CAUSALITY AND COINTEGRATION AMONG STOCK MARKET INDICES: A STUDY OF DEVELOPED MARKETS WITH SENSEX

The aim of this paper is to examine the existence of degree of interdependence between Sensex and various stock markets of the American and European regions. The study attempts to analyse the dynamic interactions among 22 global indices. The daily closing prices of indices were obtained from the respective stock exchange websites from January 2005 to May 2018. The normality, stationarity, and causality of the time series were evaluated in the first section using statistical techniques such as the Jarque-Bera statistic, ADF test, and Granger Causality test. The second part of the approach focused on analysing the interdependencies of various stock markets, determining the degree of association, and measuring market efficiency using techniques such as Johansen's Cointegration test, Cross-Correlation test, and Hurst Exponent. The results indicate that there is a significant amount of interdependence between stock markets. It was also observed that there is an association between markets. This study also found bi-directional as well as uni-directional causality among the stock market indices. The study found that interdependence of markets leads to improvements in short-term as well as long-term returns/gains for investors possibly due to international portfolio diversification if there are stronger co-movements of prices across the markets.


INTRODUCTION
stock market crash of October 1987, Asian Financial Crisis of 1997 and Global Financial Crisis of 2008 to cointegration and interlinkages of stock markets.
Normally, the long-term equilibrium relationship is specified by a bivariate cointegration relationship. In such relationship, the deviation from the equilibrium relationship is found to be stationary with a mean value of zero. It can be interpreted into an application, which can be assessed as a combination of two non-stationary series, which itself is stationary. According to (Engle & Granger, 1987), such bivariate series is considered to be cointegrated. Such bivariate relationship can be expanded to multivariate relationship. In such relationship, a deviation in the price factors from the long-term relationship can be created from grouping of all the time series. A change in the degree of cointegration among the factors/variables can explain the long-term relationship among global stock markets. This can be achieved through the comparison of cointegration relationship over various sub-sample periods. In this study, the multivariate approach of cointegration is adopted to investigate the cointegration of multiple countries.

