is a conservative choice that limits the magnitude of damages that we project. Furthermore, back-of-the-envelope calculations indicate that the projected damages are consistent with the magnitude and patterns of historical economic development (see Supplementary Discussion Section  5 ).

Missing impacts and spatial spillovers

Despite assessing several climatic components from which economic impacts have recently been identified 3 , 7 , 8 , this assessment of aggregate climate damages should not be considered comprehensive. Important channels such as impacts from heatwaves 31 , sea-level rise 36 , tropical cyclones 37 and tipping points 38 , 39 , as well as non-market damages such as those to ecosystems 40 and human health 41 , are not considered in these estimates. Sea-level rise is unlikely to be feasibly incorporated into empirical assessments such as this because historical sea-level variability is mostly small. Non-market damages are inherently intractable within our estimates of impacts on aggregate monetary output and estimates of these impacts could arguably be considered as extra to those identified here. Recent empirical work suggests that accounting for these channels would probably raise estimates of these committed damages, with larger damages continuing to arise in the global south 31 , 36 , 37 , 38 , 39 , 40 , 41 , 42 .

Moreover, our main empirical analysis does not explicitly evaluate the potential for impacts in local regions to produce effects that ‘spill over’ into other regions. Such effects may further mitigate or amplify the impacts we estimate, for example, if companies relocate production from one affected region to another or if impacts propagate along supply chains. The current literature indicates that trade plays a substantial role in propagating spillover effects 43 , 44 , making their assessment at the sub-national level challenging without available data on sub-national trade dependencies. Studies accounting for only spatially adjacent neighbours indicate that negative impacts in one region induce further negative impacts in neighbouring regions 45 , 46 , 47 , 48 , suggesting that our projected damages are probably conservative by excluding these effects. In Supplementary Fig. 14 , we assess spillovers from neighbouring regions using a spatial-lag model. For simplicity, this analysis excludes temporal lags, focusing only on contemporaneous effects. The results show that accounting for spatial spillovers can amplify the overall magnitude, and also the heterogeneity, of impacts. Consistent with previous literature, this indicates that the overall magnitude (Fig. 1 ) and heterogeneity (Fig. 3 ) of damages that we project in our main specification may be conservative without explicitly accounting for spillovers. We note that further analysis that addresses both spatially and trade-connected spillovers, while also accounting for delayed impacts using temporal lags, would be necessary to adequately address this question fully. These approaches offer fruitful avenues for further research but are beyond the scope of this manuscript, which primarily aims to explore the impacts of different climate conditions and their persistence.

Policy implications

We find that the economic damages resulting from climate change until 2049 are those to which the world economy is already committed and that these greatly outweigh the costs required to mitigate emissions in line with the 2 °C target of the Paris Climate Agreement (Fig. 1 ). This assessment is complementary to formal analyses of the net costs and benefits associated with moving from one emission path to another, which typically find that net benefits of mitigation only emerge in the second half of the century 5 . Our simple comparison of the magnitude of damages and mitigation costs makes clear that this is primarily because damages are indistinguishable across emissions scenarios—that is, committed—until mid-century (Fig. 1 ) and that they are actually already much larger than mitigation costs. For simplicity, and owing to the availability of data, we compare damages to mitigation costs at the global level. Regional estimates of mitigation costs may shed further light on the national incentives for mitigation to which our results already hint, of relevance for international climate policy. Although these damages are committed from a mitigation perspective, adaptation may provide an opportunity to reduce them. Moreover, the strong divergence of damages after mid-century reemphasizes the clear benefits of mitigation from a purely economic perspective, as highlighted in previous studies 1 , 4 , 6 , 24 .

Historical climate data

Historical daily 2-m temperature and precipitation totals (in mm) are obtained for the period 1979–2019 from the W5E5 database. The W5E5 dataset comes from ERA-5, a state-of-the-art reanalysis of historical observations, but has been bias-adjusted by applying version 2.0 of the WATCH Forcing Data to ERA-5 reanalysis data and precipitation data from version 2.3 of the Global Precipitation Climatology Project to better reflect ground-based measurements 49 , 50 , 51 . We obtain these data on a 0.5° × 0.5° grid from the Inter-Sectoral Impact Model Intercomparison Project (ISIMIP) database. Notably, these historical data have been used to bias-adjust future climate projections from CMIP-6 (see the following section), ensuring consistency between the distribution of historical daily weather on which our empirical models were estimated and the climate projections used to estimate future damages. These data are publicly available from the ISIMIP database. See refs.  7 , 8 for robustness tests of the empirical models to the choice of climate data reanalysis products.

