Time-varying Correlation Between Indian Equity Market and Selected Asian and US Stock Markets

Abstract

The purpose of this article is to examine the dynamic relationship between the Indian stock market and the selected Asian and US stock markets during the post-crisis period. This article uses univariate GARCH (Generalized Autoregressive Conditional Heteroskedasticity) family models on daily observations from March 2009 to December 2015 to evaluate the volatility persistence and leverage effect on Asian developed (Japan, Singapore and Hong Kong) and emerging markets (India, China, Indonesia, Korea, Malaysia and Taiwan) along with the US stock market. AR (Autoregressive) (1)-GARCH (1, 1)-ADCC (Asymmetric DCC) model is employed to find out the dynamic correlation between the Indian equity market and other selected stock markets. The results of the present study give evidence of the leverage effect in conditional volatility but not in conditional correlation, which implies that the rise in conditional volatility is more due to negative shocks than positive ones. On the other hand, dynamic conditional correlation (DCC) does not support any asymmetric effect for the time-varying correlation. The result of average conditional correlation shows the existence of higher diversification opportunities for Indian investors in Malaysian, Chinese and Japanese stock markets (having lower conditional correlation) than in Hong Kong, Indonesian and South Korean markets. The DCC fluctuates more in the cases of India with Singapore, Hong Kong and Indonesia over the sample period. It indicates that the stability of DCC is less reliable and the coefficient of correlation may not be used as a guide for portfolio decisions. But the cases of India with the USA, Japan and China show more stable conditional correlation coefficients. This article investigates the volatility persistence and time-varying relationship among Asian stock markets during the recent period, 2009–2015. The results of this article may be helpful in international portfolio planning and will contribute towards the literature on asymmetric time-varying relationships among Asian markets.

Keywords

Asymmetric DCC-GARCH model Asian capital markets univariate GARCH model time-varying correlation leverage effect

Introduction

The concept of the modern portfolio theory reveals that investors can reduce their portfolio risk by adding low or negatively correlated financial assets to their portfolio. The effects of international portfolio management, risk assessment and diversification strategies mostly fluctuate due to the dynamic value of correlation behaviour of the international financial market. In other words, correlation (market integration or contagion) plays a vital role for both the international investors and the policymakers. The total portfolio risk can be reduced if the correlation coefficient between the stock markets is low (Yang, 2005). The degree of financial market integration and co-movements among the financial markets can be defined as the higher correlation coefficient between them. Total portfolio invested by India (in top 10 destinations)¹

The top 10 total portfolio data are collected from the Coordinated Portfolio Investment Survey (CPIS) database of International Monetary Fund (IMF) as on 15 March 2016.

was US$1,366 million (till December 2009) and US$1,489 million (till June 2015) while the share of equity and investment fund was US$1,327 million (till December 2009) and US$1,480 million (till June 2015) and the rest of the amount was invested in debt instruments. In both cases, whether equity or total funds invested by Indian investors, most of the portion is invested in the USA (United States of America), followed by Indonesia, Hong Kong, Thailand, Korea, Japan, Singapore and China. The second major proportion of total funds invested by India is in Indonesia and Thailand. From December 2009 to June 2015, the total amount invested by India (in equity and investable funds) increased continuously from US$291 million (22% of total investment) to US$642 million (43% of total investment) in the US stock market, while average investment percentage in Indonesia between 2009 and 2015 remains 3 per cent. Total investment in equity reduced from 6 per cent (till December 2009) to 2 per cent (till June 2015) in the case of Hong Kong; and in the case of Thailand, the investment reduced to 1 per cent (after December 2012). Therefore, this study focuses on the dynamic correlation of Indian stock market with selected Asian stock markets (developed as well as emerging) and the stock market of the USA.

The rest of the article is structured as follows: the second section describes the past empirical literature on financial markets and ends with the research gap. In the third section, the DCC and ADCC models are discussed. The fourth section defines the sample data. Results and their interpretations are presented in the fifth section, while the sixth section contains the findings and conclusion of the study.

Review of Literature

This section describes the body of literature, that is, past empirical studies on dynamic correlation (linkages) between stock markets and other financial markets among the Asian and other markets internationally.²

See Sharma and Seth (2012) reviewed the integration among world equity markets.

It has been organized on the basis of the markets or the approaches used by the authors to identify the dynamic behaviour of the financial markets.

Yang (2005) examined the market correlation of Japan with four other countries (Taiwan, Singapore, Hong Kong and South Korea) during 1990–2003 and observed that the correlation was inconsistent during the study period. It was also observed that there was an increase in correlation during the period of high market volatility. Bellotti and Williams (2005) attempted to study the dynamic volatility transmission among emerging Asian and Latin American equity markets by employing BEKK-GARCH (1, 1).³

BEKK stand for Baba, Engle, Kraft and Kroner.

The results showed strong evidence of cross-border interdependency between Latin American and Asian markets.

