Analyzing time-different connectedness among systemic financial markets during the financial crisis and conventional era: New evidence from the VARX-DCC-MEGARCH model

ABSTRACT This investigation utilized the VARX-DCC-MEGARCH model assimilated with skewed-t density to analyze the time-different (i.e., daytime, overnight, and daily) connectedness among S&P 500, DAX 30, FTSE-100, Nikkei 225, and Shanghai Composite Index. This investigation discovered that the current daytime returns transmission from the DAX 30, FTSE 100, and Nikkei 225 index to ensuing overnight returns of the S&P 500 index was inconsequential during the stable period. The study also quantified that shocks befallen in the current overnight returns of the S&P 500 partake bidirectional and negative ties with shocks that occurred in subsequent day-wise returns of the DAX 30 index. Moreover, during crises, only the Shanghai composite index spillovers the volatility of the FTSE 100 index. The study revealed a leverage effect for the day-wise return of the S&P 500, DAX 30, and overnight returns of the FTSE 100 index.


Introduction
The mounting trend of globalization and liberalization has transformed whole nations into one economy, instigating the integration of financial markets among the nations (Shehzad, Liu, et al., 2021).Besides, Information and Communication Technology (ICT) has played a vital role in connecting people worldwide.Notably, digital apps like bloom berg, yahoo finance, Merril Edge, Charles Schwab, and TD Ameritrade offer opportunities to financiers of any nation to register and buy stocks online at any time in the world (Rosenberg, 2020).So, on account of advanced ICT and globalization, a piece of economic news, political news, industry-specific news, or any other good or abysmal news related to financial markets occurring in any part of the globe would directly impinge on the prices of financial assets at the national level and worldwide (Bala & Takimoto, 2017).Consequently, high vacillations in the asset returns may intensify the financial risk, leading to financial calamities in the markets.In a similar vein, the history of financial markets demonstrates that economic crises, CONTACT Khurram Shehzad khurramscholar64@hotmail.com; 233189917@seu.edu.cnSchool of Economics and Management, Southeast University, Building 9, Juyuan, Jiulonghu Campus, Nanjing, China such as sovereign debt crises (1982), stock market crashes (1987), Mexican crises (1994), Asian crises (1997)(1998), Russian debt crises (1998), Greek debt crises (2009), and global financial crises (GFC) (2007)(2008)(2009), had a significant impact on the stability of the global financial system (Shehzad et al., 2020).Jonathan Law (2008) argued that systemic risk was the vital motive of GFC.Thus, the study regarding the assimilation of financial markets and the reckoning of financial risk has grown into an indispensable subject and seized the attention of policymakers, academicians, and finance managers (Shehzad, Bilgili, et al., 2021).
Numerous studies (Berkowitz & O'Brien, 2002;McNeil & Frey, 2000;MKP & PLH, 2006) employed univariate GARCH models to discover the volatilities.Given that, to deal with multiple asset returns in a portfolio, a multivariate version of the GARCH model is suitable to evaluate the volatility pattern.Likewise, several multivariate GARCH models have been instituted to quantify the conditional variance and covariance of financial assets, i.e., GO-GARCH, BEKK-GARCH, and CCC-GARCH models (for more detail on MGARCH models, see (Ghalanos, 2015;Silvennoinen & Teräsvirta, 2009).This investigation utilized the Dynamic Conditional Correlation (DCC) Multivariate Exponential Generalized Autoregressive Conditional Heteroskedasticity (MEGARCH) model (Nelson, 1991;R. Engle, 2002), merged with a robust version of the Vector Autoregressive with exogenous instruments (VARX) model.The DCC model cogitates the time-varying correlation between the factors and can manage the vast extent of matrices (Ahmad et al., 2013).Besides, the MEGARCH model can figure out the asymmetric effect (Shehzad, Liu, et al., 2021).Furthermore, a good volatility model not only considers the nature of tail distribution appropriately but can also handle many assets (Malz, 2011).Countless studies have been conducted to define the transmission of the returns and shock spillover among developed, emerging, and under-developing nations (e.g., Ali & Afzal, 2012;BenSaïda et al., 2018a;Jebran & Iqbal, 2016;Li, 2007;Sikhosana & Aye, 2018).However, prior studies do