Globalization and Emerging Stock Market Integration:
             Evidence from a FIVECM-MGARCH Model
                    ...
I. Introduction


       Globalization has been gaining momentum in recent years. Financial markets are at
the forefront o...
shares. 1 The Chinese deregulation of financial markets picked up steam after China joined
the WTO in 2001.
       Officia...
Integrated Vector Error Correction Model (FIVECM) to detect the co-movements of the pairs
of stock markets, namely China-I...
The rest of the paper is organized as follows: Section II offers a review of the relevant
literature; Section III describe...
Von-Furstenberg (1990) show stronger co-movement among international stock indices after
the 1987 crash. Worthington et al...
VECM (see, e.g. Bailllie and Bollerslev, 1994; Baillie, 1996) to study the co-movement of
the pairs of markets. Furthermor...
observations is 731. Logarithms of the stock indices for the Indian, Chinese and U.S. markets

at time t are denoted INDt ...
Ψ (B ) Φ(B )(1 − B) d z t = at
          −1
                          ˆ                                                   ...
Because it is often observed that the conditional volatilities of financial return series
exhibit time varying characteris...
eigenvalues of matrix A1 ⊗ A1 + B1 ⊗ B1 are less than unity in modulus, where ⊗ stands for

Kronecker product of matrices ...
have long memory. Therefore, we proceed to fit an ARFIMA model to each of the series. The
choice of ARFIMA order is based ...
nonsignificance of both φ12 and φ 21 terms indicates that there is no return transmission
                         1      ...
tests for both standardized residuals and squared residual series in Table 6 are larger than
conventional levels, we can c...
simple relation between the volatilities of the two index return series. Again, the highly
significant diagonal elements i...
significance of both ARCH(2,1) and GARCH(2,1) terms indicates that there is volatility
spillover from the Indian market to...
response to disequilibrium with both the U.S. and Chinese markets; the Chinese market
adjusts to disequilibrium conditions...
References
Aizenman, J., (2003), “On the hidden links between financial and trade opening,” NBER
       working paper w990...
Forbes, K.J. and R. Rigobon, (2002), “No contagion, only interdependence: Measuring stock
        market comovements,” Jou...
on the Asia-Pacific region: Does it matter?” Journal of Asian Economics, 14,
       219-241.
Hsiao, C. (1981), “Autoregres...
indices,” Review of Economics and Statistics, 55(3), 356-361.
Stock, J.H. and M.W.Watson, (1993). “A simple Estimator of C...
Table 1.    Descriptive Statistics for the Return Series
  Statistic                 ΔINDt                       ΔCHN t   ...
Table 4. Stationarity Tests on Cointegration Residuals
     Test                     Range Over Standard Deviation (R/S) t...
Table 6. FIVECM-BEKK(1,1) Model for India-U.S.
                                             Panel A. Model Estimates
     ...
Table 7. FIVECM-BEKK(1,1) Model for China-U.S.

                                          Panel A. Model Estimates
       ...
Table 8. FIVECM-BEKK(1,1) Model for India-China

                                           Panel A. Model Estimates
   Pa...
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Globalization and Emerging Stock Market Integration: Evidence ...