Khalid and Rajaguru (2006) employed VAR-MGARCH-BEKK (Vector Autoregressive-Multivariate GARCH-Baba-Engle-Kraft-Kroner)⁴

VAR-MGARCH stands for vector autoregressive multivariate GARCH.

during the Asian crisis period on East Asian currency markets and concluded that the currency market linkage increased during and after the crisis. Bhar and Nikolova (2009) used the results of bivariate DCC-EGARCH⁵

DCC-EGARCH stands for dynamic conditional correlation-exponential GARCH.

to conclude that a high-level integration exists among BRIC stock markets at both regional and global levels. Yu, Fung, and Tam (2010) studied the Asian equity market integration with 10 selected markets over 15 years and concluded that the degree of integration between developed and emerging markets differed significantly. Zhao (2010) used the VAR-MGARCH-BEKK model to test the hypothesis of bi-directional volatility spillover and dynamic long-term equilibrium relationship between the Chinese currency and the stock market. Durai and Bhaduri (2011) examined the dynamic correlation between Indian equity markets and 10 other world indices. The study showed that the correlation of India with both Asian and developed indices was low, which supported the diversification opportunities for the world market to invest in India. Johansson (2011) examined the dynamic linkages by employing correlation copula (tail dependency model) on 20 East Asian and Western European stock markets during the Global Financial Crisis (GFC) and found a stable volatility and correlation pattern up to the second half quarter of 2008, while regional correlation strongly declined during the third quarter and after that increased in both the regions.

Kenourgios and Padhi (2012) found significant co-integration and causality among emerging stock markets during the Russian and Asian crisis, from both bond and stock markets during the subprime crisis and no significant results from the Argentina crisis by using Johansen co-integration and asymmetric generalized dynamic conditional correlation (AGDCC). Hwang (2012) analysed the dynamic correlation between the Asia-Pacific region and the USA. The results suggested very high correlation during the financial crisis that does not support the portfolio opportunities for global investors and found the asymmetric effect on conditional variance (except China and Malaysia) from the threshold autoregressive-GARCH model. Gupta and Guidi (2012) employed different co-integration models (such as Engle and Granger co-integration, Johansen co-integration, Gregory and Hansen co-integration and Granger causality test) for co-integration and the DCC-GARCH model for time-varying co-movement between India and the developed Asian and US stock markets covering 20 years of daily observations. The study found that the correlation returned to their initial level after showing an increase during the crisis period. Zhang, Li, and Yu (2013) investigated whether the GFC permanently changed the correlation among BRICS and developed the market by using GJR-GARCH-M-Asymmetric DCC (ADCC) model and found an upward long-run trend in conditional correlation. Bekiros (2014) found strong integration between BRIC markets after the GFC that supported vulnerability in international contagion in the future. Moore and Wang (2014) found evidence for supporting the dynamic linkage between exchange rate and stock price among the Asian emerging markets and selected developed markets. The results showed that the US market influenced both the stock and foreign exchange market in the Asian region and concluded that DCC mostly fluctuated due to trade balance (in the case of Asian markets) and interest rate differentials (in the case of developed markets). Baumöhl and Lyócsa (2014) used 32 worldwide emerging and frontier equity markets to analyse the volatility and dynamic correlation through the DCC-GARCH model and found a positive significant relationship between volatility and DCC, which indicates the decreasing diversification benefits during a high volatility period. Chittedi (2015) found a significant increment average time-varying correlation during the crisis period and reported the evidence of contagion effects from the USA to India during the crisis period. Jin and An (2016) employed AR(1)-GARCH (1, 1)-BEKK, DCC-GARCH and volatility impulse response function (VIRF) during the GFC on the BRICS markets and suggested that the impact of the US shock affected the market volatility after the crisis and the effect of the shock depended upon the individual integration of equity markets with the international economy. Mongi and Dhouha (2016) investigated the stock-commodities market linkage in the USA and found insignificant cross-market relations from the CCC (Constant Conditional Correlation) model while a significant dynamic correlation (for all time) from DCC model. Chiang and Chen (2016) found the highest correlation of China with Hong Kong, followed by Taiwan and Korea, and low correlation between Europe and the USA.

Nguyen and Elisabeta (2016) investigated the integration among China and Association of South East Asian Nations’ (ASEAN) stock as well as the sectoral market (consumer goods, financial, industrial, Properties and real estate) by employing the DCC-MGARCH model with a discrete wavelet transformation (DWT), and Paramati, Roca, and Gupta (2016) investigated integration and dynamic linkage in 10 Asian markets over 13 years of weekly observations through co-integration, ADCC and panel regression models and found increasing economic integration both in the short and in the long run among the sample markets during the study period. Rehman (2017) examined the time-varying co-movements of Japanese stock markets with selected economic fundamentals (such as implied volatility index, policy uncertainty index, oil price, exchange rate and inflation) and reported a significant impact of exchange rate and oil price changes on the time-varying correlation between implied volatility index and stock market returns.

From the above review of past empirical studies on financial market linkages, it can be concluded that there are very few studies on the Indian stock market as well as the ADCC model. Thus, the main objective of this article is to analyse the dynamic linkages or time-varying correlation between India and other selected markets by employing the AR(1)-GARCH (1, 1)-ADCC model.

Objective of the Study

India is the second largest growing country among the Asian emerging markets after China. The studies based on the ADCC model are very limited especially with reference to Indian stock markets. Thus, the objective of this study is to examine the dynamic linkage between the Indian stock markets with selected Asian and US stock markets during the post-crisis period.

Methodology

This study is basically focused on Indian equity markets in the course of the post-crisis period. This study estimates the volatility parameters on the basis of the AR(1)-GARCH (1, 1) process. After collecting the standardized residuals we proceed for estimating dynamic linkages through the DCC model introduced by Engle (2002) and Cappiello, Engle, and Sheppard (2006).