Future climate data

Daily 2-m temperature and precipitation totals (in mm) are taken from 21 climate models participating in CMIP-6 under a high (RCP8.5) and a low (RCP2.6) greenhouse gas emission scenario from 2015 to 2100. The data have been bias-adjusted and statistically downscaled to a common half-degree grid to reflect the historical distribution of daily temperature and precipitation of the W5E5 dataset using the trend-preserving method developed by the ISIMIP 50 , 52 . As such, the climate model data reproduce observed climatological patterns exceptionally well (Supplementary Table 5 ). Gridded data are publicly available from the ISIMIP database.

Historical economic data

Historical economic data come from the DOSE database of sub-national economic output 53 . We use a recent revision to the DOSE dataset that provides data across 83 countries, 1,660 sub-national regions with varying temporal coverage from 1960 to 2019. Sub-national units constitute the first administrative division below national, for example, states for the USA and provinces for China. Data come from measures of gross regional product per capita (GRPpc) or income per capita in local currencies, reflecting the values reported in national statistical agencies, yearbooks and, in some cases, academic literature. We follow previous literature 3 , 7 , 8 , 54 and assess real sub-national output per capita by first converting values from local currencies to US dollars to account for diverging national inflationary tendencies and then account for US inflation using a US deflator. Alternatively, one might first account for national inflation and then convert between currencies. Supplementary Fig. 12 demonstrates that our conclusions are consistent when accounting for price changes in the reversed order, although the magnitude of estimated damages varies. See the documentation of the DOSE dataset for further discussion of these choices. Conversions between currencies are conducted using exchange rates from the FRED database of the Federal Reserve Bank of St. Louis 55 and the national deflators from the World Bank 56 .

Future socio-economic data

Baseline gridded gross domestic product (GDP) and population data for the period 2015–2100 are taken from the middle-of-the-road scenario SSP2 (ref.  15 ). Population data have been downscaled to a half-degree grid by the ISIMIP following the methodologies of refs.  57 , 58 , which we then aggregate to the sub-national level of our economic data using the spatial aggregation procedure described below. Because current methodologies for downscaling the GDP of the SSPs use downscaled population to do so, per-capita estimates of GDP with a realistic distribution at the sub-national level are not readily available for the SSPs. We therefore use national-level GDP per capita (GDPpc) projections for all sub-national regions of a given country, assuming homogeneity within countries in terms of baseline GDPpc. Here we use projections that have been updated to account for the impact of the COVID-19 pandemic on the trajectory of future income, while remaining consistent with the long-term development of the SSPs 59 . The choice of baseline SSP alters the magnitude of projected climate damages in monetary terms, but when assessed in terms of percentage change from the baseline, the choice of socio-economic scenario is inconsequential. Gridded SSP population data and national-level GDPpc data are publicly available from the ISIMIP database. Sub-national estimates as used in this study are available in the code and data replication files.

Climate variables

Following recent literature 3 , 7 , 8 , we calculate an array of climate variables for which substantial impacts on macroeconomic output have been identified empirically, supported by further evidence at the micro level for plausible underlying mechanisms. See refs.  7 , 8 for an extensive motivation for the use of these particular climate variables and for detailed empirical tests on the nature and robustness of their effects on economic output. To summarize, these studies have found evidence for independent impacts on economic growth rates from annual average temperature, daily temperature variability, total annual precipitation, the annual number of wet days and extreme daily rainfall. Assessments of daily temperature variability were motivated by evidence of impacts on agricultural output and human health, as well as macroeconomic literature on the impacts of volatility on growth when manifest in different dimensions, such as government spending, exchange rates and even output itself 7 . Assessments of precipitation impacts were motivated by evidence of impacts on agricultural productivity, metropolitan labour outcomes and conflict, as well as damages caused by flash flooding 8 . See Extended Data Table 1 for detailed references to empirical studies of these physical mechanisms. Marked impacts of daily temperature variability, total annual precipitation, the number of wet days and extreme daily rainfall on macroeconomic output were identified robustly across different climate datasets, spatial aggregation schemes, specifications of regional time trends and error-clustering approaches. They were also found to be robust to the consideration of temperature extremes 7 , 8 . Furthermore, these climate variables were identified as having independent effects on economic output 7 , 8 , which we further explain here using Monte Carlo simulations to demonstrate the robustness of the results to concerns of imperfect multicollinearity between climate variables (Supplementary Methods Section  2 ), as well as by using information criteria (Supplementary Table 1 ) to demonstrate that including several lagged climate variables provides a preferable trade-off between optimally describing the data and limiting the possibility of overfitting.

