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Stock Market Prediction Using Machine Learning: Evidence from India

• First Online: 28 August 2024

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• Subhamitra Patra 7 ,
• Trilok Nath Pandey 8 &
• Biswabhusan Bhuyan 9  

Part of the book series: Intelligent Systems Reference Library ((ISRL,volume 254))

Literature deciphers the dynamics of the stock market environment across the regions. Moreover, the emerging stock market like India has been experiencing several ups and downturns due to its continuous economic reforms since the early 1990s, which makes the Indian stock markets exhibit the diversified information characteristics. The chapter predicts the movements of the Indian stock markets over 2000–2022, and observes certain dynamism in both the actual and predicted trends of the Indian stock markets. The results revealed that Long Short-Term Memory holding the time-independence characteristics and greater extent of prediction accuracy proved as the best machine learning technique to predict the movement of the Indian stock markets. Moreover, the degree of prediction accuracy of all the machine learning techniques except Long-short term memory varies from one time to other. On the other hand, Support vector machines and linear regression models with their lowest degree of prediction accuracy and highest errors proved least appropriate in predicting the movements of Nifty, and Sensex respectively. The robustness of our method would benefit for testing it on another markets, and time periods. The study also discusses the strengths and weaknesses of several machine learning techniques and provide important insights in applying advanced technologies for stock market prediction of an emerging economy like India. Our prediction approach provides a potentially beneficial alternative for the investors to identify the return opportunities and achieve the diversification benefits by mitigating risk while investing in the Indian stock markets.

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EMH indicates that the stock market in order to become informationally efficient needs to follow the random-walk benchmark, which makes the stock price movement unpredictable over time.

Lo [ 32 ] proposed AMH, which indicates that the financial markets rather than being an all-or-none condition evolves over time, and therefore remains adaptive to several economic and non-economic events.

The process to learn the historical data is known as learning or training the dataset in machine learning approach.

The process to make prediction about the new data is known as testing the dataset in machine learning approach.

Note : a and b report the splitting of the Nifty and Sensex dataset respectively. Our total sample period (i.e. 3rd January 2000–11th October 2022) in both the markets is divided into 2 parts, such as training sample (reported in the blue line, i.e. from 3rd January 2000–11th October 2018), and testing sample (reported in orange line, i.e. from 12th October 2018–11th October 2022)

The Government of India mainly focused on stabilizing the monetary policy, and creating a sound interaction between monetary and fiscal policy to encourage financial stability in the post-pandemic world. For details refer https://www.bis.org/publ/bppdf/bispap122_j.pdf , assessed on 25th September 2023 at 8:30 PM.

Note This figure reports the prediction of Nifty and Sensex indices respectively using ANN technique. The red trend line in both the figures represents the movement of predicted stock prices, whereas the green trend line represents the movement of actual stock prices. Here, due to better prediction accuracy particularly in the post-pandemic period (i.e. after 2020), both the actual and predicted trend lines are overlapping with each other.

Note This figure reports the prediction of Nifty and Sensex market respectively using LSTM technique. The red and green trend lines in both the figures represent the movement of LSTM-predicted and actual stock prices respectively. Here, due to the highest prediction accuracy, both the actual (i.e. red colored line) and predicted trend lines (i.e. green colored line) coincide with each other over the period.

MAE explains the average distance between the actual price, and predicted price. The value of MAE closer to zero indicates that the model provides the accurate predicted prices, and the trends of both the actual and predicted prices coincides with each other.

RMSE is a measure of the average deviation between the predicted values from a model and the actual observed values. It calculates the square root of the average of the squared differences between predicted and actual values. Smaller RMSE values indicate better predictive performance, and vice versa.

R-squared, often denoted as R 2 , is a statistical measure used to assess the goodness of fit of a regression model. R 2 provides an indication of how well the model fits the data. Adjusted R-squared (Adj R 2 ) adjusts the R 2 value to account for the number of predictors in the model. The closer the value of R 2 and Adj R 2 to 1, the better the model fits the data.

Here, the level of predicted prices computed by different ML techniques varies from each other. Among all the techniques, LSTM model provides the accurate predicted prices irrespective of all the time phases, which coincides with the trends of the actual prices over time (see Fig.  17.3 ).

Note This figure reports the prediction of Nifty and Sensex market respectively using DT model. The red and green trend lines in both the figures represents the movement of DT-predicted and actual stock prices respectively. Here, both the actual (i.e. red colored line) and DT-predicted trend lines (i.e. green colored line) are similar, but there exists certain gap between them indicating lower degree of prediction accuracy than LSTM model.

Note This figure reports the prediction of Nifty and Sensex market respectively using RF approach. The red and green trend lines in both the figures represents the movement of RF-predicted and actual stock prices respectively. Here, both the actual (i.e. red colored line) and RF-predicted trend lines (i.e. green colored line) are similar, but there exists certain gap between them indicating a comparatively lower degree of prediction accuracy than LSTM model.

Note This figure reports the prediction of Nifty and Sensex market respectively using SVM approach. The red and green trend lines in both the figures represents the movement of SVM-predicted and actual stock prices respectively. Here, both the actual (i.e. red colored line) and SVM-predicted trend lines (i.e. green colored line) are similar, but there exists certain gap between them indicating a comparatively lower degree of prediction accuracy than LSTM model, particularly in the pre-pandemic period.

Note This figure reports the prediction of Nifty and Sensex market respectively using LR approach. The red and green trend lines in both the figures represents the movement of LR-predicted and actual stock prices respectively.

Note This figure reports the prediction of Nifty and Sensex market respectively using RR approach. The red and green trend lines in both the figures represents the movement of RR-predicted and actual stock prices respectively. Here, both the actual (i.e. red colored line) and RR-predicted trend lines (i.e. green colored line) are similar, but there exists certain gap between them indicating a comparatively lower degree of prediction accuracy than LSTM model.

Note This figure reports the prediction of Nifty and Sensex market respectively using KNN approach. The red and green trend lines in both the figures represents the movement of KNN-predicted and actual stock prices respectively. Here, both the actual (i.e. red colored line) and KNN-predicted trend lines (i.e. green colored line) are similar, but there exists certain gap between them indicating a comparatively lower degree of prediction accuracy than LSTM model. 

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Subhamitra Patra

School of Computer Science and Engineering, Vellore Institute of Technology, Chennai, Tamil Nadu, 600127, India

Trilok Nath Pandey

Department of Economics, Maharaja Purna Chandra (Autonomous) College, Baripada, Odisha, 757003, India

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Patra, S., Pandey, T.N., Bhuyan, B. (2024). Stock Market Prediction Using Machine Learning: Evidence from India. In: Maglaras, L.A., Das, S., Tripathy, N., Patnaik, S. (eds) Machine Learning Approaches in Financial Analytics. Intelligent Systems Reference Library, vol 254. Springer, Cham. https://doi.org/10.1007/978-3-031-61037-0_17

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Testing the market efficiency in Indian stock market: evidence from Bombay Stock Exchange broad market indices

Journal of Economics, Finance and Administrative Science

ISSN : 2218-0648

Article publication date: 5 April 2022

Issue publication date: 13 December 2022

Despite volumes of research on the efficient market hypothesis (EMH) over the last six decades, the results are inconclusive as some studies supported the hypothesis, and some studies rejected it. The study aims to examine the market efficiency of the Indian stock market.

Design/methodology/approach

For analysis, nine Bombay Stock Exchange (BSE) broad market indices were selected covering the study period from 01 January 2011 to 31 December 2020. The data collected for this study are daily open, high, low and closing prices of selected indices. The tools used in this study are: (1) unit root test to check the stationarity of time series, (2) descriptive statistics, (3) autocorrelation and (4) runs test.

The empirical findings of the study reveal that BSE broad market indices do not follow a random walk and Indian stock market is as weak-form inefficient.

Research limitations/implications

The findings from this study provide several avenues for future research. One of the research implications is that anomalies in the statistical results by different academicians in the finance area need to be explained by future researchers.

Practical implications

Investment companies need to understand that extraordinary skills are required to beat the market to make abnormal returns. In an inefficient market where securities do not reflect the complete available information, it is challenging for the investment brokers to convince the customers about the portfolios they recommend to the public that the rate of return would be more than expected.

Social implications

As economic growth is related to the growth in the financial sector, developing countries like India depend on the accuracy of the information. In the presence of asymmetric information, the fluctuations in the stock market would have serious harmful consequences on the economy.

Originality/value

Amid several controversies surrounding the EMH testing, this study is a modest attempt to provide evidence that the Indian stock market is in weak-form inefficient. However, it is essential to link investors' behaviour and trends observed in the financial sector to fully understand the implications of EMH.