not ponder the time difference to determine the transmission of returns, shock spillover, and portfolio VaR among the financial markets.The actual examination used data from the FTSE 100, S&P 500, Nikkei 225, DAX 30, and Shanghai Composite index (SSEC) to determine the nominations for the United Kingdom, United States, Japan, Germany, and Chinese stock markets, respectively.Figure 1 exhibits the time dissimilarity of each nation with other nations.According to Greenwich Mean Time (GMT), the financial sun arises from London (UK), which is 5 h ahead of the US.Though Japan, China, and Germany are 14 h, 13 h, and 6 h ahead of the US, respectively.The plots displayed that Japan is 1 h ahead of China, 8 h ahead of Germany, and 9 h ahead of London.In comparison, China unveiled 7 h difference from Germany and 8 h from London.In the end, Germany designates a 1 h difference from London.Thus, the stockholders of one's market are aware of the returns of other markets.Given the time difference between the closing of one market and the opening of another market may provide profitable trading occasions.This phenomenon presents the importance of choosing these stock markets.Moreover, these markets are known as the most developed markets and substantiate a considerable portion of the world's financial market capitalization (Bayoumi & Bui, 2012).Also, Belke and Dubova (2017) referred to the equity and bond markets of the US, Europe, the UK, and Japan as systemic financial markets.Furthermore, these stock markets also have prominence because the currency of these countries is listed in the Currency Basket. 1 of International Monetary Fund (International Monetary Fund, 2016), and acute fluxes befallen in these markets can harm the world's economy.Consequently, it turns essential to understand the financial risk pattern of these markets during and after the GFC era.So, effective policies can be generated, and any financial calamities in the future can be managed efficiently and timely.
The critical contribution of this investigation is to scrutinize the time-different pattern of returns and volatility linkages among DAX 30, S&P 500, Nikkei 225, SSEC, and FTSE 100 index so that it can be determined which markets are significant transmitters and receivers of risk, and whose returns have a bidirectional, unidirectional, positive, and negative association with other markets.Combining these markets should bring superfluous understandings into financial management research.This research also recognized the summary and plots of time-varying correlation among these markets.Besides, it enlightened the role of global oil prices for return changes in these stock markets.The general research questions of this investigation are as follows.First, does the return transmission of these equity markets show any directional configuration, and can timedifferent return transmission offer profitable opportunities?Second, what is the nature of time-different shock spillovers among these markets?Third, how differently do return transmission and shock spillover behave during financial crises compared to stable periods?Fourth, is financial risk diversification possible within these equity markets?Fifth, does the time-varying correlation of a stable period differ from GFC? Finally, what 1 A currency basket contains different currencies with specific weights.These currencies are used to determine the market value of other currencies.The currency basket of IMF includes five currencies, i.e., the US dollar, Japanese Yen, Euro, Chinese RMB, and British Pound.
insinuations can be derived from this analysis, especially to understand the financial risk pattern of these stocks?After answering these questions, we aim to extend our knowledge about these markets' time-different financial risk patterns.
According to the author's best knowledge, no existing investigation has employed this strategy to evaluate these markets' returns transmission, volatility spillovers, and portfolio VaR.The analysis of this study will offer essential policy suggestions for investors, policy builders, finance managers, and portfolio managers.The rest of this article is structured as follows.Section 2 confers the enhanced literature review, section 3 refers to the superior and comprehensive data and methodology of this investigation, section 5 gives an interpretation and detailed discussion of results, and section 6 expresses the conclusion, policy implications, and future recommendations.Finally, the references used in this study are given in section 6.