We calculate these variables from the distribution of daily, d , temperature, T x , d , and precipitation, P x , d , at the grid-cell, x , level for both the historical and future climate data. As well as annual mean temperature, \({\bar{T}}_{x,y}\) , and annual total precipitation, P x , y , we calculate annual, y , measures of daily temperature variability, \({\widetilde{T}}_{x,y}\) :

the number of wet days, Pwd x , y :

and extreme daily rainfall:

in which T x , d , m , y is the grid-cell-specific daily temperature in month m and year y , \({\bar{T}}_{x,m,{y}}\) is the year and grid-cell-specific monthly, m , mean temperature, D m and D y the number of days in a given month m or year y , respectively, H the Heaviside step function, 1 mm the threshold used to define wet days and P 99.9 x is the 99.9th percentile of historical (1979–2019) daily precipitation at the grid-cell level. Units of the climate measures are degrees Celsius for annual mean temperature and daily temperature variability, millimetres for total annual precipitation and extreme daily precipitation, and simply the number of days for the annual number of wet days.

We also calculated weighted standard deviations of monthly rainfall totals as also used in ref.  8 but do not include them in our projections as we find that, when accounting for delayed effects, their effect becomes statistically indistinct and is better captured by changes in total annual rainfall.

Spatial aggregation

We aggregate grid-cell-level historical and future climate measures, as well as grid-cell-level future GDPpc and population, to the level of the first administrative unit below national level of the GADM database, using an area-weighting algorithm that estimates the portion of each grid cell falling within an administrative boundary. We use this as our baseline specification following previous findings that the effect of area or population weighting at the sub-national level is negligible 7 , 8 .

Empirical model specification: fixed-effects distributed lag models

Following a wide range of climate econometric literature 16 , 60 , we use panel regression models with a selection of fixed effects and time trends to isolate plausibly exogenous variation with which to maximize confidence in a causal interpretation of the effects of climate on economic growth rates. The use of region fixed effects, μ r , accounts for unobserved time-invariant differences between regions, such as prevailing climatic norms and growth rates owing to historical and geopolitical factors. The use of yearly fixed effects, η y , accounts for regionally invariant annual shocks to the global climate or economy such as the El Niño–Southern Oscillation or global recessions. In our baseline specification, we also include region-specific linear time trends, k r y , to exclude the possibility of spurious correlations resulting from common slow-moving trends in climate and growth.

The persistence of climate impacts on economic growth rates is a key determinant of the long-term magnitude of damages. Methods for inferring the extent of persistence in impacts on growth rates have typically used lagged climate variables to evaluate the presence of delayed effects or catch-up dynamics 2 , 18 . For example, consider starting from a model in which a climate condition, C r , y , (for example, annual mean temperature) affects the growth rate, Δlgrp r , y (the first difference of the logarithm of gross regional product) of region r in year y :

which we refer to as a ‘pure growth effects’ model in the main text. Typically, further lags are included,

and the cumulative effect of all lagged terms is evaluated to assess the extent to which climate impacts on growth rates persist. Following ref.  18 , in the case that,

the implication is that impacts on the growth rate persist up to NL years after the initial shock (possibly to a weaker or a stronger extent), whereas if

then the initial impact on the growth rate is recovered after NL years and the effect is only one on the level of output. However, we note that such approaches are limited by the fact that, when including an insufficient number of lags to detect a recovery of the growth rates, one may find equation ( 6 ) to be satisfied and incorrectly assume that a change in climatic conditions affects the growth rate indefinitely. In practice, given a limited record of historical data, including too few lags to confidently conclude in an infinitely persistent impact on the growth rate is likely, particularly over the long timescales over which future climate damages are often projected 2 , 24 . To avoid this issue, we instead begin our analysis with a model for which the level of output, lgrp r , y , depends on the level of a climate variable, C r , y :

Given the non-stationarity of the level of output, we follow the literature 19 and estimate such an equation in first-differenced form as,

which we refer to as a model of ‘pure level effects’ in the main text. This model constitutes a baseline specification in which a permanent change in the climate variable produces an instantaneous impact on the growth rate and a permanent effect only on the level of output. By including lagged variables in this specification,

we are able to test whether the impacts on the growth rate persist any further than instantaneously by evaluating whether α L  > 0 are statistically significantly different from zero. Even though this framework is also limited by the possibility of including too few lags, the choice of a baseline model specification in which impacts on the growth rate do not persist means that, in the case of including too few lags, the framework reverts to the baseline specification of level effects. As such, this framework is conservative with respect to the persistence of impacts and the magnitude of future damages. It naturally avoids assumptions of infinite persistence and we are able to interpret any persistence that we identify with equation ( 9 ) as a lower bound on the extent of climate impact persistence on growth rates. See the main text for further discussion of this specification choice, in particular about its conservative nature compared with previous literature estimates, such as refs.  2 , 18 .