• Efficient market hypothesis
• Autocorrelation
• Indian stock market

Elangovan, R. , Irudayasamy, F.G. and Parayitam, S. (2022), "Testing the market efficiency in Indian stock market: evidence from Bombay Stock Exchange broad market indices", Journal of Economics, Finance and Administrative Science , Vol. 27 No. 54, pp. 313-327. https://doi.org/10.1108/JEFAS-04-2021-0040

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Copyright © 2022, Rajesh Elangovan, Francis Gnanasekar Irudayasamy and Satyanarayana Parayitam

Published in Journal of Economics, Finance and Administrative Science . Published by Emerald Publishing Limited. This article is published under the Creative Commons Attribution (CC BY 4.0) licence. Anyone may reproduce, distribute, translate and create derivative works of this article (for both commercial and non-commercial purposes), subject to full attribution to the original publication and authors. The full terms of this licence maybe seen at http://creativecommons.org/licences/by/4.0/legalcode

1. Introduction

The efficient market hypothesis (EMH) postulates that an efficient market represents that all marketable securities and assets reflect newly released information immediately so that it is impossible to beat the market by using information and making extraordinary profits. The basic tenet of EMH is that stock returns are random in an efficient market. Second, investors cannot earn excess profits in an efficient market.

There has been a plethora of research on testing the EMH for over eight decades ( Brown, 2020 ; Chan et al. , 1997 ; Degutis and Novickytė, 2014 ; Fama, 1970 ; Jain et al. , 2020 ; Kelikume et al. , 2020 ; Patel et al. , 2018 ; Samsa, 2021 ; Shiller, 2003 ; Vidya, 2018 ). In addition, extensive academic research on EMH documented consensus that no one can make money by trading securities when the markets are efficient. However, the EMH assumes that capital markets come to equilibrium because the market is dominated by “informed and rational agents,” which may not be accurate. Therefore, there are many situations where EMH fails. That is the reason why several scholars time and again attempt to test EMH and see whether the market is efficient in weak, semi-strong and strong forms. Our study also takes the same path and attempt to test the EMH.

We are interested in studying EMH in the context of India because of the following reasons. First, extant research documented that the results were inconclusive, as some studies supported, and most studies did not support random walk theory. In this study, we attempt to examine the market efficiency in the Indian market during the decade 2010–2020, a period characterized by remarkable growth in the Indian economy because of increasing privatization and technological advancements. With the technology change, it is assumed that information is readily available to the investors to accurately predict the stock prices based on the available information immediately. It is also believed that stock prices reflect such information. So, the rationale for this study stems from the changing financial market, changing investors' behaviour, technological developments and the incredible rate of economic growth in India.

The second reason for this study is, in the world of availability of complete information, there is no reason why EMH should fail because the present-day prices reflect all the available information. So then, what are the reasons why EMH fails? Scholars in behavioural finance (e.g. Malkiel, 2003 ) argue that security prices reflect the behavioural intentions of investors. The third reason why we want to test EMH in India is that during the decade of 2010–2020, several economic reforms took place, and the Indian economy was characterized by phenomenon growth, though recession occurred for a brief period (around 2008–2009 because of the crash of real estate bubble in Western countries). Finally, we selected the Bombay Stock Exchange (BSE) in our study because of several reasons. First, BSE was established in 1875 and is the oldest stock exchange in Asia. Second, located in Dalal Street of Mumbai, BSE represents the financial capital of India. Third, BSE is the fastest, with a speed of around six microseconds, in the world accounting for speedy transactions. So, with these novel ideas, this study is conducted. In this paper, in the literature review, we explain the evolution of EMH and present the modern approach of EMH, followed by testing the EMH in the context of the Indian Stock market.

2. Literature review

After the formal introduction of EMH in the 1970s, Grossman (1976) has outlined the market efficiency paradox because of inconclusive results. The basic argument in the paradox is that the greater the belief in market efficiency by investors, the lesser the market efficiency. The intuitive logic behind this inefficiency is that if the investors believe that market is efficient, they will become lazy to collect information, which leads to market inefficiency. Though EMH has remained one of the most controversial research areas in finance and economics, some researchers argue that theory can be considered “half-true” ( Shiller, 2003 ), while the line of argument is that today's stock prices cannot determine the stock prices tomorrow because of volatility and information asymmetry. Therefore, contemporary researchers focus on analysing the stock prices in the presence of (vs absence) of information and adjusting for the announcements (such as mergers, amalgamations, stock splits) ( Jain et al. , 2020 ; Parthasarathy, 2016 ). In one of the studies, Fama and French (1988) argued that risk taken depends less on the company size and market return. Recently, some researchers focused on the “value effect” and documented that return was not necessarily associated with the amount of risk taken. Amid arguments in favour of EMH and contradictions against EMH, we test the hypothesis in the context of the Indian stock market in this study. As explained before, three forms of market efficiency were weak, semi-strong and strong. A market is said to be efficient when investors can predict future market values of individual securities based on the information available freely to all rational participants. The weak form represents a random walk where one cannot make profits by investing in the stocks where prices reflect perfect information. In the semi-strong form, the prices of financial assets reflect the available information in the market; but, in addition, prices change rapidly without any bias to new public information. The operational implication is that in semi-strong form, the investor cannot split the stock to obtain profitability significantly higher than they can achieve in a randomized portfolio of assets ( Samsa, 2021 ).

There are several studies conducted in the Indian context. For want of space, we mention only a few for reference. In the latest study by Jain et al. (2020) conducted on the efficiency of the stock market in India, from April 2010 to March 2019, based on BSE and National Stock Exchange, it was revealed that the Indian stock market is weak-form inefficient and therefore can be outperformed. In another study by Vidya (2018) , it was found that changes in stock market prices are random, and the market is efficient in the weak form. By performing runs test, Patel et al. (2018) found that from April 2015 to March 2018, the three-year daily closing points reveal that market is not efficient to adjust rapidly to the news, thus allowing the investors to outperform, especially when they keep in touch with the changes.

The objective of the study is to demonstrate whether the Indian stock market is weak-form efficient empirically. We determine this by examining whether the return series is stationary or not and identifying whether markets follow a normal distribution and by the descriptive statistics for BSE broad market indices for the return series. In this study, we have the following hypotheses.

The return series of BSE broad market indices are normally distributed.

There is no stationarity in the return series of BSE broad market indices.

The BSE broad market indices follow a random walk.

3.1 Research design

To examine the weak-form market efficiency in the Indian stock market, we have chosen the BSE broad market indices. As of 25 March 2021, BSE has 19 broad market indices and out of which nine indices were selected in this study covering the study period from 01 January 2011 to 31 December 2020. The selected indices are Standard and Poor Bombay Stock Exchange Sensitivity Index (S&P BSE SENSEX), Standard and Poor Bombay Stock Exchange All Capitalization (S&P BSE AllCap), S&P BSE 100, S&P BSE 200, S&P BSE 500, Standard and Poor Bombay Stock Exchange Large Market Capitalization (S&P BSE LargeCap), Standard and Poor Bombay Stock Exchange Mid-Capitalization (S&P BSE MidCap), S&P BSE SENSEX Next 50 and S&P BSE SmallCap. We selected nine indices because only these nine indices are available, and the information about the other ten indices is not available.

3.2 Data collection

The data collected for this empirical study are daily open, high, low and closing prices of BSE broad market indices. Instead of using the closing price itself, the researcher used the average of these four prices. The logic behind the average values of these four prices is that volatility in changes in prices is controlled to some extent. While prior researchers have used only closing prices, assuming trading is done at the closing price, Lodha and Sora (2015) recommend using the average of the four prices to nullify the fluctuations, and volatility is controlled at least partially. All the data have been collected from the official website of the BSE.

3.3 Analytical procedure

The tools used in this study are: (1) unit root test [The Augmented Dickey–Fuller [(ADF)] test to check the stationarity of time series, (2) descriptive statistics (average monthly returns, maximum, minimum, standard deviation, skewness, kurtosis and Jarque–Bera Test), (3) autocorrelation (measuring the linear relationship between lagged values of a time series) and (4) runs test (to check whether observations vary around a constant mean, have constant variance and are probabilistically independent). To calculate the daily returns, we used the formula [(LN (Today closing price/yesterday closing price) × 100]. These tools have been used by several researchers in the past ( Degutis and Novickytė, 2014 ; Harshita et al. , 2018 ; Titan, 2015 ). The procedures and techniques used in this study are consistent with the earlier research in the literature.

The ADF statistics used in the test should be a negative number, and the more the negative number, the stronger the rejection of the null hypothesis that there is a unit root. The runs test, a non-parametric test, is concerned with the price changes rather than the magnitude of price changes. It just considers whether the series consists of increasing values or decreasing values. The null hypothesis of the runs test is that the data set is from a random process.

First, we examined the descriptive statistics. Table 1 captures the results of descriptive statistics for BSE broad market indices. For the time-series data, it is essential to check the normality of the data which can be found by observing the descriptive statistics. Therefore, we did a preliminary analysis of the descriptive statistics, namely, mean, standard deviation, variance, minimum, maximum, skewness and kurtosis. The mean of BSE SENSEX and BSE 200 shows the maximum mean return of (0.0340). In order that the distribution is normal, the condition is that both skewness and kurtosis must be equal to 0 and 3, respectively. As can be seen from Table 1 , the value of skewness of the returns was found to be negative for all indices and therefore the distribution of the daily returns was asymmetrical. The value of Kurtosis is greater than 3 (which represents Leptokurtic distribution) for all the indices. Based on these descriptive statistics, we reject H01 and conclude that the distribution of returns is not normal.