In this article, the DCC model of Engle (2002) and ADCC model of Cappiello et al. (2006) are used to analyse the financial linkages between India and other selected Asian markets and the US stock market. Cappiello et al. (2006) generalized the DCC-GARCH model of Engle (2002) and introduced ADCC. In the first step, the AR(1)-GARCH (1, 1) model is employed to obtain standardized residuals. The return equation is:

\begin{array}{l} r_{i t} = C_{0} + C_{1} r_{i t - 1} + ε_{i t} \\ ε_{i t} \sim N (0, H_{i t}) \end{array}

(1)

r_it is the multivariate return series of i and ε_it is the random error term which follows normal distribution with zero mean and constant conditional variance, H_it. r_it-1 refers to AR(1) approach, which follows the conditional approach of the DCC framework and the coefficient C₁ captures the speed of the market information reflected on the stock price of i. This study uses different univariate GARCH(1, 1) models [GARCH (Bollerslev, 1986), EGARCH (Exponential GARCH) (Nelson, 1991), GJR-GARCH (Glosten, Jagannathan, & Runkle, 1993), APARCH (Ding, Granger, & Engle, 1993), CSGARCH (Lee & Engle, 1999) and IGARCH (Integrated GARCH) (Lumsdaine, 1996)] with different error distributions (normal, student-t and generalized error distributions). The best GARCH specification and DCC-GARCH specification (whether they follow normal or student-t distribution) are selected on the basis of Bayesian information criteria (BIC).

The conditional variance and covariance matrix H_it of the GARCH(1, 1) model can be expressed as follows:

H_{i t} = ω_{1} + \sum_{i = 1}^{q} α_{i} ε_{i t - i}^{2} + \sum_{j = 1}^{p} β_{j} H_{i t - j}

(2)

And in case of JGR-GARCH(1, 1):

H_{i t} = ω_{1} + \sum_{i = 1}^{q} α_{i} ε_{i t - i}^{2} + \sum_{i = 1}^{q} γ_{i} ε_{i t - i}^{2} I_{t - i} + \sum_{j = 1}^{p} β_{j} H_{i t - j}

(3)

z_{i t} = ε_{i t} / \sqrt{H_{i t}} and z_{i t} \sim N (0, 1)

(4)

$ω, α_{i}, β_{j} and γ_{i}$ represent constant, ARCH, GARCH and asymmetric terms, respectively, in the conditional variance equation. Significant positive coefficients of the asymmetric term indicate that negative shocks have more impact on volatility as compared to positive shocks. I(.) represents dummy variable equal to one if . $ε_{it- 1} < 0, otherwise zero . α_{i} > 0$ and $α_{i} + β_{i} < 1$ are purposed to ensure a positive and stable conditional variance. $z_{it} = ε_{it} / \sqrt{H_{it}}$ represents the standardized residuals which follow a normal distribution with zero mean and unit variance. From the first step (of the univariate GARCH model), standardized residual series can be collected for proceeding to the second step, that is, DCC model. The standard DCC model given by Engle (2002) is mentioned as below:

\begin{array}{l} Q_{t} = (1 - a - b) \bar{P} + a z_{t - 1} z_{t - 1}^{'} + b Q_{t - 1} \\ \bar{P} = E [z_{t} z_{t}^{'}] a n d a + b < 1 \end{array}

(5)

$P_{t} = Q *_{t}^{- 1} Q_{t} Q *_{t}^{- 1}$ represents the conditional correlation matrix

$Q *_{t} = q *_{i i, t} = \sqrt{q_{i i, t}}$ is a diagonal matrix with the square root of the element of Q_t on the ith diagonal position. To allow the asset-specific news and smoothing parameters (or asymmetric term), Cappiello et al. (2006) modify the above DCC model as:

Q_{t} = (\bar{P} - A^{'} \bar{P} A - B^{'} \bar{P} B - G^{'} \bar{N} G) + A^{'} z_{t - 1} z_{t - 1}^{'} A + B^{'} Q_{t - 1 B} + G^{'} n_{t - 1} n_{t - 1}^{'} G

(6)

A, B and G (kXk) are parameters matrix, $\bar{P} a n d \bar{N}$ are unconditional correlation matrix of z_t and n_t.

The negative standardized residuals for asymmetric impact n_t are defined by $n_{t - 1} < 0 = 1, otherwise zero$ If matrix A, B and G is replaced by scalar a, b and g, then ADCC(1, 1) model can be extracted from AG-DCC(1, 1) (see Kenourgios, 2014). And finally, the DCC matrix is given by the following equation:

P_{t} = Q *_{t}^{- 1} Q_{t} Q *_{t}^{- 1}

(7)

In the ADCC(1, 1) model, a,b and g represent the ARCH,GARCH and leverage term about the time-varying correlation.

Data

The dataset consists of the daily closing prices of 10 emerging and developed stock indices⁶

10 stock indices consist of six (India, China, Indonesia, South Korea, Malaysia and Taiwan) emerging Asia, three developed Asia (Japan, Hong Kong and Singapore) and the US stock indices. According to the portfolio data given above, a certain percentage of amount is always invested by India in the Thailand market. But due to the unavailability of the data, the market is excluded from the set of Asian emerging markets.

from 1 March 2009 to 31 December 2015.⁷

The study period covering the period of the post-crisis period of GFC 2007–2008, which may be represented as the recent financial period. From the past literature, it observed that the linkage was stronger during the crisis period (Apostolakis, 2016) as well as after the crisis period.