We allow the response to climatic changes to vary across regions, using interactions of the climate variables with historical average (1979–2019) climatic conditions reflecting heterogenous effects identified in previous work 7 , 8 . Following this previous work, the moderating variables of these interaction terms constitute the historical average of either the variable itself or of the seasonal temperature difference, \({\hat{T}}_{r}\) , or annual mean temperature, \({\bar{T}}_{r}\) , in the case of daily temperature variability 7 and extreme daily rainfall, respectively 8 .

The resulting regression equation with N and M lagged variables, respectively, reads:

in which Δlgrp r , y is the annual, regional GRPpc growth rate, measured as the first difference of the logarithm of real GRPpc, following previous work 2 , 3 , 7 , 8 , 18 , 19 . Fixed-effects regressions were run using the fixest package in R (ref.  61 ).

Estimates of the coefficients of interest α i , L are shown in Extended Data Fig. 1 for N  =  M  = 10 lags and for our preferred choice of the number of lags in Supplementary Figs. 1 – 3 . In Extended Data Fig. 1 , errors are shown clustered at the regional level, but for the construction of damage projections, we block-bootstrap the regressions by region 1,000 times to provide a range of parameter estimates with which to sample the projection uncertainty (following refs.  2 , 31 ).

Spatial-lag model

In Supplementary Fig. 14 , we present the results from a spatial-lag model that explores the potential for climate impacts to ‘spill over’ into spatially neighbouring regions. We measure the distance between centroids of each pair of sub-national regions and construct spatial lags that take the average of the first-differenced climate variables and their interaction terms over neighbouring regions that are at distances of 0–500, 500–1,000, 1,000–1,500 and 1,500–2000 km (spatial lags, ‘SL’, 1 to 4). For simplicity, we then assess a spatial-lag model without temporal lags to assess spatial spillovers of contemporaneous climate impacts. This model takes the form:

in which SL indicates the spatial lag of each climate variable and interaction term. In Supplementary Fig. 14 , we plot the cumulative marginal effect of each climate variable at different baseline climate conditions by summing the coefficients for each climate variable and interaction term, for example, for average temperature impacts as:

These cumulative marginal effects can be regarded as the overall spatially dependent impact to an individual region given a one-unit shock to a climate variable in that region and all neighbouring regions at a given value of the moderating variable of the interaction term.

Constructing projections of economic damage from future climate change

We construct projections of future climate damages by applying the coefficients estimated in equation ( 10 ) and shown in Supplementary Tables 2 – 4 (when including only lags with statistically significant effects in specifications that limit overfitting; see Supplementary Methods Section  1 ) to projections of future climate change from the CMIP-6 models. Year-on-year changes in each primary climate variable of interest are calculated to reflect the year-to-year variations used in the empirical models. 30-year moving averages of the moderating variables of the interaction terms are calculated to reflect the long-term average of climatic conditions that were used for the moderating variables in the empirical models. By using moving averages in the projections, we account for the changing vulnerability to climate shocks based on the evolving long-term conditions (Supplementary Figs. 10 and 11 show that the results are robust to the precise choice of the window of this moving average). Although these climate variables are not differenced, the fact that the bias-adjusted climate models reproduce observed climatological patterns across regions for these moderating variables very accurately (Supplementary Table 6 ) with limited spread across models (<3%) precludes the possibility that any considerable bias or uncertainty is introduced by this methodological choice. However, we impose caps on these moderating variables at the 95th percentile at which they were observed in the historical data to prevent extrapolation of the marginal effects outside the range in which the regressions were estimated. This is a conservative choice that limits the magnitude of our damage projections.

Time series of primary climate variables and moderating climate variables are then combined with estimates of the empirical model parameters to evaluate the regression coefficients in equation ( 10 ), producing a time series of annual GRPpc growth-rate reductions for a given emission scenario, climate model and set of empirical model parameters. The resulting time series of growth-rate impacts reflects those occurring owing to future climate change. By contrast, a future scenario with no climate change would be one in which climate variables do not change (other than with random year-to-year fluctuations) and hence the time-averaged evaluation of equation ( 10 ) would be zero. Our approach therefore implicitly compares the future climate-change scenario to this no-climate-change baseline scenario.