LITERATURE REVIEW
Over the years, various researchers emphasising numerous cointegration parameters such as risk, return, volatility, and prices have conducted a number of studies. Darrat et al. (2000) investigated the integration of emerging stock markets in the Middle East and found numerous differences in trading patterns, especially in terms of market integration at the national level. Using a VAR model with multivariate GARCH, (Scheicher, 2001) observed cointegration between Eastern European and Western European markets and concluded that Eastern markets were more influenced by Western markets. Brooks and Del Negro (2004) argued that the international equity market has the lowest degree of correlation returns across national stock markets. After the financial crisis (Click & Plummer, 2005;Majid et al., 2009;Phuan et al., 2009) investigated stock market integration in ASEAN and found that cointegration of five ASEAN markets had not been completed in economic sense. (Mukherjee & Mishra, 2005) observed long-term cointegration among Indian stock market and other Asian stock markets. However, (Gupta & Guidi, 2012) found no evidence of cointegration between the Indian and Asian stock markets. According to the study, the long-term benefits of investing in India are extremely small. Another research (Chittedi, 2010) looked at the relationship between the stock markets of developed countries and the stock markets of India and noticed that they were not cointegrated. This is in line with the findings of Nath & Verma (2003), who found no cointegration between three South Asian stock markets: India, Taiwan, and Singapore. Bhunia and Das (2012) looked into the integration of financial markets in India and a few other South Asian countries. Authors observed no cointegration of the developed markets with the Indian stock market. Bhunia & Das (2012) looked into the integration of financial markets in India and a few other South Asian countries. Authors observed no cointegration of the developed markets with the Indian stock market. Joshi (2013) examined at the cointegration of BRIC stock indices and found that India and Russia had a long-term equilibrium relationship, but not with Brazil. (Patel, 2014) presented an investigation into the cointegration of Indian and Asian capital markets. The study revealed that stock indices from China, Sri Lanka, Singapore, and Japan influenced India's stock market. Bhattacharjee & Swaminathan (2016) examined at the stock market integration of India and a few other countries and observed that cointegration of the Indian market with other indices has strengthened over time because of liberalisation, and that during the slowdown; the Indian market was more open to Asian markets. Thalassinos & Thalassinos (2006) found that the establishment of the EMU had a major impact on European stock market integration as compared to other countries. They also concluded that there was a relation between bilateral import dependency and the degree of stock market integration. Wang and Moore (2008) analysed the stock market integration for the transition economies by using time-varying conditional correlation. Since joining the European Union, they found a very high degree of correlation. Chen amd Shen (2009) investigated the cointegration of stock markets in the United Kingdom, the United States, Japan, and Germany and found market integration. Chancharat (2009) used econometric techniques such as the cointegration test, factor analysis, and GARCH models to investigate the relationship between economic variables and stock market integration. Raju & Khanapuri (2009) investigated cointegration among Asian emerging stock markets and discovered a high degree of cointegration among the markets. According to Modi et al. (2010), the US market is the most influential. Baumöhl & Výrost (2010) examined at cointegration with non-synchronous trading effects using the granger causality test and found that there was no substantial lead-lag relationship of stock market integration in the pre-and post-crisis period. According to Yeoh et al. (2010), the Malaysian stock market has a higher degree of cointegration. Sharma and Seth (2012) used the Granger causality test and the Johnsen cointegration test to investigate market cointegration between Asian and US markets and observed short and long term cointegration. Mitra & Bhattacharjee (2015) found cointegration of the BSE with other markets. Using beta-convergence and sigma-convergence methods, (Babecký et al., 2013) investigated cointegration between Chinese and Russian stock markets. Birǎu & Trivedi, (2013) investigated emerging market stock market cointegration and contagion in the context of the global financial crisis. The instability in the financial sector has resulted in a significant drop in stock markets around the world. Down markets have higher levels of contemporaneous systematic risk and a higher market risk premium, according to Bhattacharya et al. (2020). Shahzad et al. (2016) used ARDL approach to investigate cointegration among stock markets and found the existence of cointegration. Okon (2018) aimed at the cointegration and causality of macroeconomic factors and terrorism in Nigeria and concluded that trade openness should be maintained and strategic macroeconomic policies should be implemented in order to develop the Nigerian economy. Kiviet and Chen (2018) reviewed the literature on the study of cointegration between stock price indices or realised returns at different markets and found a number of common methodological flaws, including omitted regressor problems, failing to check agreement of estimation outcomes with adopted model assumptions, and using specific statistical tests in inappropriate situations and, occasionally and lack of identification. Nautiyal and Kavidayal (2018) used VECM to analyse cross-country returns and cointegration of 11 stock indices from developed and developing countries. They detected a sluggish but significant price adjustment as well as stock market cointegration. On the Dhaka stock exchange, Golder et al. (2020) found a causal relationship between foreign exchange reserves, exchange rate, and index.

HYPOTHESIS DEVELOPMENT
H0 1 : Stock indices follow normally distribution. H0 2 : The time series are not stationary. (Dickey & Fuller, 1979, 1981 H0 3 : x(t) doesn't Granger-cause y(t). (There is no causal relationship between stock indices) The focus of the methodology's second section is on analysing stock market interdependencies, determining the degree of linkage, and examining market integration using various approaches such as Johansen's Cointegration test, Cross Correlation test, and Hurst Exponent. The trace test and the eigenvalue value were used in conjunction with Johansen's Cointegration test.
H0 4 : the number of cointegration vectors is r = r* < k (Null Hypothesis for trace test as well as eigenvalue test) H0 5 : cross-correlation is not significantly different from zero. H0 6 : stock price variations are independent.

METHOD Data Sources
The closing data of daily prices of several indices were obtained from the respective stock exchange websites from January 2005 to December 2018, for this study. The behaviour of SENSEX along with 21 stock indices from European and American markets are studied to investigate cointegration. The major stock indices of European markets (AEX, ATX, BEL20, BIST100, CAC40, DAX, FTSE100, IBEX, OMX, OSE ALL SHARE, RTSI, SMI and STOXX50) and stock indices of American market (DJIA, GSPC, IBOVESPA, IPC, MERVAL, NASDAQ, NYSE and S&P TSX) were selected for this study along with Indian stock market index (SENSEX).