The beginning date of the data was the day on which the global financial crisis ends (Kenourgios & Dimitrios, 2014, 2015) and the last date was the day of data collection. The purpose of considering this time period is to analyse the post-crisis period. The stock indices considered for the present study are India’s Sensex-30 (BSE), China’s Shanghai Composite (SSE), Indonesia’s Jakarta Composite (JC), South Korea’s Seoul Composite (KOSPI), Malaysia’s KLSE Composite (KLCI), Taiwan’s Taiwan Weighted (TEX), Hong-Kong’s Hang Seng (HIS), Japan’s Nikkei 225 (NIK), Singapore’s Straits Times (STI) and USA’s S&P 500 (S.P). The data of stock indices are collected from www.yahoofinance.com and the missing observations arising due to holidays and special events are replaced by the previous day’s closing price. Daily stock market returns can be computed by taking the logarithmic difference of the daily stock indices and multiplying it by hundred, that is,

r_{t} = (\log P_{t} - P_{t - 1}) * 100

Analysis

Descriptive Statistics of Return Series

The summary statistics for the return series is presented in Table 1. The average returns of all the indices over the sample period showed positive values and range from 0.0295 (SSE) to 0.0728 (JC). The highest average return was found in the case of JC (0.0728) followed by BSE (0.0617), SP (0.0601), and NIK (0.0532). SSE return series depicted a highly volatile market with standard deviation (SD) of 1.4879, while KLCI indicated a low volatility market with SD of 0.9068. The volatility of the BSE was found to be lower than SSE, NIK and HIS but higher than the rest of the sample markets. The results of the skewness, Kurtosis and JB (Jarque-Bera) test reported the non-normality of the return series. From the results of Ljung-Box and McLeod-Li tests, it is found that the series has the problem of serial autocorrelation and ARCH effect. Thus, the presence of the ARCH effect and autocorrelation supports GARCH-specific models to find out better results using the return series. Table 2 reports cross-country unconditional correlation between BSE and other selected countries. The Indian market shows the highest correlation with STI, followed by HIS, JC, KOSPI, TEX, SP, NIK, SSE and KLCI.

Figure 1 represents the percentage of the daily returns for 10 selected stock indices from Asia and the USA. STI, KLCI, HIS and BSE showed high volatility at the beginning of 2009, which may be due to the effects of the GFC in 2008. Due to the effects of the debt crisis in Europe, most of the indices such as TEX, STI, KOSPI, HIS, JC and SP indicated increased volatility clustering between mid-2011 and 2012. Also, during mid-2015, HIS and SSE indicated high volatility. On the other hand, the volatility clustering for KLCI returns series displayed an average movement over the sample period.

DCC and ADCC GARCH

Table 3 presents the univariate GARCH model selection procedures. The AR(1)-GARCH (1, 1) (GARCH, EGARCH, GJR-GARCH, CGARCH, IGARCH and APARCH) models are used with the assumption that the error follows normal, student-t and generalized error distribution. On the basis of BIC, the best specification is selected (low BIC value out of all specifications) for every individual return series. From Table 3, it was found that most of the series follow generalized error distribution (except KLCI, which follows student-t distribution) rather than a normal distribution. On the other hand, most of the return series follow GJR-GARCH(1, 1) specification (except that SP, NIK and KLCI follow EGARCH, and SSE and JC follow IGARCH processes).

Table 1.

Descriptive Statistic of Return Percentage

Series	Mean	Median	SD	Skew	Kurt	JB	p-Value	ARCH-LM (10)	p-Value	Q(20)	p-Value	Q²(20)	p-Value	Obj
BSE	0.0617	0	1.1932	1.3281	19.3193	28309.51	0	54.0338	0	49.2154	3.00E-04	88.1533	0	1782
SSE	0.0295	0	1.4879	−0.7155	5.1311	2114.133	0	238.5766	0	64.736	0	868.8249	0	1782
JC	0.0728	0.0515	1.1926	−0.383	5.007	1911.815	0	185.7651	0	59.797	0	426.734	0	1782
KLCI	0.0369	0.0154	0.9068	0.0979	147.1608	1611672	0	764.3169	0	100.229	0	437.1648	0	1782
KOSPI	0.0368	0	1.041	−0.313	3.6972	1048.228	0	256.6729	0	38.2324	0.0083	1028.927	0	1782
TEX	0.0355	0.0239	1.0437	−0.213	3.5403	947.9761	0	179.2933	0	77.661	0	539.6817	0	1782
NIK	0.0532	0.004	1.3653	−0.4755	4.5385	1602.355	0	147.3391	0	32.2911	0.0403	260.1767	0	1782
HIS	0.0323	0	1.2779	0.0056	2.7688	571.8859	0	204.5332	0	41.7292	0.003	786.8471	0	1782
STI	0.0354	1.00E-04	0.9162	0.2432	4.7309	1685.519	0	399.6	0	38.5767	0.0075	1338.393	0	1782
SP	0.0601	0.0425	1.0635	−0.1225	4.7124	1659.369	0	312.7982	0	63.9742	0	979.5109	0	1782

Source: The authors.

Notes: JB indicates the Jarque-Bera test of statistic to test the normality of the return series. Q(m) and Q²(m) are Ljung-Box and McLeod-Li tests of serial correlation up to (m) order in the level and the square return. ARCH-LM (m) is the test of conditional heteroskedasticity up to (m) order.

H(0) of Q²(10) LM test: no serial correlation in the square of return series.

H(0) of Q(10) LM test: no serial correlation in the return series.

H(0) of JB: the return series is normally distributed.

H(0) of ARCH-LM (10): no ARCH effect in the return series.

Table 2.