To test the stationarity in the BSE broad market indices, an ADF test was conducted. Table 2 displays the results of the ADF test. The ADF test statistic values of intercept are less than critical values at a 1% significance level. Hence, H02 was rejected and concluded that there is no stationarity in the return series of BSE broad market indices. These results show that data has exhibited stationarity.

4.1 Autocorrelation

There are 16 lag periods associated with autocorrelation for all the indices (in Tables 3–11 ).

The results of autocorrelation for S&P BSE SENSEX are presented in Table 3 .

The first lag depicts an autocorrelation of 0.262 ( Q -statistic = 170.33, p  < 0.05), suggesting that the stock market in India does not follow a random walk. It is also interesting to note that the autocorrelation values for the lags 6, 10, 11, 13, 15 and 16 were negative ( p  < 0.05) and these results support that stock returns are not random.

The results of autocorrelation for S&P BSE AllCap are shown in Table 4 .

As shown in Table 4 , the first lag shows an autocorrelation of 0.182 ( Q -statistic = 81.897, p  < 0.05) which suggests that stock returns in the Indian stock market do not follow a random walk. Further, the lags 6, 11, 13, 15 and 16 showed negative autocorrelations ( p  < 0.05) corroborating that the stock returns are not random.

The results of autocorrelation for S&P BSE 100 are exhibited in Table 5 .

As can be seen in Table 5 , there are 16 lag periods related to the autocorrelation test. The first lag depicts an autocorrelation of 0.286 ( Q -statistic = 203.17, p  < 0.05), and the lags 6, 11, 13, 15 and 16 had negative autocorrelations ( p  < 0.05). These results suggest that stock returns on the Indian stock market are not random.

Table 6 shows the results of autocorrelation for S&P BSE 200.

As presented in Table 6 , there are 16 lag periods associated with the autocorrelation test. The first lag depicts an autocorrelation of 0.296 ( Q -statistic = 216.61, p  < 0.05), and the lags 6, 11, 13, 15 and 16 had negative autocorrelations ( p  < 0.05). These results indicate that stock returns in the Indian stock market are not random.

The results of autocorrelation for S&P BSE 500 are presented in Table 7 .

As can be seen in Table 7 , the first lag depicts an autocorrelation of 0.310 ( Q -statistic = 238.73, p  < 0.05), and the lags 6,11,13,15 and 16 showed negative autocorrelations ( p  < 0.05). These results corroborate that stock returns in the Indian stock market do not follow a random walk.

The results of the autocorrelation test for S&P BSE LargeCap are detailed in Table 8 .

As detailed in Table 8 , the first lag depicts an autocorrelation of 0.146 ( Q -statistic = 52.786, p  < 0.05), and the lags 6, 11, 13, 15 and 16 had negative autocorrelations ( p  < 0.05). These results indicate that the stock returns of the Indian stock market do not follow a random walk.

The results of the autocorrelation test for S&P BSE MidCap are presented in Table 9 .

As shown in Table 9 , there are 16 lag periods related to the autocorrelation test. The first lag depicts an autocorrelation of 0.299 ( Q -statistic = 221.42, p  < 0.05), and the lags 6, 13, 14 and 15 had negative autocorrelations ( p  < 0.05), thus documenting that stock returns in the Indian stock market are not random.

The results of the autocorrelation test for S&P BSE SENSEX NEXT50 are presented in Table 10 .

As can be seen in Table 10 , the first lag depicts an autocorrelation of 0.181 ( Q -statistic = 81.107, p  < 0.05), and the lags 4, 5, 6, 11, 13, 15 and 16 all showed negative autocorrelations ( p  < 0.05). These results reveal that stock returns on the Indian stock market are not random.

Table 11 shows the results of the autocorrelation test for S&P BSE SmallCap.

As Table 11 details, the first lag depicts an autocorrelation of 0.373 ( Q -statistic = 345.56, p  < 0.05), and the lags, 13, 14 and 15 showed negative autocorrelations ( p  < 0.05). The results document that stock returns on the Indian stock market are not random.

The results of runs test for BSE broad market indices are exhibited in Table 12 .

As shown in Table 12 , the Z value negative for all the BSE broad market indices and found that the critical value of Z for 95% level of confidence is ± 1.96. Hence, the null hypothesis, i.e. BSE broad market indices follow a random walk is rejected at a 5% level of significance. Moreover, the p -value is also 0.000 which is less than the alpha (0.05), and therefore, the null hypothesis is rejected. The runs test of this study indicates that BSE broad market indices do not follow a random walk and it is evident that the Indian stock market is in weak-form inefficient.

5. Discussion

The objective of this study is to test the EMH in the Indian stock market. The rationale for this study stems from the fact that though several studies on EMH were conducted in India, the results were mixed. This prompted us to study the EMH, especially during the last decade (2010–2020), a period characterized by unprecedented economic changes, and the Indian economy has been on the growth track. Our results were consistent with most of the previous studies. Our results are fascinating because even when much information is available because of technological improvements and transparency in the data, the EMH does not hold good.

First, the results indicate that the value of skewness returns distribution was negative for all indices. It is documented that the distribution of the daily returns is asymmetrical nature. The value of Kurtosis is greater than 3, representing Leptokurtic distribution for all the indices. The distribution is, therefore, was not normally distributed ( H01 ). The autocorrelation test reveals that the stock returns of the Indian stock market do not follow a random walk for all the indices. Second, the findings from this study indicated that the ADF test statistic values of intercept are less than critical values at a 1% significance level. Hence, the null hypothesis is rejected, and the results reveal that data has exhibited stationarity in nature ( H02 ). When the data are non-stationary, the time series contains unit root implying that the mean, variance and covariance are not constant over time. The ADF statistic contains significant negative values and corroborates that the series does not contain a unit root. If data contains the unit root, the data follows a random walk. The results from this study indicate that the unit root is not present, and the data showed stationarity. Finally, the runs test of this study indicates that BSE broad market indices do not follow a random walk, and it is evident that the Indian stock market is as weak-form inefficient ( H03 ). To sum, the results from our study do not support EMH as evidenced by critics of the theory. Asymmetrical distribution, Leptokurtic distribution and the runs test result show that BSE broad market indices do not follow a random walk. Therefore, the Indian stock market is weak-form inefficient.

5.1 Theoretical implications

The study has several theoretical implications. First, the results add to the growing body of literature on EMH, and the results are consistent with most of the earlier studies. Second, though some studies in the past have shown different and opposite effects (see Tables 1 and 2 ), our study provides a fresh look at the EMH during a decade of 2010–2020. Most importantly, the results from this study corroborate the findings conducted a decade back that tested the weak form of market efficiency of stock market returns in 14 countries (Pakistan, India, Sri Lanka, China, Korea, Hong Kong, Indonesia, Malaysia, Philippines, Singapore, Thailand, Taiwan, Japan and Australia), which documented that stock prices do not follow random walks in all countries of Asian-Pacific region ( Hamid et al. , 2010 ). Therefore, investors in these countries employed strategies of the arbitrage process to enjoy the stream of benefits. Thus, our results are consistent with the previous studies and vouch for the failure of the EMH hypothesis.

Third, from the theoretical standpoint, the results suggest diagnosing the plausible reasons for the failure of EMH in the Indian context, besides all other countries in the Asia–Pacific region. We argue that two fundamental reasons for the failure of EMH in the Indian context: the unpredictability of investors' behaviour and uncertainty about the investment. Many studies in the Western countries and the Middle East have concluded that the market should be seen in only relative terms. There is consensus among academicians that EMH fails to explain the excess volatility in security prices, unexpected bubbles in the stock market, irrational customers and overreactive behaviour. While analysing market efficiency, academicians need to consider the dynamics of changing markets that may tilt the results and vouch for EMH failure.

5.2 Practical implications

The research findings of this study have several implications for the stakeholders, including the stockbrokers and investors. First, the results reported in this study portrayed that the stock market in India exhibited the weak-form inefficient; the investment brokers and investors should exercise caution before selecting their investment portfolios. In India, being a thickly populated developing country, there is a wide variety of investors with varying financial requirements. Some investors seek a long-term return on their investment, whereas some prefer to have secured returns every month. Some investors are risk-takers, whereas some are risk-avoiders. Since people with different portfolio requirements influence the stock market, behavioural finance scholars suggest examining the effect of personality factors on investment behaviour. For example, some researchers documented that the personality characteristics of individuals have a significant impact on investment behaviour ( Isidore and Christie, 2017 ; Sadiq and Khan, 2019 ). Second, financial literacy plays a vital role in investment decisions. Therefore, in addition to the technical analysis of the stock market, the analysts need to consider the level of financial literacy, information access, subjective financial knowledge, risk propensity, etc., that may profoundly impact investor behaviour. As provided in this study, the results from stock market analysis guide the investors in making decisions and not getting lured by false promises of stockbrokers ( Aren and Aydemir, 2015 ; Barber et al. , 2021 ).