Literature review
One of the critical concerns in financial markets is the notion of financial risk due to information spillovers.Numerous essential studies related to the financial market's risk and their dependence on each other have been reviewed in this study.For example, Aumeboonsuke (2019) identified that co-movements among equity markets upsurge financial instability.The outcomes of the vector error correction model recommend that returns of US and UK stock markets have some degree of sway on ASEAN markets.However, investment in ASEAN markets provides a healthier mean-variance portfolio.The study of Natarajan et al. (2014) stated that mean returns of the US meaningfully transfer to Australia and Germany.The analysis also found high volatility persistence for these markets.Furthermore, Jawadi et al. (2015) found weak evidence of volatility transmission between European and US markets, while through the post crises period, the inspection recorded bidirectional volatility spillover and returns transmission impact between US and European equity markets.Yoon et al. (2019) stated that the US is a major contributor to the transmission of returns, and financial crises intensify the spillover effects among financial markets.Y. Wang et al. (2018) argued that GARCH models present poor out-of-sample forecast results.The study used an in-sample strategy to gauge the stock markets of Canada, Japan, Germany, the US, and the UK and revealed noteworthy volatility spillover evidence from the US to other nations.Additionally, Belke and Dubova (2017) analyzed volatility transmission among equity and bond markets of the US, Europe, the UK, and Japan.The investigation indicated that these nations' equity and bond markets highly accompany each other.Further, Sarwar et al. (2019) exploited daily data from SSEC, the Nikkei index, the Bombay stock exchange, and the oil market.The investigation publicized that oil returns and Nikkei index returns have a bidirectional spillover relationship.The study suggested that investors should choose more equity markets than oil assets to gain more profit.
Indeed, BenSaïda et al. (2018b) examined volatility spillover impact across financial markets for GFC and tranquillity.The examination discovered that during the GFC, directional volatility spillovers grow into highly intensive and vary among net risk transmission and net risk receivers, while during the standard period, it showed a moderate impact.Moreover, Lien et al. (2018) questioned the shock spillovers among East Asian and US equity markets during the period of US subprime credit crises and Asian currency crises.The consequences revealed a unidirectional shock spillover effect from the US to East Asian markets during both periods.However, Yarovaya et al. (2016) Stated that financial markets are highly vulnerable to local and region-specific volatility.Likewise, Smolović et al. (2017) evaluated different GARCH models using the daily returns of the Montenegrin stock market index.The study made known that ARMA (1, 2)-TS-GARCH (1, 1), ARMA (1, 2)-T-GARCH (1, 1), and ARMA (1, 2)-EGARCH (1, 1) combined with student-t distribution and Johansen distribution has accepted the Christoffersen test at 95% confidence level.Additionally, Louzis et al. (2011) utilized the fully parametric approach and mentioned that GARCH and realized volatility models united through filtered historical simulation and extreme value theory methods guesstimate superior VaR during the GFC.The study also stated that skewed student distribution is a good alternative when high market fluctuations.
This recent literature review exposed that, according to many studies, shocks significantly impact the stability of other markets.It designates the importance of unveiling the world's largest stock markets' behavior.Moreover, the literature showed that no investigation had considered the time difference among the US, Japan, China, Germany, and the UK stock markets to capture returns transmission and volatility spillover effects.Additionally, we could not find a study that employed the VARX-DCC-GARCH model combined with skewed-t density to evaluate the volatilities.Therefore, to fill the gap, this research ponders the difference between these stock markets' opening and closing times and evaluates the returns transmission and volatility spillover during and after the GFC period.

Data
This study has employed daily data from five stock markets of reformist economies, e.g., S&P 500 (US), Nikkei 225 (JAPAN), DAX 30 (Germany), SSEC (China), and FTSE 100 (UK).This investigation has utilized the data from 2007 to 2019 and divided it into two panels, i.e., panel A from 4 January 2010 to 27 November 2019, which epitomizes the regular period, and panel B from 4 January 2007 to 31 December 2009, which represents the GFC.The study also includes the impact of crude oil prices as an exogenous factor, and all the data is occupied from the database of yahoo finance and US Energy Information and Administration.