Unconditional Cross-correlation of the Return Series

	BSE	SSE	KOSPI	KLCI	TEX	JC	NIK	HIS	STI	SP
BSE	1
SSE	0.211567	1
KOSPI	0.351672	0.291713	1
KLCI	0.197141	0.127036	0.29333	1
TEX	0.34781	0.304725	0.672001	0.305329	1
JC	0.415294	0.252989	0.467509	0.330678	0.467277	1
NIK	0.255883	0.26102	0.533705	0.278948	0.493874	0.387347	1
HIS	0.487579	0.495358	0.604489	0.325036	0.596274	0.541553	0.509102	1
STI	0.528565	0.32361	0.532859	0.339026	0.567007	0.584403	0.47624	0.703464	1
SP	0.29765	0.138117	0.230782	0.07998	0.200075	0.180504	0.135959	0.233818	0.318375	1

Source: The authors.

Note: Bold indicates high correlation and italic indicates a low correlation between the countries.

Figure 1.

Source: The authors.

Figure 2.

Source: The authors.

Figure 3.

Source: The authors.

Table 3.

Univariate GARCH Model Selection

Indices	Selected Models	BIC
BSE	AR(1)-GJR-GARCH (1, 1)-ged	2.92
SSE	AR(1)-IGARCH (1, 1)-ged	3.287
KOSPI	AR(1)-GJR-GARCH (1, 1)-ged	2.641
KLCI	AR(1)-EGARCH (1, 1)-std	1.673
TEX	AR(1)-GJR-GARCH (1, 1)-ged	2.669
JC	AR(1)-IGARCH (1, 1)-ged	2.9
NIK	AR(1)-EGARCH (1, 1)-ged	3.287
HIS	AR(1)-GJR-GARCH (1, 1)-ged	3.101
STI	AR(1)-GJR-GARCH (1, 1)-ged	2.304
SP	AR(1)-EGARCH (1, 1)-ged	2.582

Source: The authors.

Note: ‘ged’, ‘std’ and ‘BIC’ indicate generalized error distribution, student-t distribution, and BIC.

Table 4 presents the estimated result of the AR(1)-GARCH (1, 1)-DCC model. Panel A of Table 4 presents the result of the univariate GARCH (1, 1) model with the separate specification (see Table 3). Panels B and C show the results of DCC and ADCC models while panel D represents the reliability of the DCC model through model diagnostics of the AR(1)-GARCH (1, 1)-DCC model. In panel A, the autoregressive term (ar1) was not significant in all the cases except KLCI and JC. In the case of KLCI, (ar1) a positively significant result indicated that previous-day information significantly affected next-day returns in the same direction while in the case of JC (ar1) which was negatively significant, it implied that next-day returns fluctuated similar to previous-day returns but in the opposite direction. In all the cases, ARCH (alpha1) and GARCH (beta1) terms were found to be highly significant and the GARCH term was more than 0.90 (except JC, 0.888) which supports the higher persistence behaviour of the return series. The asymmetric term (gamma1) was positively significant at 1 per cent in most of the cases and supported the leverage effect in return series, implying that past negative shocks have more impact on current conditional volatility than positive shocks. In other words, conditional volatility rose higher due to a negative shock rather than a positive one. The shape parameter presented highly significant results with positive signs which means that it supports the GARCH (1, 1) specification with generalized error distribution (or student-t). From panel B, GARCH term of DCC (dccb1) was positively significant at 1 per cent level, but the ARCH term of DCC (dcca1) was significant only in the correlation of BSE with KOSPI (0.0427**), KLCI (0.0455***), TEX (0.044*), HIS (0.031**) and STI (0.0258***). The level of volatility persistence was also not very high in BSE-TEX (0.5645). BSE-KOSPI (0.7738), BSE-NIK (0.7808) and BSE-KLCI (0.866) are pairs of conditional correlation series. In panel C, leverage parameter in ADCC (i.e., Dccg1) was not significant in any pairs of conditional correlation between stock returns of BSE and other selected markets except between BSE and KLCI (0.06**),which indicates that negative innovation does not affect differently compared to positive innovation and does not support the asymmetric specification of the time-varying correlation model. Panel D presents DCC model and Q(10) LM (Lagrange Multiplier) test which shows the Ljung-Box test of serial correlation with no serial correlation and Q²(10) LM test indicated multivariate generalized LM test of Engle (1982) of the 10th order. In most of the cases, the null hypothesis of serial interdependence in the level and square of standardized residuals was rejected, which gives the evidence of better specification of the DCC model. Table 5 presents the BIC and log likelihood (LLH) value derived from different specifications of the DCC model. First, the DCC and ADCC models were applied with multivariate normal and student-t distribution to collect the BIC and LLH values. The BIC with lower values implies the best specification of the model. All pairs of the countries represented DCC with the multivariate student-t distribution having lower BIC value when compared to other specifications (such as DCC-mvnorm, ADCC-mvnorm and ADCC-mvt). Further, it was found that the BIC value of the ADCC specification was always higher than DCC specification, implying that the DCC results of all the markets were more reliable than the ADCC model.

The Statistical Analysis of DCC Series

In this section of statistical analysis, summary statistics of the DCC series is used and regression with AR(1) is applied, which is defined as follows:

ρ_{t} = C_{1} + C_{2} ρ_{t - 1} + v_{t}

(8)

where ρ_t is time-varying correlation at time ‘t’. The coefficient of AR(1) term (i. e., C₂) captures the effect of previous-day conditional correlation on today’s correlation. It can be observed from Table 6⁸

Table 6 reported the summary statistic of the DCC series.

that all the DCC series having a problem of heteroscedasticity, that is, Ljung-Box statistic, provides significant results in both DCC and square DCC series. Therefore, to determine the stability and instability of the DCC coefficient, this article has used the following GARCH (1, 1) specification:

H_{ρ i t} = C_{3} + \sum_{i = 1}^{q} C_{4 i} v_{ρ i t - i}^{2} + \sum_{i = 1}^{q} C_{5 i} v_{ρ i t - i}^{2} I_{t - i} + \sum_{j = 1}^{p} C_{6 j} H_{ρ i t - j}

(9)

C_4i and C_6j coefficients capture the ARCH and GARCH effect and C_5t captures leverage effect in DCC series. If both the coefficients (ARCH and GARCH) are significant, it indicates that conditional correlation may not provide a useful result for the purpose of portfolio evaluation.