The findings from the study help investors to make correct investment decisions. The effectiveness of investment decisions largely depends on market efficiency and the investors' financial knowledge and various investment opportunities with varying degrees of return on investment. Although theoretically, rational decision-making considers identifying multiple available alternatives and choosing suitable options, it is not possible in reality because of information asymmetry and market anomalies ( Sitkin and Weingart, 1995 ), and investors make decisions based on the available information. Therefore, failure to consider the market anomalies may result in flawed decision-making. Moreover, in the present-day technological sophistication where information is readily available from multiple sources, it is expected that investors will have complete information. Despite this, the reasons for the failure of EMH need further investigation. Investors diversify their investments based on their financial knowledge, and available empirical evidence shows that increased financial knowledge influences financial management attitudes, resulting in healthy financial behaviours ( Borden et al. , 2008 ).

5.3 Future research agenda

This study offers several avenues for future research. The results from this research vouch against the EMH and call for further studies to identify the reasons for the rejection of EMH. Though it was documented that in Asian countries, stock markets failed to support EMH, and the researchers explained the possible causes for lack of support for EMH, the information was not adequately explained. During this study period (2011–2020), the market did not exhibit high volatility, and it is suggested to identify the reasons for not supporting the well-established random walk theory. As we omitted 11 indices, future researchers can focus on those indices to see if the results from the study can be replicated. Second, future research can focus on liquidity's role in asset pricing in the stock market ( Miralles-Quirós et al. , 2017 ) and see how liquidity affects the EMH in the Indian stock market. Third, sometimes the investors may make frugal decisions, either lack information or habituate to making fast decisions (called heuristic) that challenge the EMH. The essence is that decisions taken by irrational investors may lead to inefficiencies in the stock market ( Akerlof and Shiller, 2010 ; Lobao et al. , 2017 ). Future researchers can also throw light on the effect of heuristic decisions made by investors on the efficiency of the stock market. Finally, as financial literacy plays an essential role in the investor's behaviour, it would be interesting to put on the agenda of future research to study the impact of financial literacy and financial illiteracy on the effectiveness of the stock market ( Rasool and Ullah, 2020 ).

6. Conclusions

The basic tenet of EMH is that if the stock market is working efficiently, the prices will follow a random walk, and the prices will reflect the intrinsic values, and no one can benefit from trading. However, there is the possibility that investors may be reluctant to agree with this hypothesis. Hence, some investors tend to buy stock, and some others may sell the stock so that the price is not affected significantly ( Latham, 1985 ). Amid several studies that have been conducted in India, this study was a modest attempt to empirically examine whether the stock market in India is weak-form efficient. The data was collected (daily open, high, low and closing prices) on nine BSE broad market indices and analysed using the standard tests (unit root, descriptive statistics, autocorrelation and runs test) covering the period from 1 January 2011 to 31 December 2020. The results did not support random walk theory, thus contributing to supporting the theory against EMH. Therefore, it is concluded that the Indian stock market, based on the results from the study, is a weak-form inefficient.

EMH proposes that security prices reflect all the available information. If this hypothesis is true, the asset managers need to demonstrate extraordinary skills to convince the investors that the recommended stock outperforms other securities ( Brown, 2020 ). Since the rapid growth of technology makes information accessible in no time, prices must reflect all information. EMH must be more valid in the present-day context than when Fama (1970) postulated the hypothesis. While the academicians do not consider the costs involved in acquiring information, the investment analyses do think the cost involved, and hence Fama (1970) argued that prices reflect the information only to the extent the expenses do not outweigh the benefits. One of the implications of EMH, as critics argue, is that there will be equilibrium in capital markets because of the presence of rational and informed agents. However, in real life, not all traders are perfectly rational. So, in the imperfect world, as behavioural financial scholars contend, EMH is valid only in theory (in spirit) but not accurate in practice. Some examples are that the financial crisis around 2008 around the world was a total failure of EMH, as the stock market largely depends on behavioural needs rather than financial arithmetic ( Malkiel, 2003 ). As things stand now, as there is no consensus among financial management scholars and economists about all three forms of EMH, there is a near-consensus that EMH is a theory simple to describe but difficult to put to the empirical test. Despite the onslaught against the EMH over the last two decades, the puzzling set of stock market anomalies could be considered chance events; some supporters argue that it is hard to find profit even if the market is highly volatile ( Roll, 1994 ). Lack of finding support for EMH may be considered as a shortcoming of the basic model. It would not be an exaggeration that the EMH has not lost its charisma and is expected to be on the agenda of financial economists.

Descriptive statistics for BSE broad market indices

	Mean	Max	Min	S.D.	Skew	Kur	Jarque-Bera (J.B.)	Prob	Obs
SENSEX	0.0340	6.5859	−8.3547	0.8900	−0.5534	11.6277	7,809	0.0000	2,477
AllCap	0.0331	5.8426	−7.9346	0.9683	−0.6938	9.2752	4,251	0.0000	2,470
BSE 100	0.0330	6.1051	−8.1651	0.8870	−0.6198	11.0119	6,784	0.0000	2,477
BSE 200	0.0340	5.9772	−7.9975	0.8793	−0.6619	10.8955	6,615	0.0000	2,477
BSE 500	0.0334	5.8701	−7.9652	0.8738	−0.7248	10.9034	6,664	0.0000	2,477
LargeCap	0.0324	6.2000	−8.1588	0.9825	−0.5226	9.1916	4,058	0.0000	2,470
MidCap	0.0333	5.2333	−6.9040	0.9944	−0.6805	6.9284	1,784	0.0000	2,477
SENSEX Next 50	0.0315	5.2653	−8.4137	1.1358	−0.6622	6.9671	1,799	0.0000	2,468
SmallCap	0.0246	5.6568	−7.2551	1.0486	−0.8362	7.1473	2,064	0.0000	2,477

AllCap, All Capitalization; BSE, Bombay Stock Exchange; LargeCap, Large Market Capitalization; MidCap, Mid-Capitalization; S.D., Standard Deviation; SENSEX, Sensitivity Index

Compiled from EViews 10

Indices	-value	Critical values
		1%	5%	10%
S&P BSE SENSEX	−38.03359	−3.432797	−2.862507	−2.567330
S&P BSE AllCap	−41.32011	−3.432804	−2.862510	−2.567332
S&P BSE 100	−37.05268	−3.432797	−2.862507	−2.567330
S&P BSE 200	−36.67706	−3.432797	−2.862507	−2.567330
S&P BSE 500	−36.08718	−3.432797	−2.862507	−2.567330
S&P BSE LargeCap	−42.87290	−3.432804	−2.862510	−2.567332
S&P BSE MidCap	−36.54468	−3.432797	−2.862507	−2.567330
S&P BSE SENSEX Next 50	−41.33689	−3.432807	−2.862511	−2.567332
S&P BSE SmallCap	−33.59785	−3.432797	−2.862507	−2.567330

BSE, Bombay Stock Exchange; S&P BSE AllCap, Standard and Poor Bombay Stock Exchange All Capitalization; S&P BSE LargeCap, Standard and Poor Bombay Stock Exchange Large market Capitalization; S&P BSE MidCap, Standard and Poor Bombay Stock Exchange Mid-Capitalization; S&P BSE SENSEX, Standard and Poor Bombay Stock Exchange Sensitivity Index; SENSEX, Sensitivity Index

Compiled from EViews 10

Note(s): AllCap, All Capitalization; BSE, Bombay Stock Exchange; LargeCap, Large Market Capitalization; MidCap, Mid-Capitalization; S.D., Standard Deviation; SENSEX, Sensitivity Index

Source(s): Compiled from EViews 10

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Acknowledgements

The authors are thankful to the Editor-in-Chief, Professor Nestor U. Salcedo, and the anonymous reviewers for their constructive suggestions in the earlier version of the manuscript.

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• Open access
• Published: 11 July 2019

Stock market and macroeconomic variables: new evidence from India

• R. Gopinathan 1 &
• S. Raja Sethu Durai 2  

Financial Innovation volume  5 , Article number:  29 ( 2019 ) Cite this article

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Understanding the relationship between macroeconomic variables and the stock market is important because macroeconomic variables have a systematic effect on stock market returns. This study uses monthly data from India for the period from April 1994 to July 2018 to examine the long-run relationship between the stock market and macroeconomic variables. The empirical findings suggest that standard cointegration tests fail to identify any relationship among these variables. However, a transformation that extracts the actual functional relationship between these variables using the alternating conditional expectations algorithm of (J Am Stat Assoc 80:580–598, 1985) identifies strong evidence of cointegration and indicates nonlinearity in the long-run relationship. Further, the continuous partial wavelet coherency model identifies strong coherency at a lower frequency for the transformed variables, establishing the fact that the long-run relationship between stock prices and macroeconomic variables in India is nonlinear and time-varying. This evidence has far-reaching implications for understanding the dynamic relationships between the stock market and macroeconomic variables.