Methodology
The examination has premeditated the daily returns by following the methodology of Bhuyan et al. (2016) as follows, Moreover, this examination has alienated daily returns into overnight returns and daywise returns as follows,  (Nelson, 1991;R. Engle, 2002) with the combination of a robust version of Vector Autoregressive incorporated with exogenous variable (VARX) model (Croux & Joossens, 2008).The VARX-DCC-MEGARCH model has plentiful qualities as compared to standard GARCH models.The GARCH model only ruminates the magnitude of stock returns to compute future volatility, and an increase or decrease in stock returns is ignored.Whereas the MEGARCH model assumes a parametric approach for conditional heteroskedasticity.Moreover, the GARCH model placed some constraints on parameters despoiled by estimated coefficients and confines the procedure of conditional variance.Also, in the GARHC model, it is hard to ensure that shocks to conditional volatility persist or not (Nelson, 1991).However, the MEGARCH model can handle asymmetric volatility shocks as it does not impose non-negativity constraints on parameters (Shehzad, Liu, et al., 2021).Financial risk analysis and asset allocation mainly rely on correlations among financial assets, requiring many correlation series (BenSaïda et al., 2018a).Further, building an optimal portfolio with maximum return and minimum variance needs forecasting of the covariance matrix of asset returns, and it is also needed to determine the standard deviation of a portfolio.The DCC GARCH model estimates the covariance matrix and conditional correlation directly.Moreover, the number of factors to be evaluated in the correlation procedure is not dependent on the number of series.Consequently, calculating the copious quantity of correlation matrices becomes possible (R.Engle, 2002).

Weighing up of the VARX model
This investigation employed a robust version of the VAR model by utilizing the Multivariate Least Trimmed Square (MLTS) estimator.Hence, by way of (Croux & Joossens, 2008), we postulate VARs with one lag for both periods as (Liu et al., 2022); Here, in the mean model Eq. ( 4), r i;t denotes assets return series i at time t, and w i;0 nominates the constant term of series i at time t.However, when i�0 then w i;j nominates the coefficient that quantifies the transmission impact of financial asset return series j to i.However, when i = j, it calculates the lagged impact of its own returns on the succeeding value.Furthermore, v i:t indicates the error term of series i at time t, and n represents the number of variables included in the study, i.e., n = 10.

DCC-MEGARCH model
; for i ¼ 1; . . .; n: (5) Similarly, in the variance equation Eq. ( 5), σ 2 i;t signifies the conditional variance of series i at time t.Additionally, μ i symbolizes the constant term of variance series i, and when i �j, n i,j is the factor that delineates risk transmission impact from financial asset series j to i. Nonetheless, when i = j, n i,j represents the ARCH coefficient that reckons the impact of shocks in returns on its own variance series i at time t + 1.Moreover, δ i and @ j determine the impact of changes in the volatility of its own variance series i at time t + 1, i.e., GARCH effect, and asymmetry impact of return series j, i.e., leverage effect, respectively.Moreover, DCC incorporated with a skewed-t density model delivers enriched findings (Bala & Takimoto, 2017).By following (Bauwens & Laurent, 2005), this study considers the multivariate skewed-t student distribution as follows, and here in Eq. ( 6)-( 11), m i and s 2 i are not the further factors, but these are functions of υandψ, and υ symbolizes the asymmetric/skewness parameter vector of series i.While ψ and n denote the degree of freedom and number of variables involved in the model, respectively.Moreover, s i stands for standard deviation, and m i is the mean value of series i. Besides, whenlnυ i > 0, it is called right skewness, but when lnυ i < 0, it nominates the left skewness of the distribution of series i (Bauwens & Laurent, 2005).This study follows the methodology of (R. Engle, 2002) to model the DCC as follows, where H t denotes the k � k covariance matrix and conditional volatility, and < t stands for the conditional correlation matrix among the financial return series.Whereas = t designates the diagonal standard deviation matrix.
here; ϕ t Can also be outlined as; where ϕ is the k � k correlation matrix of standardized residuals, and z t is the k � 1 vector of standardized residuals.Further, the DCC factors ω and # are supposed to have positive values whose sum does not increase from unity.Hence, the time-varying DCC matrix can be computed as follows; C ij;t ¼ ς i;j;t; ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ς i;i;t ς j;j;t p (17)