Methodology
A two-stage technique was used in this investigation. The normality, stationarity, and causality of the time series were verified in the first section using statistical techniques such as the Jarque-Bera Statistic, ADF Test, and Granger Causality Test. Cointegration analysis, cross-correlation analysis, and Hurst Exponent analysis are all included in the second section.

Descriptive Statistics
The descriptive statistics show that the mean daily returns of the majority of the indices in the sample were positive, however the SENSEX index had the highest returns (0.06) among all the indices, followed by the IPC index, and the OSE index had the lowest (-0.02) among all. Statistics on the standard deviation of daily returns in emerging markets show that these markets are more volatile. In general, developed market returns are less volatile than emerging market returns, with a lower standard deviation. However, the standard deviation of US DJIA (4.71) is highest, while the Australian market has the lowest level of volatility in the developed market sample. Emerging market skewness values, such as Russia's, have an asymmetrical distribution with a long tail to the left, whereas India's condition is close to zero and has merely an asymmetrical distribution. The US stock market has a symmetric distribution around the average value in developed markets. Other established markets, such as the United Kingdom exhibits left skewed distribution. All of the stock market Kurtosis values in this study are greater than three, indicating a leptokurtic curve. These findings are consistent with (Harvey, 1995), (Bekaert et al., 1998). The use of a sub-optimal mean-variance criterion in portfolio construction can result in significant opportunity cost for risk-averse investors. The ADF test was used to determine that the variables are stationary or not. All the time series was found stationary at 1 st difference.

Test for Causality
Granger causality test was performed to examine the causal relationship among these markets. Since cointegration at any level exists, the Granger causality testing is appropriate for bilateral pairs of markets. As (Granger, 1988) pointed out, if two variables are cointegrated, causality must exist at least unidirectional.
The granger causality test was conducted by dividing the data into 3 sub-periods (Period 1: 2005(Period 1: -2009Period 2: 2010Period 2: -2014Period 3: 2015Period 3: -2018. The causality of most of the indices remained consistent across all sub-periods. However, in the case of several indices, causality was found in one subperiod (either bi-directional or uni-directional) but not in another sub-period. In a few situations, causality between two indices was uni-directional for one sub-period, bi-directional for another sub-period, and there was no causality between those two indices for the third sub-period. This resulted in a fascinating shift in trend during the short-term Granger causality results. These results for each of the sub-period are shown in the Appendix A and B. These appendices show the results of bi-directional or uni-directional causality of an index with other indices for the long-term i.e. for the entire duration of the study. These long-term results are the combination of all short-term results, which include bi-directional and unidirectional causality of an index with other indices, as well as the bi-directional and uni-directional causality of an index with other indices, which were found in all three sub-periods listed below. For example, the ATX index causes 12 indices from 2005 to 2009, 13 from 2010 to 2014, and 11 from 2015 to 2018.

Cointegration Test
The efficient maximum likelihood test (Johansen, 1988(Johansen, , 1991(Johansen, , 1995 was employed to look for a longterm association between indices. A Johansen model with a linear trend in level and intercept in the cointegrating equations was utilised (CE). Because we have trending series with stochastic trends, this version was found to be more appropriate for our data. The test was carried out with a VAR model that had a lag duration specified by AIC and Akaike's Final Prediction Error (FPE). The eigenvalue and trace statistics values are used to calculate the cointegration rank (r).
Maximum likelihood estimators of the cointegrating vectors for an autoregressive process were derived by Johansen (1988) and Johansen & Juselius (1990) by considering the following equation.
VAR model can be estimated at first level difference i.e. 1(1) as majority of time series variables are non-stationary at level 1(0). The above-mentioned equation (1) of Johansen and Juselius (1990) can be represented by introducing first level difference operator as follows: Π Matrix can be used to trace cointegration. First level difference i.e. 1(1) might be preferred when all Xt value are found to have unit roots which can be determined if p x p matrix Π has rank 0.
Cointegration between the SENSEX and other indices is shown in Table 2. Because the trace statistic at r=o was higher than the critical value of 5%, the null hypothesis of no cointegration was rejected. The result implied that there was at most one cointegrating equation between the two variables. The results of the OSE and IPC cointegration test were consistent with the correlation analysis, which found that the relationship between the two stock markets' movements was substantially positive.
At the 5% significance level, trace statistics and Eigen value statistics revealed one cointegrating vector among the markets, as shown in table 2. Because the trace statistic exceeds the 5% critical value, the null hypothesis of no cointegrating vectors can be rejected, indicating that one or more cointegrating equations exist.