Introduction

Understanding the relationship between macroeconomic variables and the stock market is important because macroeconomic variables have a systematic effect on stock market returns. Economic forces affect discount rates, and through this mechanism, macroeconomic variables become part of the risk factors in equity markets [Chen et al. 1986 ]. Arbitrage pricing theory assumes that financial stocks can be influenced by the behavior of macroeconomic fundamentals; there are many channels for the relationships between the stock market and key macroeconomic variables. For example, Friedman (1988) advocated the wealth and substitution effects to measure the relationship between the stock market and money. Moreover, three separate hypotheses have been proposed to explain the theoretical relationship between the stock market and the exchange rate: Frenkel’s (1976) asset market hypothesis, Dornbusch and Fischer’s ( 1980 ) goods market hypothesis, and Frankel’s (1983) portfolio balance hypothesis.

Studies have shown that the choice of the financial and macroeconomic variables that influence the stock market is intriguing and puzzling, and have attempted to explain the anomalous relationship through different hypotheses [Fama ( 1981 ), Geske and Richard ( 1983 ), Ram and Spencer ( 1983 ), Fama ( 1990 ), Schwert ( 1990 ), Cochrane ( 1991 ) and Lee ( 1992 )]. Fama ( 1981 ) explained the anomalous negative correlation between inflation and real stock returns by proposing a proxy hypothesis, where the anomalous negative correlation is the result of the negative relationship between inflation and real output and the strong positive relationship between real output and real stock returns. Ram and Spencer ( 1983 ) found evidence of a positive relationship between inflation and real output, consistent with the Phillips curve hypothesis.

While many researchers provide empirical support for linear long-run relationships between stock markets and macroeconomic variables, studies like Mukherjee and Naka ( 1995 ), Cheung and Ng ( 1998 ), Binswanger ( 2004 ), Nasseh and Strauss ( 2000 ), Wongbangpo and Sharma ( 2002 ), Kizys and Pierdzioch ( 2009 ), Bekhet and Matar ( 2013 ), Inci and Lee ( 2014 ) and Lawala et al. ( 2018 ) employed Engle and Granger’s ( 1987 ) methodology to infer causal relationships and Granger’s ( 1988 ) and Johansen’s ( 1991 ) methodology for cointegration between these variables. Most of the earlier empirical studies implicitly assumed that the relationships between the stock market and macroeconomic variables are linear in nature and time-invariant. In their cointegration analyses, most of these studies failed to test the stability of the parameters over time or the asymmetric long-run relationships among these variables. Hansen and Johansen ( 1999 ) and Johansen et al. ( 2000 ) emphasized that the results of cointegration analysis are highly sensitive to sample selection and have potential parameter instability over time.

In this regard, McMillian ( 2005 ) estimated the time-varying relationships between the stock market and other macroeconomic variables for U.S. data using Johansen’s ( 1991 ) cointegration test in a rolling and recursive sample window and suggested that the long-run relationships between these variables are time varying. The main drawback of implementing a rolling or recursive cointegration is that the variables under consideration should have the same time series properties for all sample windows; if these properties change for a given subsample of windows, then the interpretations from the analysis are biased. On the other hand, a good number of recent studies have examined the nonlinear relationships between key macroeconomic variables such as output, inflation, and exchange rates, and found evidence in favor of the asymmetric behavior of these variables over a period. Studies like Falk ( 1986 ), Ramsey and Rothman ( 1996 ), and Bradley and Jansen ( 1997 ) all support various forms of nonlinear adjustment among key macroeconomic variables. In line with these findings, studies by Boucher ( 2007 ) and Kizys and Pierdzioch ( 2009 ) highlight that the relationships between the stock market and macroeconomic variables are asymmetric and these relationships will change in the long run.

The nonlinearities in financial markets are explained by many studies, such as Dumas ( 1992 ), Brock and LeBaron ( 1996 ), Sarantis ( 2001 ), Shleifer and Robert ( 2003 ), and Humpe and Macmillan ( 2014 ). These studies all identify the interaction between informed and noise traders, suggesting speculators are the main source for the market’s nonlinear behavior.

From an empirical standpoint, the functional form of any relationship should be appropriate before performing any analysis. When the relationship is nonlinear, a linear analysis may lead to misleading conclusions, with the potential of inferences that there is no relationship between the variables under consideration. Although some studies highlight the possible nonlinear relationships between the stock market and macroeconomic fundamentals, the issue has received little comprehensive attention in the empirical literature. A few studies, like Kanas ( 2003 , 2005 ), Zhou ( 2010 ), and Tang and Zhou ( 2013 ), have documented nonlinear relationships for different variables, and explored the alternating conditional expectations (ACE) algorithm developed by Breiman and Friedman ( 1985 ) to identify the correct functional form and transform the variables to be used in the empirical analysis. The results from these studies show that the advantage of using the ACE algorithm is its ability to identify the exact functional form of the nonlinear relationship. Once the correct functional form of the variables has been identified, further investigation can proceed.

Recent advances in time-series econometrics have produced methodologies for analyzing the relationships between variables in a frequency domain, where the actual relationship might vary at different frequencies. For example, some studies of India have used frequency domains and wavelet analysis. Durai and Bhaduri ( 2009 ) examined the stock market and economic activity using discrete wavelets to decompose the time series of the variables into different frequencies; the results suggest that the variables are connected in different ways at different frequency levels. Tiwari et al. ( 2013 ) used the continuous wavelet transformation (CWT) developed by Conraria and Soares ( 2011 ). The advantage of the CWT over discrete wavelet transformation (DWT) is the identification of the correlation between variables in different frequencies over time scales. Even though the CWT has a major disadvantage it can be used only for two variables the concepts of wavelet multiple coherencies and partial wavelet coherency to some extent compensate, allowing the CWT to move beyond bivariate analysis.

The purpose of the present study is to extend the existing nonlinear and time-varying empirical literature to clarify the relationship between stock prices and key macroeconomic fundamentals in the Indian context. The study’s main contribution is twofold. First, the analysis of nonlinearity in the relationships between the stock market and other key macroeconomic variables for Indian data provides a developing country perspective. Second, using continuous wavelets to understand the coherency between two variables in the frequency domain for different time scales provides a better understanding than implementation of a rolling or recursive cointegration.

The remainder of the paper is organized as follows. Section 2 describes the nonlinear cointegration approach using an ACE algorithm and provides a brief outline of the CWT methodology used in the study. Section 3 describes the data, and in section 4, the results of the empirical estimation are reported. Finally, section 5 draws conclusions based on the study’s empirical findings.

Nonlinear and time-varying relationships

The conventional cointegration tests of Engel and Granger (1987) and Johansen ( 1991 ) implicitly assume linearity and time invariance. The inferences drawn from these tests may be misleading if the relationships are nonlinear and time-varying. Following McMillian (2005), this study uses a rolling cointegration test for stock prices and other macroeconomic variables. In the rolling framework, we fix the size of a rolling sample window, Footnote 1 and move the sample window by adding one observation to the end and removing the first one. For each rolling sample window, we conduct conventional augmented Dickey-Fuller (ADF) unit root tests to determine the order of integration for each of the variables used in every rolling window. If the test ensures all variables are integrated of order one in all rolling windows, then we can move to implement the conventional Johansen ( 1991 ) cointegration test and the trace statistics can be observed and scaled by their 5% critical values. The null hypothesis of no cointegration can be rejected at a 5% level for the specified sub-sample period if the value of the scaled test statistic is greater than one.

The ACE algorithm and nonlinear cointegration

The ace algorithm.

Granger and Hallman ( 1991 ) and Meese and Rose ( 1991 ) analyzed the non-parametric ACE algorithm Footnote 2 developed by Breiman and Friedman ( 1985 ) for raw variables to obtain nonlinear transformations of their respective variables and used a causality test for the transformed variables to infer a nonlinear causal relationship. The ACE method converts the original variables into transformed variables, ensuring that there is maximum correlation between the variables with the highest R-squared; ACE procedures adopt extremely weak distributional assumptions and can handle a wide variety of nonlinear transformations of the data by utilizing flexible data smoothing techniques. Thus, any test on these transformed variables can be viewed as evidence for nonlinearity.

Assume a linear regression model contains k independent variables, namely x 1 t , x 2 t , … ., and x kt , and a dependent variable y t :

Where, δ 0 , δ (i = 1,2,…,k) are the regression coefficients to be estimated, and ε t is an error term. Thus eq. ( 1 ) assumes that y t, the dependent variable, is a linear function of k independent variables. An ACE algorithm using the regression model in eq. ( 1 ) can be written as.

Where f is a function of the dependent variable y, and n i is a function of the independent variables x i (i = 1,2,…,k). Equation ( 2 ) shows f (·), n 1 (·), n 2 (·) …, and nk (·) is the optimal transformation to be estimated. The ACE regression normalizes the coefficients to unity.