Results and discussions
Table 1 belongs to the descriptive statistics for both categories evaluated in this investigation.The outcomes showed that in the course of GFC, most indices showed negative mean returns except LSEDR and SSEDR, with high standard deviation values.The study showed that skewness values of all the variables are negative except LSEDR and OIL, while during the GFC period, DAXDR, LSEDR, SSENR, and OIL showed positive skewness.Further, the kurtosis values of all the variables for both categories are more than usual, which implies that there are high chances of tremendous earnings or loss (Shehzad, Xiaoxing, et al., 2021).This investigation applied the Augmented Dickey-Fuller (ADF) test (Dickey & Fuller, 1979), and found that all the indices are stationary at the level for both sets.Moreover, the examination employed ARCH LM (R. F. Engle, 1982) test, and the Ljung-Box test, and discovered that variables have a strong ARCH effect and serial correlation for both ages, respectively.Also, Figure 2 provides evidence of volatility clustering in the data.
Table 4 defines the outcomes of Eq. 5.The study found that intercept (μ) values of all stock returns are significant except DAXNR, DAXDR, and LSEDR, which reveals that mean values are different from zero.The domino effect displayed that the volatility of SPNR has a bidirectional and negative impression on the variance of DAXDR and NKNR; also, the volatility of NKDR has a negative and bidirectional risk spillover relationship with LSENR's impulsiveness.Besides, risk spillover from DAXNR (n1, 3) and NKDR (n1, 10) significantly sways the volatility of SPNR.While the volatility of SPNR (n2, 1) and NKDR (n2, 10) showed negative, the volatility of SSEDR exerts a positive influence on the fluctuations of SPDR.The upshots quantified that risk spillover of DAXNR (n4, 3), LSENR (n4, 5), and NKNR (n4, 9) negatively deviates the variability of DAXDR.Additionally, the shocks figured through the standardized residuals of DAXDR (n2, 4), LSENR (n2, 5), and LSEDR (n2, 6) significantly spillover the instability of SPDR.The GARCH (δ1-δ10) elements of all the stock returns are significantly positive and near to unity, which indicates that the shock effect persists for long-term periods in these markets, except LSEDR, which confirms fair value, i.e., 0.762.These results are in line with the study of (Natarajan et al., 2014) and (Dedi & Yavas, 2016).Further, the positive and significant gamma coefficient for all markets signifies the symmetric impact for these markets during a stable period.Moon and Yu    (2010) discovered the symmetric spillover effect from Chinese markets to the US.Further, (P.Wang & Wang, 2010) reported the symmetric effect for Japan and the US.
As well, the statistically significant and positive ARCH coefficient of DAXNR (n3, 3), LSENR (n5, 5), SSEDR (n8, 8), NKNR (n9, 9), and NKDR (n10, 10) stipulates that shocks determined through standardized residuals increased the conditional volatility of their own returns in the following day.Besides, the sum of assessed DCC coefficients ω and ϑ is significantly positive and less than unity, which verifies that our model is mean-reverting.This study seized the negative skewness of DAXDR, SSENR, and NKNR.Moreover, the degree of freedom parameter is moderate and significant, which means this assignment has successfully apprehended the actual fat-tailed returns distribution of these stock markets.(Li, 2007) and (Moon & Yu, 2010) captured the positive skewness values for the US and Chinese stock markets.
Table 5 pageants the fallouts of the variance equation for the period of GFC.The study used the MEGARCH (2, 1) model based on the Akaike information criterion for the period of GFC. 2he findings stated that shocks befallen in DAXDR have negative and bidirectional spillover liaison with the variance of SPNR.Likewise, the volatility of LSEDR (n1, 6) and SSENR (n1, 7) significantly amplifies the instability of SPNR.Also, the risk ascended due to DAXDR (n2, 4), LSENR (n2, 5), and LSEDR (n2, 6), significantly moving the volatility of SPDR in an upward direction.Also, the shocks that occurred in SSEDR showed significant bonding with the conditional variance of LSENR (n5, 8) and LSEDR (n6, 8).However, the volatility of DAXNR (n8, 3) and DAXDR (n8, 4) have positive and significant impacts on the variance uncertainty of SSEDR.The investigation explored that the volatility of NKNR significantly spillovers the volatility of DAXNR (n3, 9) and SSENR (n7, 9).At the same time, the variance changes of SPNR have a positive liaison with the variance change of LSENR (n5, 1).Further, the volatility of SSEDR showed a negative connection with the volatility of NKNR (n9, 8).The coefficients (δ1 to δ10) indicated that these markets have a significant GARCH effect, meaning that previous volatility has a striking impact on the present-day volatility of personal returns.The significant ARCH elements of SPNR (n1, 1), DAXDR (n4, 4), SSENR (n7, 7), SSEDR (n8, 8), and NKNR (n9, 9) enunciate that the shocks figured by standardized residual significantly upset the volatility of their own returns in the subsequent period ( (Mohammadi & Tan, 2015)).Furthermore, significant and negative first-moment gamma parameters of SPDR (∂2a), DAXDR (∂4a), and LSENR (∂5a) implied that adverse shocks have more influence on the volatility of these stock returns as compared to positive shocks of the same magnitude, concluding that the influence is asymmetric and leverage impact exists for these stock returns (R. F. Engle & Patton, 2001).Hence, these results indicated that lousy news affects more during financial crises than good news.The returns distribution of SPDR (υ2), DAXNR (υ3), LSEDR (υ6), NKNR (υ9), and NKDR (υ10) possessed negative and significant skewness, and others showed positive skewness.Bekiros (2014) mentioned both positive and negative skewness of DAX 30 during different periods.The degree of freedom parameters (ψ1 to ψ10) are significant and earned an adequate value range from 2.76 to 16.02.Significant DCC parameter ω definite that the current volatility of returns has an essential influence on the dynamic association amongst these markets.The crucial value of parameter # is also adjacent to unity, signifying that the dynamic tie concerning these markets would lengthen for an elongated term period (Jiang et al., 2019).