Cross Correlation and Serial Correlation
Portfolio managers use correlation as one of the simplest but most often used methods in making asset allocation decisions. The measure of strength or degree of linear relationship between two variables is the focus of correlation analysis. The correlation structure of stock market returns provides an initial indication of stock market interconnections. Stock markets with high correlation coefficients can be perceived as having strong connections. Low correlation, on the other hand, demonstrates the stock market's separation property and, as a result, the possibility of risk diversification. Furthermore, markets in the same region are more correlated since they are more susceptible to being influenced by regional news and developments, as well as trade and economic linkages. The correlation structure of emerging and mature markets was investigated to see if there was any preliminary evidence of potential diversification benefits in the region. The existence of timing differences between emerging stock markets and select developed stock markets, particularly for the US stock market, is one of the procedural difficulties to be handled in the context of the log return correlation matrix in the table. The remaining markets in the sample interact with one another in a single day, and all of the emerging markets under consideration operate in the same time zone. As a result, the contemporaneous correlation between the US market and the selected markets is of little significance. As a result, the correlation matrix is calculated using one-day lagged returns for the US market. Throughout the investigation, the same technique is used for subsequent examination of return data.
The examination of correlation structure of log returns from Table 3, 4 and 5 gives following important findings Emerging market stock markets have a mixed correlation coefficient with each other and with a few developed stock markets. At the same time, it is worth noting that for the whole sample period, emerging equity markets exhibit low correlation coefficients (less than 0.50). Russia's stock market has a strong correlation coefficient with developed stock markets such as the United Kingdom and the United States, as well as a positive correlation with India.
With respect to the Indian stock market, the lowest correlation coefficients are with the German (European) stock market, and India has no negative correlation with any index. With emerging market Russia, followed by India, the developed US stock market has a positive correlation coefficient.
Sensex is positively correlated with all the indices. It indicates that Sensex, BIST100, SMI and DAX indices following the same trend. There is low positive correlation exist between Sensex and BIST100, SMI and DAX.
In the case of developed countries, the majority of the lags values are positive, indicating a positive correlation between the stock returns of Germany and the stock returns of the United States. The stock returns in Germany and the United States are clearly going in lockstep. We can claim that the stock return in Germany is influenced by the stock return in the United States. In the instance of the UK cross correlation test, seven out of eleven lags are positive, indicating a positive connection between the UK and US stock markets. The UK stock market and the US stock market are clearly moving in tandem. We can say that the UK stock market dependent on US stock market. France and Italy's cross-correlation data demonstrate that there are mainly positive lags values, indicating a positive connection with US market returns. The stock markets in France and Italy are clearly moving in unison with the stock markets in the United States. To examine if there is a problem of serial correlation, the Durbin Watson statistics of the model is 2.14, which infers that there is no problem of serial correlation. Regression is spurious if the residual of the regression is auto-correlated i.e. they are not stationary at level. Autocorrelation among residuals is checked using correlogram of residuals and unit root test; estimates of Q-statistics are statistically insignificant for all 36 lags. This means the null hypothesis of no autocorrelation cannot be rejected. Furthermore, the residuals are also stationary. This finding implies the existence of a long-run equilibrium relationship among the variables. In this case, OLS estimation is consistent, and there is no problem of spurious regression.