  1. 1. Globalization and Emerging Stock Market Integration: Evidence from a FIVECM-MGARCH Model Heng Chen, Bento J. Lobo* and Wing-Keung Wong RMI Working Paper No. 07/23 Submitted: March 27, 2007 Abstract This paper examines the issue of globalization by studying the interaction of two of the fastest growing emerging markets of our time, namely China and India. We study the integration of the two stock markets and contrast this relationship with the interaction each market has with global markets, using the U.S. stock market as a proxy. We use a Fractionally Integrated Vector Error Correction Model (FIVECM) to examine the cointegration mechanism between markets. By augmenting the FIVECM with a multivariate GARCH formulation, we study the first and second moment spillover effects simultaneously. Our empirical results show that all three pairs of stock markets are fractionally cointegrated. The U.S. stock market plays a dominant role in the relations with the other two markets, whereas there is an interactive relationship between the Indian and Chinese stock markets. In particular, the Indian stock market dominates the first moment feedback with the Chinese market, while China dominates the second moment feedback with India. Our study supports the notion that the forces of globalization have contributed to the integration of national stock markets. Keywords: Globalization, Stock markets, Fractionally Integrated Vector Error Correction Model, Multivariate GARCH. Heng Chen Wing-Keung Wong NUS Risk Management Institute and NUS Risk Management Institute and Department of Economics Department of Economics Faculty of Arts and Social Sciences National University of Singapore National University of Singapore Block S16, Level 5, 6 Science Drive 2 21 Lower Kent Ridge Road Singapore 117546 Singapore 119077 Tel: (65) 6516-6014 Phone: (65) 65168-974 Fax: (65) 6775-2646 Email: stach@nus.edu.sg Email: rmiwwk@nus.edu.sg Bento J. Lobo NUS Risk Management Institute and University of Tennessee at Chattanooga Department of Finance 615 McCallie Avenue Chattanooga TN 37343, USA. Phone: 423-425-1700 Email: Bento-Lobo@utc.edu * Dr. Lobo is the U.C. Foundation Associate Professor of Finance in the College of Business at UTC where he teaches courses in Corporate Finance, International Finance and Financial Institutions & Markets at the undergraduate, MBA and EMBA levels. His research covers theoretical and applied issues in finance and economics including work in the areas of monetary policy, domestic & international asset valuation, project analysis and political risk. He is also extensively involved in consulting. © 2007 Heng Chen. Views expressed herein are those of the author and do not necessarily reflect the views of the Berkley-NUS Risk Management Institute (RMI).
  2. 2. I. Introduction Globalization has been gaining momentum in recent years. Financial markets are at the forefront of this process. The last two decades have witnessed rapid international capital mobility in the form of both direct and indirect investments. This phenomenon is a result of the increasing interaction of world economies, both developed and emerging. The liberalization of capital markets coupled with advances in information technology have also contributed to this rapidly moving process. This paper aims to contribute to our understanding of the globalization and integration of stock markets by examining the bilateral interaction of two of the fastest growing emerging markets of our time, namely China and India. We contrast this relationship with the relationship each market has with global markets using the U.S. stock market as a proxy. Home to almost one-third of all humanity, India and China have averaged real GDP growth of 9 percent and 6 percent per year over the last two decades, respectively, and have become the second and fourth largest economies in the world in PPP-adjusted GDP terms, according to the World Bank. The world’s largest communist state (China) and the world’s largest democracy (India) have been growing in different ways. While manufacturing accounts for over 50 percent of China’s GDP, India’s growth has been more knowledge-intensive, with services accounting for almost two-thirds of GDP. Moreover, while China attracted $60 billion in FDI in 2004, India attracted roughly a tenth of global FDI flows in the same period. Although the Indian stock market has a much longer history than its Chinese counterpart, it was not till early 1991 that financial liberalization reforms commenced, at roughly the same time that the Chinese stock market took birth. In September 1992, foreign institutional investors were permitted to invest in the Indian stock market. Meanwhile, the Chinese stock market has kept evolving during its 15 year history, thanks to continuing reform and liberalization measures. Nonetheless, unique trading restrictions and capital controls mean that foreign and domestic investors in China must trade separately and in different types of 2
  3. 3. shares. 1 The Chinese deregulation of financial markets picked up steam after China joined the WTO in 2001. Official trade between India and China resumed in 1978 and joint efforts to boost mutual economic activity has resulted in China becoming India’s second largest trading partner in 2005, with growth rates suggesting that China could replace the U.S. as India’s principal trading partner in the near future. 2 A deeper understanding of the links between the Indian and Chinese stock markets could shed light on the extent to which these economies are integrated. Increasing globalization of the world economy should have an impact on the behavior of national stock markets. The relaxation of economic barriers and developments in information technology should induce stronger stock market integration. With integrated stock markets, information originating from one market should be important to other markets. This assumption has motivated an intensive area of empirical research on the transmission of information across equity markets. However, existing work on emerging markets shows that in the presence of high trade openness, external de jure financial openness is neither sufficient nor necessary for the de facto openness of domestic capital markets (Aizenman, 2003). It would appear then that the degree of global integration of capital markets must be empirically examined. This paper studies the information spillover between the Chinese and Indian stock markets from 1993 to 2004. We contrast this relationship with the relationship each market has with global markets using the U.S. stock market as a proxy. 3 We apply a Fractionally 1 In the official markets, China offers three types of shares. "A" share listings are for Chinese investors; companies that are joint ventures are allowed to sell "B" shares to foreigners, and these are also traded on the exchange. B share prices are quoted in yuan, but transactions are settled in U.S. dollars in Shanghai and Hong Kong dollars in Shenzhen. "H" shares are mainland company listings in overseas markets. Chinese enterprises have listed H shares in Hong Kong and foreign markets. 2 The average annual growth rate in trade from 1995-2003 was 26.4 percent. 3 The influence of the U.S. economy and stock market on global markets is pervasive and well documented. Both China and India rely heavily on the U.S. market. The U.S. is the biggest trade partner and largest foreign investment source to both India and China. As of 2004, the trade volume between India and the U.S. was $22.1 billion, whereas that of the U.S. and China was about $170 billion, around 10 percent of China’s GDP. Also, India and China are important export destinations for the U.S., and both countries finance a significant portion of the U.S. budget deficit by buying U.S. Treasury bonds with their fast growing foreign exchange reserves. 3