The time series of growth-rate impacts owing to future climate change in region r and year y , δ r , y , are then added to the future baseline growth rates, π r , y (in log-diff form), obtained from the SSP2 scenario to yield trajectories of damaged GRPpc growth rates, ρ r , y . These trajectories are aggregated over time to estimate the future trajectory of GRPpc with future climate impacts:

in which GRPpc r , y =2020 is the initial log level of GRPpc. We begin damage estimates in 2020 to reflect the damages occurring since the end of the period for which we estimate the empirical models (1979–2019) and to match the timing of mitigation-cost estimates from most IAMs (see below).

For each emission scenario, this procedure is repeated 1,000 times while randomly sampling from the selection of climate models, the selection of empirical models with different numbers of lags (shown in Supplementary Figs. 1 – 3 and Supplementary Tables 2 – 4 ) and bootstrapped estimates of the regression parameters. The result is an ensemble of future GRPpc trajectories that reflect uncertainty from both physical climate change and the structural and sampling uncertainty of the empirical models.

Estimates of mitigation costs

We obtain IPCC estimates of the aggregate costs of emission mitigation from the AR6 Scenario Explorer and Database hosted by IIASA 23 . Specifically, we search the AR6 Scenarios Database World v1.1 for IAMs that provided estimates of global GDP and population under both a SSP2 baseline and a SSP2-RCP2.6 scenario to maintain consistency with the socio-economic and emission scenarios of the climate damage projections. We find five IAMs that provide data for these scenarios, namely, MESSAGE-GLOBIOM 1.0, REMIND-MAgPIE 1.5, AIM/GCE 2.0, GCAM 4.2 and WITCH-GLOBIOM 3.1. Of these five IAMs, we use the results only from the first three that passed the IPCC vetting procedure for reproducing historical emission and climate trajectories. We then estimate global mitigation costs as the percentage difference in global per capita GDP between the SSP2 baseline and the SSP2-RCP2.6 emission scenario. In the case of one of these IAMs, estimates of mitigation costs begin in 2020, whereas in the case of two others, mitigation costs begin in 2010. The mitigation cost estimates before 2020 in these two IAMs are mostly negligible, and our choice to begin comparison with damage estimates in 2020 is conservative with respect to the relative weight of climate damages compared with mitigation costs for these two IAMs.

Data availability

Data on economic production and ERA-5 climate data are publicly available at https://doi.org/10.5281/zenodo.4681306 (ref. 62 ) and https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5 , respectively. Data on mitigation costs are publicly available at https://data.ene.iiasa.ac.at/ar6/#/downloads . Processed climate and economic data, as well as all other necessary data for reproduction of the results, are available at the public repository https://doi.org/10.5281/zenodo.10562951  (ref. 63 ).

Code availability

All code necessary for reproduction of the results is available at the public repository https://doi.org/10.5281/zenodo.10562951  (ref. 63 ).

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Acknowledgements

We gratefully acknowledge financing from the Volkswagen Foundation and the Deutsche Gesellschaft für Internationale Zusammenarbeit (GIZ) GmbH on behalf of the Government of the Federal Republic of Germany and Federal Ministry for Economic Cooperation and Development (BMZ).

Open access funding provided by Potsdam-Institut für Klimafolgenforschung (PIK) e.V.

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Maximilian Kotz, Anders Levermann & Leonie Wenz

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Maximilian Kotz & Anders Levermann

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All authors contributed to the design of the analysis. M.K. conducted the analysis and produced the figures. All authors contributed to the interpretation and presentation of the results. M.K. and L.W. wrote the manuscript.

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Extended data figures and tables

Extended data fig. 1 constraining the persistence of historical climate impacts on economic growth rates..