The coefficients of autoregression () and GARCH term () were positively significant for all pairs of the DCC series. A high degree of volatility persistency was observed in cases of BSE to SSE, KOSPI and JC, while a lower degree of persistency in DCC of BSE to HIS and NIK. It can be observed from Table 7 that both the Q(m) and Q²(m) statistic indicate significant results in most of the cases; thus, the result may be interpreted on the basis of unconditional SD in state of conditional SD. Average conditional correlation and its SD indicated the existence of correlation between BSE and other selected countries. It followed the same order of correlation as the result found from unconditional correlation but the average conditional correlation coefficient was found to be less than the unconditional correlation for all the pairs of countries. Further, a higher correlation coefficient was found from the ADCC model as compared to the DCC model (see Figure 2). The stability of average DCC is evaluated through its SD. The correlation of BSE with STI (0.1058) showed highest SD followed by KLCI (0.0724), HIS (0.0703), KOSPI (0.0546), JC (0.0539), TEX (0.0463), NIK (0.035), SSE (0.0234) and SP (0). The behaviour of conditional correlation between the Indian stock market and rest of the sample markets is presented in Figure 3 and indicates that the time-varying correlation for BSE and SP was comparatively stable when BSE is compared with STI, KLCI, HIS, KOSPI and JC over the period.

Table 4.

Results of AR(1)-GARCH (1, 1)-DCC

Panel A: Results from the Univariate Garch Model
	BSE	SSE	KOSPI	KLCI	TEX	JC	NIK	HIS	STI	SP
Mu	0.0111	0	0.0079	0.0404***	0.0267	0.0708***	0.0475*	0.0018	0.0159	0.047**
ar1	0.0425	0	−0.0044	0.0919***	0.036	−0.0113**	−0.031	0.002	−0.0014	−0.0318
Omega	0.0244***	0.025*	0.0132*	−0.0748***	0.0142	0.0199**	0.0303*	0.0186**	0.0059**	−0.0129*
alpha1	0.0223**	0.0703***	0.0178*	−0.038**	0.0189*	0.1117***	−0.1224***	0.0251***	0.0378***	−0.213***
beta1	0.9051***	0.929745	0.9237***	0.9297***	0.9245***	0.888278	0.9355***	0.9298***	0.9193***	0.9579***
gamma1	0.1238***		0.0926***	0.1894***	0.0834**		0.1887***	0.0701***	0.0703***	0.2027***
Shape	1.1928***	0.8397***	1.2244***	3.8623***	1.1735***	1.1091***	1.2145***	1.1991***	1.4434***	1.2252***
Panel B: Result from DCC model
		BSE-SSE	BSE-KOSPI	BSE-KLCI	BSE-TEX	BSE-JC	BSE-NIK	BSE-HIS	BSE-STI	BSE-SP
dcca1		0.0105	0.0427**	0.0455***	0.044*	0.0239	0.0228	0.031**	0.0258***	0
dccb1		0.8964***	0.7311***	0.8205***	0.5205***	0.9069***	0.758***	0.9208***	0.9566***	0.9254***
Mshape		5.4988***	7.0702***	4.9799***	6.6701***	5.8628***	7.2351***	7.1523***	7.6644***	6.4832***
Persistency		0.9069	0.7738	0.866	0.5645	0.9308	0.7808	0.9518	0.9824	0.9254
Panel C: Result from ADCC model
dcca1		0	0.0427*	0.0083	0.044	0.0239	0.0087	0.0226*	0.0222***	0
dccb1		0.5521**	0.7311***	0.8486***	0.5204***	0.9069***	0.8853***	0.9173***	0.957***	0.9466***
Dccg1		0.0805	0	0.06**	0	0	0.0153	0.0217	0.0094	0
Mshape		5.519***	7.0703***	5.0503***	6.6701***	5.8628***	7.2784***	7.302***	7.8184***	6.4832***
Persistency		0.5521	0.7738	0.8569	0.5644	0.9308	0.894	0.9399	0.9792	0.9466
Panel D: Results of Model Diagnostics on AR(1)-GARCH (1, 1)-DCC
Q²(10) LM test:		18.7**	8.205	0.2638	9.012	8.642	7.935	12.99	27.63***	20.96**
Rank-based test:		17.16*	13.49	19.2**	7.785	5.702	11.91	13.59	9.209	4.277
Q2 –k(10) test:		41.39	57.92**	13.23	41.4	42.45	56.45**	34.59	90***	73.37***
Robust test:		56.01**	40.2	51.97*	56.76**	42.46	48.63	74.15***	46.64	49.59
Q(10) LM test:		15.31	9.162	0.1608	8.3	8.517	9.432	8.805	45.79***	18.06*
Rank-based test:		18.1*	10.92	19.16**	5.194	5.995	9.431	11.88	9.133	3.762
Q –k(10) test:		39.93	55.75*	10.78	40.27	42.53	65.29***	30.13	126.2***	68.54***
Robust test:		47.13	57.66**	46.63	46.61	37.36	55.04	59.7**	43.25	47.51

Source: The authors.