Hurst Exponent Analysis
The independence of stock price changes is a fundamental assumption in quantitative finance theories. Brownian motion can be used to demonstrate such changes. Hurst exponent analysis is used to test for independence in time series data for this purpose. Hurst exponent value of 0.5 explains that the time series is independent. Predetermined Brownian motion data, on the other hand, will yield a Hurst exponent value that can be greater or lower than 0.5. In the absence of a suitable test, such a value could be misinterpreted as evidence of long-term memory.
Based on the Hurst exponent value H, a time series can be classified into three categories.
Mean-reversion is an attribute of a time series, which is anti-persistent. The term "meanreversion" refers to the movement of a previous value in the opposite direction. In the case of the Hurst Exponent, the property of mean-reversion improves as H approaches 0. A persistent time series, on the other hand, reinforces the previous value trend. When the value of H approaches 1, the consistency of the trend improves. When the Hurst exponent value is greater than 0.5, the majority of the time series are determined to be persistent.  Table 6 shows that 16 of the 22 indices in the sample follow the persistence trend, 3 indices follow the random trend, and the other 3 indices follow the anti-persistence trend. An increase in values in a persistent time-series will very certainly be followed by another increase in the near term, and a reduction in values will almost certainly be followed by another reduction in the near term. Random trend means there is no correlation between observations and future observations. Series of this kind is very difficult to predict. In anti-persistence trend, an increase will most likely be followed by a decrease and vice versa. This means that future numbers will tend to converge around a long-term average.

CONCLUSION
The research examined at the co-integration of 22 stock indices from around the world. The cointegration test was used to investigate stock market interdependencies and dynamic interactions, and it was found that co-integration exists between the Indian Stock Market (Sensex) and other indexes.
The null hypothesis of no co-integration was rejected since the trace statistic was higher than the crucial value of 5%. The result implied that there was at most one co-integrating equation between the two variables. Multiple equations based on the VAR model were used to conduct a co-integration test for a group of 22 stock exchanges in order to evaluate market integration as a whole. Trace statistics indicated at least one co-integrating vector at the 5 percent significance level among the markets.
This study also ascertained the degree of association between developed and emerging markets. Cross correlation was used to ascertain the association and found that out of 22 indices, there were 15 indices who were highly correlated with one or more indices. Two indices exhibited a high degree of anti-correlation, whereas the other three had a low degree of anti-correlation. The correlation analysis revealed that there was a strong positive association between the two stock markets' movements. The stock market indexes were also found to have bi-directional and uni-directional causality in this study. According to the Hurst Exponent analysis, 16 of the 22 indices in the sample follow a persistence trend, three indices follow a random trend, and the other three indices follow an anti-persistence trend.

RESEARCH IMPLICATIONS
This study contributes in the following ways. First, co-integration can be considered companionable to the perception of integration of financial markets. This embraces homogeneity in investment avenues, allowing stockholders from many markets to invest in a diverse selection of securities. Because the returns from multiple stock markets are not perfectly correlated, cointegration among stock indexes shows that increased returns from international diversification are conceivable. Institutional and overseas investors can profit from the diversification benefits of markets with low correlation. As a result, investors that diversify their portfolio across multiple countries can increase the portfolio's expected return while lowering its risk. This study can help FIIs and private investors to fathom the correlation structure and interdependence of global stock indices, allowing them to diversify their portfolios more effectively.
Further, these results are recommended to policymakers, regulators and researchers on the one hand and firms' managers as well as investors on the other. FIIs, HNIs, individual, institutional and public investors can make decisions regarding their investments based on co-integration among the markets, which may be of short as well as long-run. These results provide insights to the investors for portfolio diversification, which can help, reduce the diversifiable risk of the portfolio.

LIMITATIONS OF THE STUDY
This research is based on secondary data from stock market indices using daily closing prices. The weekly and monthly prices, which might be used for further analysis such as seasonality in stock indices, are not included in this study.
The existence of a temporal difference or difference in trading hours between emerging stock markets and select developed stock markets, particularly the US stock market, is one of the procedural difficulties to be handled in the context of log return correlation matrix. The study also has a disadvantage in that it does not address event-specific co-integration.

SCOPE FOR FURTHER RESEARCH
The study has a deeper research focus. Regression analysis can be used to investigate each market's dependence on other markets. The analysis of dependency can assist in making better financial decisions. The impact of market volatility can also be studied.