The ACE algorithm initially starts by defining arbitrary determinate mean zero transformations, f (y t ), n 1 (x 1t ), n 2 (x 2t ),. ., and n k (x kt ). To obtain the optimal transformation, the estimated model ensuring the maximum correlation among the variables and highest R-square from a regression as specified in eq. ( 2 ). Under the constraint of E [ f (y t )] 2  = 1, this is equivalent to minimizing the expected mean squared error of the regression. The expected mean squared error is given by

Minimization of u 2 with respect to n i (x i ) (i = 1,2,…,k) and f (yt) is carried out through a series of single-function minimizations, resulting in the following equations:

With \( \left\Vert \bullet \right\Vert \equiv {\left[E{\left(\bullet \right)}^2\right]}^{\frac{1}{2}} \)

The algorithm involves two basic mathematical operations: conditional expectations and iterative minimization; thus, the transformation is referred to as alternating conditional expectations. Using eq. ( 4 ) to transform all variables, one variable is fixed and the transformation of the variable in question is estimated using a nonparametric data smoothing technique; the algorithm then continues to the next variable. For each variable, the iterations continue until the mean squared error of eq. ( 3 ) has been minimized. Breiman and Friedman ( 1985 ) show that the ACE algorithm provides transformations such that f (y t ), n 1 (x 1t ), n 2 (x 2t ), …., and n k (x kt ) converge asymptotically to the true functional forms of the optimal transformations. The distinction of these transformations is that ACE does not treat the explanatory variables as fixed, but instead treats the variables as drawn from a joint distribution. After the estimation of n i (x it ) (i = 1,2,…,k), f (y t ) is estimated, conditioned on these estimates, according to eq. ( 5 ). Alternating between Eqs. ( 4 , 5 ), the ACE method iterates until eq. ( 3 ) is minimized. The transformations of n i *(x i ) (i = 1,2,…,k) and f * (y) that achieve minimization are the optimal transformations.

Nonlinear Cointegration

As argued in studies like Granger ( 1991 ), Granger and Hallman ( 1991 ), Meese and Rose ( 1991 ), Kanas ( 2003 , 2005 ) and Tang and Zhou ( 2013 ), nonlinear cointegration can be characterized from the linear cointegration of the ACE transformed variables. There are two steps involved in this procedure. First, as highlighted by Granger and Hallman ( 1991 ), in converting all original variables into ACE transformed variables, we have to ensure that the transformed variables do not deviate from the time-series properties of the original variables. Second, the usual Johansen ( 1991 ) type cointegration test is implemented for the transformed variables. This nonlinear cointegration can also be used in a rolling framework to examine time-varying nonlinearity in the relationship. If the transformed variables deviate from the time series properties of the original variables for the entire sample period or any subsample period in a rolling window, we cannot implement the usual cointegration test to capture the time varying aspect of the relationship. In that case, we propose using the continuous wavelet transform methodology to understand the relationship at different frequencies over time.

Continuous wavelet transform

CWT is a better alternative model for understanding the time-varying and nonlinearity of the relationships between stock prices and other macroeconomic variables. Wavelet coherency is used to determine the coherency between two variables for different frequencies over time, and partial wavelet coherency is used to determine the coherency between two variables conditional upon other variables for different frequencies over time. Following Conraria and Soares ( 2011 ), the methodology of deriving the CWT is as follows. The set of square integrables and the space of finite energy functions is denoted by L 2 (R) The minimum criteria to impose on a function ψ (t) ∈ L 2 (R) The wavelets begin with a mother (admissible or analyzing) wavelet, which consists of a technical portion of the admissibility condition.

Cψ denotes the constant of the admissibility or analyzing constant.

The purpose of the wavelet is to provide the time frequency of localization; the wavelet localized function gives both the time and frequency domains.

ψ denotes wiggles up and down in the time axis; the CWT starts with a mother wavelet ψ, and a family ψ τ,s of “wavelet daughters” can be obtained by simply scaling and translating ψ:

where s denotes a scaling or dilation factor that controls the width of the wavelet and τ denotes the translation parameter, which controls the location of the wavelet. Wavelet scaling indicates stretching if (| s | > 1) or (| s | < 1), whereas translating it means shifting its position in time. Given a time series, x (t) ∈ L 2 (R), the CWT of wavelet ψ is a function of two variables, W x:ψ (τ, s).

The time domain wavelet is given by τ , while the frequency domain is given by s . The wavelet transforms the time and frequency domains by mapping the original series into a function of τ and s ; the wavelet provides concurrent information on the time and frequency domains. The procedures of wavelet and Fourier transformations are somewhat similar. However, the Fourier transformation differs from the wavelet in that it has no time localization parameter. Moreover, we have two functions, cosine and sine, instead of a wavelet function. CWT may also be represented in the frequency as

To develop wavelet coherency, we need two more derivations: the cross-wavelet transform (XWT) and cross wavelet power (XWP). The cross wavelet transform of two times series, x(t) and y(t), was introduced by Hudgins et al. ( 1993 ) and defined as

where W x and W y represent the wavelet transforms of x and y, respectively. The cross-wavelet power provides a quantified indication of the similarity of power between two time series at each time and frequency and is defined as

Complex wavelet coherency

The set of two time series x(t) and y(t) describes their complex wavelet coherency:

The Wavelet Coherency is denoted as follows

W x and W y are the wavelet transforms of x and y, respectively, S denotes a smoothing operator in both time and scale; without smoothing, coherency would be identical across all scales and times. The partial wavelet coherency of x 1 and x j (2 ≤ j ≤ p) are denoted as follows:

r 1 jqj is measured as the absolute value

The Squared partial wavelet coherency of x i , j

Where φ denote the p x p matrix of all the smoothed cross-wavelet spectra S ij .

Wavelet coherency is the relationship to the product of the spectrum of each series, which can be the local correlation between the time and frequency domains in the two time series. This concept definition nearly replicates the traditional correlation coefficient. Wavelet coherence provides localized correlation coefficients in time and frequency space. When no correlation measures zero coherencies between the two time series and wavelet coherency is equal to one, it shows a strong correlation between the time and frequency domains. The statistical significance of estimated wavelet coherency can be explained through Monte Carlo simulation methods. There are no positive and negative co-movements between the time series for wavelet coherency. The information on positive and negative co-movements can distinguish the lead-lag relationships between two time series through the phase of the wavelets.

Following Conaria and Soares ( 2011 ), we can define the complex partial wavelet coherency between x and y after controlling z as follows

C xy and R xy are complex wavelet coherency and wavelet coherency, respectively, as defined in Eqs. ( 12 , 13 ). The partial wavelet coherency between x and y given z can be defined by taking the absolute value of the denominator in eq. ( 13 ). We may write the expression for partial wavelet coherency in terms of wavelet coherency as

The empirical analysis is conducted using monthly data from April 1994 to July 2018, a total of 292 observations. Monthly data of the Bombay Stock Exchange (BSE) Sensex Index, Index of Industrial Production (IIP), Wholesale Price Index (WPI), Broad Money (M3), and Exchange Rate are used. The choice of the sample is determined by the fact that a consistent new series of data is available for the sample period; it also reflects the post-liberalization period. The IIP is used as a proxy for output, while the WPI is used as a measure of inflation, and Rupees per U.S. dollar is used as a measure of the exchange rate. The data are collected from the following sources: the BSE Sensex Index is collected from their website ( www.bseindia.com ), and other macroeconomic variables are collected from the Handbook of Statistics on Indian Economy published by the Reserve Bank of India (RBI). All variables are seasonally adjusted, and subsequent analysis is performed on the natural logarithms Footnote 3 of these series.

Empirical results

To analyze the long-run relationships between the stock market and other key macroeconomic variables, it is necessary to perform the conventional Engle and Granger ( 1987 ) cointegration and Johansen ( 1991 ) tests. Before considering possible cointegration between these series, their orders of integration are examined using unit root tests. The standard ADF, Phillips Perron, and Kwaitkowski et al. (1992) (KPSS) unit root tests are used, and the results are presented in Table  1 . The test results show that all series are non-stationary at levels and stationary at first differences.

First, we used the conventional cointegration tests of Engle and Granger ( 1987 ) and Phillips and Ouliaris ( 1990 ) to examine the cointegration between stock prices and other macroeconomic variables. In these two tests, the null hypothesis is no cointegration, so if the calculated value of the EG and Pz statistics are significant, the null of no cointegration is rejected, indicating there is cointegration among the variables. For both these tests, the optimal lag length is determined by the Akaike information criterion, and the results are presented in Table  2 .

The results from Table 2 indicate both tests fail to reject the null of no cointegration between the stock market and the macroeconomic variables, showing there is no long-run relationship between these variables. To corroborate this, we used the Johansen ( 1991 ) cointegration test for the same set of variables and the results are presented in Table  3 .