Notes: Q²(10) LM test indicates multivariate generalized LM test of Engle (1982) and rank base test of Dufour and Roy (1985, 1986) on square standardized residuals with null hypothesis and no heteroscedasticity in standardized residuals. Q(10) LM test indicates multivariate LM test on standardized residuals (see Tsay, 2014, pp. 399–465).

‘Mshape’ indicates the shape parameters of the ‘distribution’. Persistency = (dcca1 + dccb1) and dccg1 captures the leverage effects in the DCC equation.

*, ** and *** indicate statistical significance at 10, 5 and 1 per cent levels, respectively.

H(0) of Q²(10) LM test: no serial correlation in the square of standardized residuals.

H(0) of Q(10) LM test: no serial correlation in the standardized residuals.

Table 5.

BIC and LLH Result from DCC and ADCC

BSE-SSE

BSE-KOSPI

BSE-KLCI

BSE-TEX

BSE-JC

BSE-NIK

BSE-HIS

BSE-STI

BSE-SP

BIC

LLH

BIC

LLH

BIC

LLH

BIC

LLH

BIC

LLH

BIC

LLH

BIC

LLH

BIC

LLH

BIC

LLH

DCC-mvnorm

6.394

−5645

5.569

−4899

5.402

−4750

5.632

−4955

5.837

−5148

6.282

−5534

5.934

−5224

5.078

−4461

5.568

−4898

DCC-mvt

6.265

−5526

5.475

−4811

4.554

−3990

5.519

−4850

5.702

−5024

6.175

−5434

5.836

−5132

4.988

−4377

5.464

−4801

ADCC-mvnorm

6.396

−5642

5.573

−4899

5.411

−4754

5.636

−4955

5.841

−5148

6.286

−5534

5.936

−5221

5.081

−4460

5.572

−4898

ADCC-mvt

6.268

−5525

5.48

−4811

4.555

−3987

5.523

−4850

5.706

−5024

6.179

−5434

5.839

−5131

4.991

−4376

5.468

−4801

Source: The authors.

Notes: ‘mvnorm’ and ‘mvt’ follow multivariate normal and multivariate student-t distribution, respectively. BIC and LLH indicate BIC and log likelihood. DCC is dynamic conditional correlation and ADCC asymmetric-DCC.

Table 6.

Descriptive Statistic of DCC Series

Series	Mean	Median	SD	Skew	Kurt	JB	p-Value	ARCH-LM (10)	p-Value	Q(20)	p-Value	Q²(20)	p-Value	Obj
BSE-SSE	0.2136	0.2122	0.0234	0.4572	1.248	177.7261	0	1452.828	0	7983.214	0	7925.536	0	1782
BSE-KOSPI	0.346	0.3486	0.0546	−0.1404	1.9509	288.4599	0	1057.979	0	2677.715	0	2623.349	0	1782
BSE-KLCI	0.2085	0.2081	0.0724	−0.2457	3	686.1926	0	1322.055	0	5609.051	0	5059.461	0	1782
BSE-TEX	0.3264	0.3261	0.0463	0.0289	6.6049	3239.421	0	597.4024	0	907.749	0	894.997	0	1782
BSE-JC	0.3819	0.3824	0.0539	0.0435	0.0973	1.2648	0.5313	1537.34	0	10311.87	0	10159.38	0	1782
BSE-NIK	0.2648	0.2653	0.035	−0.4975	7.7059	4482.59	0	1091.999	0	3019.163	0	2972.292	0	1782
BSE-HIS	0.4503	0.4516	0.0703	−0.0491	0.2351	4.8215	0.0897	1576.756	0	13581.06	0	13393.99	0	1782
BSE-STI	0.4627	0.4764	0.1058	−0.5391	0.465	102.3754	0	1700.951	0	24668.33	0	24086.21	0	1782
BSE-SP	0.2854	0.2854	0	1.1696	4.6782	2031.342	0	1507.917	0	10835.92	0	10835.92	0	1782

Source: The authors.

Notes: JB indicates the Jarque-Bera test of statistic to test the normality of the DCC series. Q(m) and Q²(m) are Ljung-Box and McLeod-Li tests of serial correlation up to (m) order in the level and the square DCC series. ARCH-LM (m) is the test of conditional heteroscedasticity up to (m) order. For H(0), see note of Table 1.

Table 7.

Statistical Analysis of DCC Series

Residual

Standardized Residuals

Persistence

arch-lm

Q(20)

Q²(20)

ARCH-LM

Q(20)

Q²(20)

BSE-SSE

Coef

0.2152 ***

0.9071 ***

0 ***

3.00E−04

0.0012

0.9903 ***

0.9912

3.9615

20.6743

30.0292 *

4.1073

20.3132

29.1928 *

p-Value

[0]

[0.8306]

[0.72]

[0]

[0.9491]

[0.4165]

[0.0694]

[0.9424]

[0.4385]

[0.084]

BSE-KOSPI

Coef

0.3473 ***

0.7626 ***

0 ***

7.00E-04

0.0164***

0.9774 ***

0.9862

16.3049 *

29.8148 *

26.0953

11.3586

23.5232

20.5075

p-Value

[0]

[0.7919]

[0.0041]

[0]

[0.0912]

[0.0729]

[0.1627]

[0.3303]

[0.2638]

[0.4266]

BSE-KLCI

Coef

0.1953 ***

0.9241 ***

0 ***

0.0107 ***

−0.0211 ***

0.9752 ***

0.9754

3.7737

24.5135

6.3286

3.9946

21.6684

8.1875

p-Value

[0]

[0.957]

[0.2207]

[0.9984]