The results of a panel-based fixed-effects distributed lag model for the effects of annual mean temperature ( a ), daily temperature variability ( b ), total annual precipitation ( c ), the number of wet days ( d ) and extreme daily precipitation ( e ) on sub-national economic growth rates. Point estimates show the effects of a 1 °C or one standard deviation increase (for temperature and precipitation variables, respectively) at the lower quartile, median and upper quartile of the relevant moderating variable (green, orange and purple, respectively) at different lagged periods after the initial shock (note that these are not cumulative effects). Climate variables are used in their first-differenced form (see main text for discussion) and the moderating climate variables are the annual mean temperature, seasonal temperature difference, total annual precipitation, number of wet days and annual mean temperature, respectively, in panels a – e (see Methods for further discussion). Error bars show the 95% confidence intervals having clustered standard errors by region. The within-region R 2 , Bayesian and Akaike information criteria for the model are shown at the top of the figure. This figure shows results with ten lags for each variable to demonstrate the observed levels of persistence, but our preferred specifications remove later lags based on the statistical significance of terms shown above and the information criteria shown in Extended Data Fig. 2 . The resulting models without later lags are shown in Supplementary Figs. 1 – 3 .

Extended Data Fig. 2 Incremental lag-selection procedure using information criteria and within-region R 2 .

Starting from a panel-based fixed-effects distributed lag model estimating the effects of climate on economic growth using the real historical data (as in equation ( 4 )) with ten lags for all climate variables (as shown in Extended Data Fig. 1 ), lags are incrementally removed for one climate variable at a time. The resulting Bayesian and Akaike information criteria are shown in a – e and f – j , respectively, and the within-region R 2 and number of observations in k – o and p – t , respectively. Different rows show the results when removing lags from different climate variables, ordered from top to bottom as annual mean temperature, daily temperature variability, total annual precipitation, the number of wet days and extreme annual precipitation. Information criteria show minima at approximately four lags for precipitation variables and ten to eight for temperature variables, indicating that including these numbers of lags does not lead to overfitting. See Supplementary Table 1 for an assessment using information criteria to determine whether including further climate variables causes overfitting.

Extended Data Fig. 3 Damages in our preferred specification that provides a robust lower bound on the persistence of climate impacts on economic growth versus damages in specifications of pure growth or pure level effects.

Estimates of future damages as shown in Fig. 1 but under the emission scenario RCP8.5 for three separate empirical specifications: in orange our preferred specification, which provides an empirical lower bound on the persistence of climate impacts on economic growth rates while avoiding assumptions of infinite persistence (see main text for further discussion); in purple a specification of ‘pure growth effects’ in which the first difference of climate variables is not taken and no lagged climate variables are included (the baseline specification of ref.  2 ); and in pink a specification of ‘pure level effects’ in which the first difference of climate variables is taken but no lagged terms are included.

Extended Data Fig. 4 Climate changes in different variables as a function of historical interannual variability.

Changes in each climate variable of interest from 1979–2019 to 2035–2065 under the high-emission scenario SSP5-RCP8.5, expressed as a percentage of the historical variability of each measure. Historical variability is estimated as the standard deviation of each detrended climate variable over the period 1979–2019 during which the empirical models were identified (detrending is appropriate because of the inclusion of region-specific linear time trends in the empirical models). See Supplementary Fig. 13 for changes expressed in standard units. Data on national administrative boundaries are obtained from the GADM database version 3.6 and are freely available for academic use ( https://gadm.org/ ).

Extended Data Fig. 5 Contribution of different climate variables to overall committed damages.

a , Climate damages in 2049 when using empirical models that account for all climate variables, changes in annual mean temperature only or changes in both annual mean temperature and one other climate variable (daily temperature variability, total annual precipitation, the number of wet days and extreme daily precipitation, respectively). b , The cumulative marginal effects of an increase in annual mean temperature of 1 °C, at different baseline temperatures, estimated from empirical models including all climate variables or annual mean temperature only. Estimates and uncertainty bars represent the median and 95% confidence intervals obtained from 1,000 block-bootstrap resamples from each of three different empirical models using eight, nine or ten lags of temperature terms.

Extended Data Fig. 6 The difference in committed damages between the upper and lower quartiles of countries when ranked by GDP and cumulative historical emissions.

Quartiles are defined using a population weighting, as are the average committed damages across each quartile group. The violin plots indicate the distribution of differences between quartiles across the two extreme emission scenarios (RCP2.6 and RCP8.5) and the uncertainty sampling procedure outlined in Methods , which accounts for uncertainty arising from the choice of lags in the empirical models, uncertainty in the empirical model parameter estimates, as well as the climate model projections. Bars indicate the median, as well as the 10th and 90th percentiles and upper and lower sixths of the distribution reflecting the very likely and likely ranges following the likelihood classification adopted by the IPCC.

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Kotz, M., Levermann, A. & Wenz, L. The economic commitment of climate change. Nature 628 , 551–557 (2024). https://doi.org/10.1038/s41586-024-07219-0

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