Time-varying correlation elucidation
Tables 6 and 7 demonstrate the correlation results for the standard and GFC periods, respectively.The end of the standard period stated that SPNR has a positive correlation with all stock returns, whereas SPDR showed a negative affiliation with SSENR.Also, the correlation of DAXDR with DAXNR, SSENR, SSEDR, and NKNR was noted as unfavorable.Although LSENR had a positive correlation with all stock returns, and LSEDR revealed a negative association with SSENR and NKNR.The correlation results during the GFC period specified that SPNR maintained a positive correlation with all stock returns.Moreover, DAXDR has a positive association with DAXNR, SSEDR, and NKNR, but during the standard period, it exposed a negative relationship with these stock returns.Also, the correlation between LSEDR and NKNR turns out to be positive, whereas, in the course of a stabled era, it displayed negative affiliation with each other.Besides, NKDR possessed a positive linkage with all stock returns.Figure 3a, 3b, 3c exhibited the time-varying correlation among these stock reruns for panel A. The upshots highlighted that the correlation of SPNR with DAXNR, DAXDR, SSENR, SSEDR, and NKDR is positive over the period.Nonetheless, the correlation between SPNR and NKNR goes negative at the beginning of 2014.Moreover, the correlation pattern between LSENR and SPNR is expressively different from the correlation pattern between LSEDR and SPNR.Furthermore, the correlation between SPDR and DAXNR reached a maximum value of 0.30, and the correlation between SPDR and DAXDR attained a maximum value of 0.60.Further, the correlation between SPDR and LSENR is less strong than the correlation between SPDR and LSEDR.The correlation of SPDR has gone negative with SSENR, SSEDR, and NKNR but remains positive with NKDR.The outcomes about the correlation history of DAXNR discovered that it has a positive liaison with LSENR, SSENR, SSEDR, NKNR, and NKDR, but it went negative with LSEDR during the year 2012.Additionally, the correlation of DAXDR with SSENR, SSEDR, and NKNR persisted negative for most of the periods.In contrast, the correlation of LSENR with SSENR, SSEDR, NKNR, and NKDR sustained positive.However, the correlation between LSEDR and SSENR becomes negative in the end.Nonetheless, the correlation between LSEDR and NKDR remained positive during the whole time.Also, the correlation of SSENR with NKNR and NKDR and SSEDR with NKDR was positive.However, the correlation between SSEDR and NKNR was reported as unfavorable at the beginning of 2019.Consequently, these upshots verified the time-varying correlation among financial markets

Performance assessment of the VARX-DCC-MEGARCH model
In order to ascertain the serial correlation in standardized residuals and the square of standardized residuals, this investigation applied the Ljung-Box test at lag 20.The consequences in Table 8 acknowledged that there is no serial correlation between the standardized residuals and the square of standardized residuals for both panels.Accordingly, the statistics produced by the VARX-DCC-MEGARCH models are correct, and the model is correctly fitted.