The results indicate that the test statistics of trace and maximum Eigen statistics are both above the critical values at the 5% significance level. Hence, we reject the null of no cointegration relationship between these variables, which means a cointegrating relationship exists between the stock market and macroeconomic variables. The Engle and Granger ( 1987 ) cointegration and Phillips and Ouliaris ( 1990 ) tests fail to reject the null of no cointegration relationship between the stock market and other macroeconomic variables; however, the Johansen ( 1991 ) cointegration test shows the presence of a long-run relationship between these variables. Inferences drawn from conventional and Johansen ( 1991 ) cointegration tests depict a contrasting result for the relationship between the stock market and other macroeconomic variables. Gonzalo and Lee ( 1998 ) established the pitfalls in Johansen type cointegration tests and highlighted that validation by the Engle-Granger cointegration test is needed to avoid the drawbacks. Since the Engle and Granger cointegration test does not validate the Johansen test results, such contrary evidence leads to further investigation of these relationships.

The scatter plots

To understand these contradictory results from the two sets of cointegration tests, we need to understand the exact relationship between stock prices and each of these macroeconomic variables. A simple scatter plot of stock prices with each of these variables is depicted in Figs. 1 , 2 , 3 , 4 .

Scatter Plot of LBSE and LIIP

Scatter Plot of LBSE and LWPI

Scatter Plot of LBSE and LM

Scatter Plot of LBSE and LE

In all scatter plots, the vertical axis measures stock prices (LBSE) and all corresponding horizontal axes measure other macroeconomic variables (LIIP, LWPI, LM, and LE). These scatter plots show the nonlinear relationships between the stock market and other macroeconomic variables; moreover, the figures also show the trend lines fitted to the data. The fitted trend line for the LBSE and LIIP stands as a polynomial of order 6, whereas the trend line for LBSE and LWPI is a polynomial of order 5. For the remaining two variables, LM and LE, the trend line exhibits two and three period moving averages, respectively. Evidence from these scatter plots shows that the relationships between the stock market and other macroeconomic variables are nonlinear. This evidence restricts any linear analysis between stock prices and other macroeconomic variables in India.

To capture the nonlinearity, we employed ACE, Breiman and Friedman’s ( 1985 ) algorithm, to convert the original variables into transformed variables Footnote 4 and test their long-run cointegration relationship. As explained, the ACE transformed variables should possess the same time series properties as the original variables, so before performing cointegration analysis, this warrants ensuring that all the transformed series retain their respective time series properties. Standard ADF, Phillips Perron, and KPSS unit root tests are used for the transformed variables to examine their stationarity. We also performed the Zivot-Andrews unit-root test Footnote 5 on the transformed series and found evidence in favor of structural breaks among the variables, which supports time variation in the relationships.

The test results in Table 4 show that all series are non-stationary at levels and stationary at first differences. Since these transformed variables possess the same properties as their original counterparts, we can now use both the conventional [Engle and Granger 1987 ; Phillips and Ouliaris 1990 , and Johansen 1991 ] cointegration tests to examine the nonlinear cointegration. The results of these tests are presented in Tables  5 and 6 .

The results from both conventional tests reject the null of no cointegration between stock prices and other macroeconomic variables, and accept that there is a long-run relationship between the transformed variables at conventional levels of significance. The Johansen ( 1991 ) test results also reject the null of no cointegration relationship between these transformed variables, which indicates a cointegrating relationship exists between the stock market and macroeconomic variables. Altogether, this empirical evidence suggests that long-run cointegration exists between the ACE transformed variables, which leads to the inference that there is a nonlinear cointegration between stock prices and other macroeconomic variables for the full sample period. The key implication from this evidence is that when there is a nonlinear relationship, a linear combination of the variables may lead to deceptive inferences.

Further, regarding the possible sensitivity of the results to sample selection and parameter instability in the relationship between stock prices and other macroeconomic variables as highlighted by McMillan ( 2005 ), this study also examines the time variation in the long-run relationship between these variables using a rolling cointegration technique. Before considering the rolling cointegration test, we verify the time series properties of these variables in each subsample. In particular, the variables involved should be non-stationary in every subsample (rolling window); otherwise, the inferences might be spurious because the test statistics will be biased. Thus, we first employ rolling ADF unit root tests to check for stationarity for all series under consideration. The rolling window size is fixed at 60 observations (5 years); each time, the window is renewed by adding one observation to the end and removing the beginning observation. Thus, the first rolling window will have a sample of the first 1 to 60 observations, the second will include 2 to 61, then 3 to 62 and so on through the last observation. The test results are presented in Figs.  5 and 6 .

Rolling Unit Root Test for original variables

Rolling Unit Root Test for ACE Transformed Variables

Figure  5 clearly shows that for all the original variables (LBSE, LIIP, LWPI, LM, and LE), the null hypothesis of non-stationarity can be rejected in some sample windows, indicating that the variables change their time series properties. Similarly, Fig.  6 shows the same results for all the transformed variables Footnote 6 (ABSE, AIIP, AWPI, AM, and AE); in some windows variables are nonstationary, while in other windows, they are stationary at the levels. Hence, we cannot implement a rolling cointegration test to identify the time-varying relationship.

To circumvent this problem, following Conraria and Soares ( 2011 ), we use CWT for both the actual and transformed variables to understand the time variation in this relationship. In this study, we concentrate only on partial wavelet coherency to determine the coherency between two variables conditional upon other variables for different frequencies over time. The main objective is to understand the relationship between stock prices and output, retaining all other variables as control variables.

In CWT, the frequencies are split into low and high frequency, with low frequency measuring the long-run coherency between the variables and the high frequency measuring the short-run coherency. Coherency is differentiated using color codes ranging from blue to red; high coherency is indicated by the red color and the level of significance is identified with black and grey borders. Figure  7 provides the wavelet partial coherency for actual data on stock prices and output after controlling for other macroeconomic variables like inflation, money supply, and the exchange rate. The figure indicates that without transformation, there is no significant partial coherency in the low frequency, which measures the long-run partial correlation between the variables. At the high-frequency level, for some points between 2002 and 2005, there is statistically significant evidence for short-run partial coherency.

Wavelet Partial Coherency for Actual Variables

In contrast to the actual variables, Fig.  8 depicts the partial wavelet coherency for the ACE transformed variables. Like the actual data, we have analyzed the transformed stock prices and output after controlling for other transformed macroeconomic variables like inflation, money supply, and the exchange rate. The figure clearly shows a strong and significant partial coherency at a high frequency, which indicates the long-run relationship over time. The interesting inference from this analysis is that unless we identify the exact functional form of the variables, it is highly misleading to derive any plausible conclusions about their relationships. The relationships between the stock market and macroeconomic variables are nonlinearly related; if we linearly analyze and interpret them, it may result in a biased conclusion.

Wavelet Partial Coherency for Transformed Variables

This study aimed at understanding the time-varying, nonlinear relationships between stock prices and other key macroeconomic variables using monthly data from India for the period of April 1994 to July 2018. After checking the time series properties of the variables, different cointegration tests are implemented to understand their long-run relationships. The conventional Engle and Granger ( 1987 ) and Phillips and Ouliaris ( 1990 ) tests show that there is no relationship between stock prices and other macroeconomic variables. However, the Johansen cointegration test shows that long-run relationships exist between these variables. These two contrasting results warranted further analysis. To investigate this issue, we plot simple scatter plots that indicate these variables are not linearly related, but exhibit nonlinearity.

To address the nonlinear relationships between stock prices and other macroeconomic variables, we used the ACE algorithm of Breiman and Friedman ( 1985 ). ACE algorithms identify and extract the function of these relationships by converting the original variables into ACE transformed series, which provides the functional relationships between the variables. As highlighted by Granger and Hallman ( 1991 ), nonlinear cointegration can be characterized by implementing a cointegration test for these ACE transformed variables. To do this, we must ensure that the transformed variables do not deviate from the time series properties of the original variables. All transformed series are integrated of order one at levels for the full sample period. The conventional Engle-Granger, Phillips-Ouliaris, and Johansen cointegration tests show that there is long-run cointegration between the ACE transformed variables, which indicates that a nonlinear cointegration exists between stock prices and other key macroeconomic variables for India.

To test the time-varying aspect of this relationship, we first resort to a rolling cointegration test, but the rolling unit root test for both the actual data and transformed data show changes in the behavior of time series properties in some subsample periods (rolling windows). Hence, we cannot proceed to analyze the cointegration test to identify the relationships between stock prices and other macroeconomic variables. To understand the time variation, we used the CWT method for both actual and transformed variables, and the results identify wavelet partial coherency only for the transformed variables, not for the actual variables. The inferences drawn from the CWT highlight that stock prices and other macroeconomic variables are related nonlinearly in India.

The evidence presented in this study has far-reaching implications for policymakers, researchers, and investors. Understanding the effects of macroeconomic variables on the stock market is imperative; proper comprehension of the risk and opportunities associated with macroeconomic variables may help investors make appropriate decisions based on policy reactions and help them manage the systematic risk associated with the stock market. The evidence of nonlinearity indicates the presence in the market of noise traders, arbitrage traders, and speculators and should be supported with further empirical evidence. Hence, the findings show that understanding the nonlinear relationships is an integral part of identifying the causes of different fluctuations in economic activity. As such, this study alerts financial professionals and investors to consider nonlinear empirical consistencies when modeling the stock market and macroeconomic variables.

We used different window size for testing rolling unit root and cointegration.