[0.9476]

[0.3588]

[0.9906]

BSE-TEX

Coef

0.3268 ***

0.5784 ***

0 **

0.0094 **

−0.0061

0.9714 ***

0.9778

11.4076

31.8684 **

54.0213 ***

4.9009

26.2076

23.0346

p-Value

[0]

[0.0263]

[0.0166]

[0.2491]

[0]

[0.3267]

[0.0447]

[1e-04]

[0.8977]

[0.1591]

[0.2871]

BSE-JC

Coef

0.3828 ***

0.9335 ***

0 ***

0.0188***

0.9813 ***

0.9907

2.6888

38.5948 ***

6.9925

3.1675

34.8631 **

8.7012

p-Value

[0]

[0.9996]

[7e-04]

[0]

[0.9878]

[0.0075]

[0.9967]

[0.9772]

[0.0208]

[0.9861]

BSE-NIK

Coef

0.2648 ***

0.7874 ***

0 ***

0.0751***

0.903 ***

0.9405

3.7599

14.1062

9.2007

3.1989

9.8465

7.022

p-Value

[0]

[6e-04]

[1]

[2e-04]

[0]

[0.9575]

[0.8251]

[0.9805]

[0.9763]

[0.9709]

[0.9966]

BSE-HIS

Coef

0.4524 ***

0.9415 ***

1e-04 ***

0.0191

0.8699 ***

0.8794

11.0731

17.3028

18.3903

11.0232

17.1212

19.0207

p-Value

[0]

[1]

[0.1638]

[0]

[0.3518]

[0.6332]

[0.5617]

[0.3557]

[0.6451]

[0.5205]

BSE-STI

Coef

0.475 ***

0.9767 ***

0 ***

0.0293***

0.9624 ***

0.9771

2.9183

27.744

15.0235

6.1466

27.3334

11.9655

p-Value

[0]

[1]

[3e-04]

[0]

[0.9833]

[0.1156]

[0.7751]

[0.8028]

[0.1261]

[0.9173]

BSE-SP

Source: The authors.

Note: Refer the footnote of Table 4.

Conclusion

This article investigated the dynamic relationship between the Indian stock market and the selected Asian markets (five emerging: China, Indonesia, South Korea, Malaysia and Taiwan and three developed: Japan, Hong Kong and Singapore) and the US market from 1 March 2009 to 31 December 2015 by using DCC and ADCC models. The sample time period begins from the end of the GFC, that is, from 2007–2008, to the end of 2015, when data was collected. The sample indices cover both emerging and developed countries from the Asian region. The USA is selected, even though it is out of the Asian region, as a major amount of fund was invested by India in the US stock market from 2009 to 2015. Primarily, this article focuses on finding out the best model specification for understanding the dynamic linkages between India and other selected Asian markets (developed and emerging) and the US stock market. This article identified the better model specification by using a lower BIC value. The univariate GARCH model was selected from AR(1)-GARCH (1, 1) models (GARCH, EGARCH, GJR-GARCH, CGARCH, IGARCH and APARCH) with the assumption that the error follows normal, student-t and generalized error distribution, and we found most of the series follow GJR-GARCH (1,1) specification with generalized error distribution (except KLCI that follows student-t distribution) rather than normal distribution. While SP and KLCI follow EGARCH, SSE and JC follow IGARCH specification. It was also found that the BIC value of the ADCC specification was always higher than DCC specification, implying that the results of DCC for all the markets may be more reliable than the results of the ADCC model and this was also supported by the leverage term (statistically not significant) from the ADCC model.

From the analysis section, the asymmetric effect on conditional volatility was found rather than the conditional correlation series, which indicates that conditional volatility reacts more to negative shocks than positive, but the conditional correlation reacts in the same manner in both positive and negative innovations. In both the cases of conditional and unconditional correlation, the degree of correlation was highest between BSE and STI followed by correlation of BSE with HIS, JC, KOSPI, TEX, SP, NIK and SSE. Also, a very low correlation was found between BSE and KLCI. The DCC between BSE and SP was stable while the dynamic correlation between BSE and STI fluctuated over the period significantly. Finally, it can be concluded that the diversification policy for Indian investors is not suitable for Singapore, Hong Kong, Indonesia and South Korea due to high correlation coefficient with uncertainty (higher SD). But Malaysian, Chinese and Japanese markets showed prominent diversification opportunities. A more stable correlation was found between the Indian and US stock markets, which indicates that any changes in the US market can directly affect the Indian stock market.

Implications and Future Scope of Research

The essence of International investors is to predict market volatility as well as identify the correlation between different markets. The implication of the studies on the time-varying correlation among stock markets plays an important role in decisions of investment allocation, portfolio evaluation, rebalancing, risk determination and taking remedial actions during and after the financial crisis period. A very high correlation between the financial markets implies few diversification opportunities for the existing as well as potential investors. The results of this article may be helpful for those academicians, investors and policymakers who are interested in further research in the same area or/and looking forward to investment in Indian and/or Asian stock markets.

As the market behaviour changes quickly and frequently within a short span of time, the research work on dynamic linkages among the stock market plays an important role in financial market research. This article models the DCC parameters on the basis of model diagnosis and the scope of this article is limited to stock markets only; thus, the future scope of this may be extended by using more dynamic econometric models such as the conditional quintile regression model and forecasting techniques by considering different financial markets.

Footnotes

Acknowledgement

The authors are grateful to the anonymous referees of the journal for their extremely useful suggestions to improve the quality of the article. Usual disclaimers apply.

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The authors received no financial support for the research, authorship and/or publication of this article.

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