Conclusion, policy insinuations, and future recommendations
The information has a momentous sway on financial markets performance, and stock proceeds devour a substantial impact on a country's economy.It has become essential to have comprehensive information about their actions and magnetic attachments.Therefore, by developing the multivariate econometric model, this study investigated the returns transmission, volatility spillovers, leverage effect, optimal portfolios, portfolio VaR and dynamic correlation among the systemic financial markets of the US, London, Japan, Germany, and China.This research applied the VARX-DCC-MEGARCH model assimilated with a skewed-t density and discovered that current day-wise returns of SSEC (SSEDR) negatively influence the subsequent overnight returns of the S&P 500 index (SPNR) and vice versa.The trade war between China and the US can be a significant reason for this negative association.This relationship can also be due to contrary sensitivities to variation in the interest rate, or these markets respond differently to external stimuli.While during crises, this liaison was found to be insignificant.It postulates that the stock markets of China and the US have profitable options for the US and Chinese investors to maximize their returns.The novel daytime returns transmission from DAX 30, FTSE 100, and Nikkei 225 index to succeeding overnight returns of the S&P 500 index was insignificant during the stable period, but during GFC, they were found to be significant.Hence, it acquaints that overnight returns of the S&P index provide profitable trading opportunities to Germany, London, Japanese, and China investors.Furthermore, during the GFC period, present daytime returns of the FTSE 100 index showed a bivariate relationship with resulting overnight returns of the S&P 500 index.However, during the standard period, these relationships do not exist.Consequently, this study argued that during regular periods, S&P 500, DAX 30, Nikkei 225, SSEC, and FTSE 100 provide profitable trading opportunities, but these stock markets become more complex during financial crises.The study stated that returns affiliation of LSENR with SPDR, DAXDR, DAXNR, SSEDR, and NKDR remains significant and negative.Hence, these outcomes revealed that the time difference between London, Germany, China, and Japan imperatively benefits, generating more returns.The reason behind this relationship can be the ratio of the stock market capitalization of the London stock exchange globally.Moreover, close competition of London stocks with these markets can also be a reason for adverse impact.The study indicated that oil prices typically bore adverse effects on both panels' stock returns.
The study also quantified that shocks befallen in the current overnight returns of the S&P 500 partake bidirectional and negative ties with shocks that occurred in subsequent day-wise returns of the DAX 30 index.Likewise, the daytime volatility of FTSE 100 positively moves the overnight instability of DAX 30, while other markets do not spillover the volatility of DAX 30.Hence, it allows US and German investors to expand their risk in these markets.However, the FTSE 100 index is a recipient of volatility from the S&P 500, DAX 30, and Nikkei 225.The examination also dogged that no stock market significantly distressed the overnight variance of the SSEC.Hence, during the standard time, investment in DAX 30, with the concoction of overnight returns of the SSEC, daytime returns of S&P 500, FTSE 100, and Nikkei 225 index, is the best option to diversify risk and gain maximum profit.However, during crises, overnight returns of SSEC with an amalgamation of FTSE 100 and daytime returns of DAX 30 can diversify financial risk.
The study revealed that during the stable period, good news has more impel on these stock returns.However, during the GFC period, the study found a leverage effect for the day-wise returns of the S&P 500, DAX 30, and overnight returns of the FTSE 100 index.Hence, the study clinched that the financial risk in these markets is high as equated to normal circumstances during financial crises.Consequently, these findings provide

Figure 2 .
Figure 2. Returns distribution and oil prices.

Table 2 .
Results of the VARX model (panel A).

Table 3 .
Results of the VARX model (panel B).