All the ACE transformations is derived using the package of “ace pack” in R

Variables are named LBSE (log of BSE), LIIP (log of IIP), LWPI (log of WPI), LM (log of M3) and LE (log of Exchange rate)

Once variables are ACE Transformed then named as ABSE, AIIP, AWPI, AM and AE.

Results are available upon request.

For each rolling window the ACE transformation is derived separately.

Abbreviations

Alternating Conditional Expectation transformed Bombay Stock Exchange Sensex Index

Alternating Conditional Expectation

Augmented Dickey-Fuller

Alternating Conditional Expectation transformed Exchange rate

Alternating Conditional Expectation transformed Index of Industrial Production

Alternating Conditional Expectation transformed Broad Money

Arbitrage pricing theory

Alternating Conditional Expectation transformed Whole Sale Price Index

Bombay Stock Exchange Sensex Index

• Continuous wavelet transformation

Index of Industrial Production

Kwiatkowski, Phillip, Schmidt and Shin

Log of Bombay Stock Exchange Sensex Index

Log of Exchange rate

Log of Index of Industrial Production

Log of Broad Money

log of Whole Sale Price Index

Broad Money

Reserve Bank of India

Whole Sale Price Index

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Acknowledgments

We thank the Editor of this Journal for all the help he extended and three anonymous referees for their useful comments and suggestions for the improvement of this paper.

The datasets used in the study were collected from BSE Sensex Index www.bseindia.com and Reverse Bank of India www.rbi.org.in

This study was not funded by any agencies, and we ensure that we have not received any grant to do this study.

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R. Gopinathan is presently an Assistant Professor in the School of Economics at Shri Mata Vaishno Devi University, India. S. Raja Sethu Durai is presently an Associate Professor in the School of Economics at University of Hyderabad, India. Both authors read and approved the final manuscript.

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Gopinathan, R., Durai, S.R.S. Stock market and macroeconomic variables: new evidence from India. Financ Innov 5 , 29 (2019). https://doi.org/10.1186/s40854-019-0145-1

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Received : 13 July 2018

Accepted : 17 June 2019

Published : 11 July 2019

DOI : https://doi.org/10.1186/s40854-019-0145-1

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Short-term impact of covid-19 on indian stock market.

1. Introduction

2. literature review, 3. data and methodology, 3.2. methodology, 3.2.1. constant mean return model, 3.2.2. market model, 3.2.3. market adjusted model, 4. results and discussions, 4.1. average abnormal returns from nifty50 index components, 4.2. impact of the pandemic in different sectors of the nifty50 index, 5. conclusions, author contributions, data availability statement, conflicts of interest.

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Varma, Y.; Venkataramani, R.; Kayal, P.; Maiti, M. Short-Term Impact of COVID-19 on Indian Stock Market. J. Risk Financial Manag. 2021 , 14 , 558. https://doi.org/10.3390/jrfm14110558

Varma Y, Venkataramani R, Kayal P, Maiti M. Short-Term Impact of COVID-19 on Indian Stock Market. Journal of Risk and Financial Management . 2021; 14(11):558. https://doi.org/10.3390/jrfm14110558

Varma, Yashraj, Renuka Venkataramani, Parthajit Kayal, and Moinak Maiti. 2021. "Short-Term Impact of COVID-19 on Indian Stock Market" Journal of Risk and Financial Management 14, no. 11: 558. https://doi.org/10.3390/jrfm14110558

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Compliance should be a low hum in the background: Sebi chief Madhabi Puri Buch

While speaking at the global fintech fest (gff) in mumbai, madhabi puri buch, in her first public appearance after the hindenburg allegations, said sebi aimed to make compliances easier so that focus can stay on doing business..

The Securities and Exchange Board of India (Sebi) chairperson, Madhabi Puri Buch, advocated automated and simplified compliance for ease of doing business in her first public appearance on Thursday after Hindenburg Research's conflict-of-interest allegations.

While speaking at the Global Fintech Fest (GFF) in Mumbai, Buch said India's capital markets regulator aimed to make compliances easier so that focus can stay on doing business. 

She said Sebi encourages automated compliance and ease of reporting so that companies can have real-time control over their operations. “If compliances are tangled, business is hard. Real-time controls within organizations and on reporting processes that are automated so that compliance becomes a low hum in the background. This is our ultimate objective."

Also Read: At Sebi, Madhabi Buch doesn't look at ICICI Securities , Blackstone matters

Minimal compliance burden.

She said for every entity Sebi was regulating, the aim was to cause minimal compliance burden. “It is like each of us is breathing, we do not have to think about breathing. There is an in and an out. The real capability of our entrepreneurs, industrialists and economy is focused on growing the country and delivering services to the citizens. Compliance should be a low hum in the background."

The Sebi chairperson, who delivered the keynote address on the role of fintech in ease of doing business, said ease of doing business consisted of the business itself and the accompanying compliances. 

Regulatory actions against a business, she clarified, depend on whether the business is benefiting investors or if it is something that is not in the investors’ long-term interest.

“If you are doing something that enhances the well-being of a consumer nine out of 10 times, the regulator will say yes. It will put some restrictions and monitor compliance, but it will say yes. But when the innovation treads the line where the investor is being shortchanged; there is opacity; there is lack of concern of what is happening to investor’s money, those with reasonable probabilities, the regulator will say no," she said.

Also Read: Sebi chair Madhabi Buch owns majority in consultancy named in Hindenburg report

Ai adoption.

Buch clarified that, as a regulator, Sebi was encouraging standardization for low-cost innovation and that it had a dozen projects using artificial intelligence (AI) to speed up approvals and supervision. “The adoption of technology has allowed far more extensive consultations."

For example, the paper on streamlining index derivatives framework received 6,000 comments, she said, adding: “Had we tried to do this manually, we would have died!"

The US-based short-seller Hindenburg Research alleged earlier this month that Sebi was unwilling to act on its January 2023 Adani report because Buch and her husband Dhaval Buch had investments in offshore funds that had links with the Adani Group.

The Sebi chief and her husband denied the allegations, terming them “baseless” and an attempted “character assassination”.

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Voith Paper Fabrics India, a smallcap company in the textile industry, has seen a significant increase in its stock price on August 28, 2024. The stock has gained 10.85%, outperforming the sector by 4.06%. The stock reached an intraday high of Rs 2849.95, showing a high volatility of 5.07% during the day. According to MarketsMOJO, a leading stock market analysis and recommendation platform, the current call for Voith Paper Fabrics India's stock is 'Hold'. This is based on the company's performance today, where it has outperformed the sector and its moving averages. The stock is currently trading higher than its 5-day, 20-day, 50-day, 100-day, and 200-day moving averages. In comparison to the Sensex, Voith Paper Fabrics India's stock has performed significantly better in the past 1 day and 1 month, with a 4.30% and 12.16% increase respectively. In contrast, the Sensex has only seen a 0.29% and 0.76% increase in the same time periods. This positive performance of Voith Paper Fabrics India's stock can be attributed to the company's strong presence in the textile industry and its consistent growth in the market. With its current stock price and performance, Voith Paper Fabrics India is a company to watch out for in the smallcap segment of the market.

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Sell signal flashing on copper stock

By  schaeffer's research, kitco commentaries opinions, ideas and markets talk.

Featuring views and opinions written by market professionals, not staff journalists.

Shares of copper miner Freeport-McMoRan Inc (NYSE:FCX) are 0.3% lower at $45.04 at last look, starting what could be a month-long trend as FCX trades near a historically bearish moving average

According to data from Schaeffer's Senior Quantitative Analyst Rocky White, FreePort-McMoRan stock just came within one standard deviation of its 50-day trendline. Per White, five similar pullbacks have occurred over the past three years. One month after 40% of these signals, FCX had negative returns, averaging a 3.9% drop. A similar move would put the shares just above the $43 level.

FCX Chart August 272024

This would also put Freeport-McMoran stock at risk of breeching its slim 5.9% year-to-date lead, and add to a 7.3% quarterly deficit. Also worth noting, FCX is on the brink of a third-straight monthly loss, so this historically bearish signal is bleeding into what could be another negative month.

A shift in analyst sentiment could also provide tailwinds. Of the 16 in coverage, 11 brokerage firms call the mining stock a "buy" or better.

For those looking to bet on FCX’s move lower, options seem to be affordably priced. The equity's Schaeffer's Volatility Index (SVI) of 33% ranks in the relatively low 20th percentile of its 12-month range, meaning options traders are pricing in low volatility expectations right now. 

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Schaeffer's Investment Research is a privately held publisher of stock and options trading recommendations headquartered in Cincinnati, Ohio. Founded by CEO Bernie Schaeffer in 1981, we're celebrating 39 years at the forefront of the thriving options industry. From our flagship Option Advisor newsletter to our expertly curated array of real-time trading services, we've got options for every investor.

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Whirlpool of India stock jumps 7%, hits 52-week high; up 86% in 6 months

Earlier in february, whirlpool mauritius limited, the promoters, had sold 30.4 million equity shares or 24 per cent stake of whirlpool india via open-market trade for $468 million to reduce debt.

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