  4. 4. Integrated Vector Error Correction Model (FIVECM) to detect the co-movements of the pairs of stock markets, namely China-India, China-U.S. and India-U.S. The FIVECM is superior to the standard VECM because it reveals not merely long-run equilibrium relations and short-run dynamics among co-integrated variables, but also accounts for the possible long memory in the cointegration residual series which may otherwise skew the estimation. Moreover, we augment the FIVECM with a multivariate GARCH representation to control for the conditional autocorrelations in the second moments of the series. The FIVECM-GARCH model is relatively novel in this line of research. Within this modeling framework, empirical lead-lag relations in the level as well as volatility of the series are simultaneously studied. The capital asset pricing model (CAPM) across countries hinges largely on the relations among international stock markets. Harvey (2005) points out that market integration plays a critical role in theoretical asset pricing models for emerging markets. 4 Given recent developments in India and China an exploration of the cointegration relations among the markets studied in this paper could provide useful insights for researchers and practitioners. This paper contributes to the literature in two important ways: first, by examining the scarcely-studied bilateral relationship and spillover effects between the Indian and Chinese stock markets, and second, by utilizing a sophisticated fractionally integrated VECM augmented with a multivariate GARCH specification. Our empirical results show that while the three markets are fractionally co-integrated, only one stock index series in each pair seems to be bound by the long run equilibrium implied by cointegration. We find that the Indian and Chinese markets show bidirectional feedback. Specifically, we find that while the Chinese market leads the Indian market in return transmission, the Indian market leads the Chinese market in volatility (or information) spillover. The U.S. market leads the Indian market in information (or second moment) spillover and leads the Chinese market in return (or first moment) transmission. Given the close economic ties among the U.S., China and India, this study seeks to explore the degree of integration and bi-directional information spillover between the three markets. 4 For asset pricing issues in emerging markets, see also Harvey (1995); Wong and Bian (2000) derive a robust inference in asset pricing models using a Bayesian approach. 4
  5. 5. The rest of the paper is organized as follows: Section II offers a review of the relevant literature; Section III describes the data and methodology; section IV presents the empirical results and implications. Finally, section V concludes. II. Literature Review Studies of stock market linkages have taken many paths. The earliest stemmed from portfolio diversification theory which assumes that relations among prices of different financial markets could help to reduce risks and increase returns of investment portfolios. Since the work of Grubel (1968) on the benefits of international portfolio diversification, the relationships among financial markets have been widely studied. Early studies by Ripley (1973) and Hilliard (1979) generally find low correlations among national stock markets, which validate the benefits of diversification in international portfolio management. Much work has been done since on the co-movement of the U.S. and other markets (e.g. Hamao et al., 1990, Koutmos and Booth, 1995). 5 Much of the empirical research in this area pivots on the North American, European and Pacific-Basin markets, namely the most developed markets in the world. Related work by Bekaert and Harvey (1997) on the nature of volatility shows that volatility in emerging markets is less influenced by world factors. By contrast, Ng (2000) finds that both world and regional factors influence the Pacific-Basin stock markets although the influence of world factors is more intense. Swartz (2006) highlights this issue in showing that emerging Asian country indices respond to regional and global shocks differently. China, for instance, has become increasingly sensitive to global common shocks especially since 2001 when China entered the WTO. On the other hand, India’s responsiveness to regional shocks has increased more than its responsiveness to global shocks in the post 1992 era of financial liberalization. In general, financial crises appear to increase the interdependence between 6 markets. Applying a VAR and impulse response function analysis, Jeon and 5 However, not all research supports integration among international stock markets. Koop (1994) uses Bayesian methods to conclude that there are no common stochastic trends in stock prices across selected countries. 6 However, not all research supports integration among international stock markets. Koop (1994) uses Bayesian 5
  6. 6. Von-Furstenberg (1990) show stronger co-movement among international stock indices after the 1987 crash. Worthington et al (2003) find heightened causal price linkages among Asian equity markets in the period surrounding the Asian financial crisis. In spite of high trade openness, existing empirical work has generally failed to find evidence of international financial integration for China (Huang et al, 2000; Hsiao et al, 2003). By contrast, Girardin and Liu (2006), using a regime-switching error correction model on weekly data, find that the Chinese A-share market index shared a long term relationship initially with the S&P500, and then with the Hong Kong Hang Seng index. They attribute financial integration to information flows and a growing awareness of valuation concepts among Chinese domestic investors over the period. Aizenman’s (2003) conclusion that de jure financial openness (as in China) is neither a sufficient nor a necessary condition for foreign stock prices to influence domestic stock prices is borne out by Phylaktis and Ravazzolo (2002) who demonstrate cases of financial integration without capital account liberalization, as well as liberalization without integration. Another major motivation for this paper stems from econometric considerations. This paper investigates the bilateral relations between stock markets by employing a bivariate cointegration technique. The cointegration study is conducted within a VECM framework (e.g. Engle and Granger, 1987; Granger, 1988). 7 However, the disequilibrium error used in the VECM applied on financial series is often neither I(1) nor I(0), but rather a fractionally integrated process, I(d), where − 0.5 < d < 0.5 . 8 Without accounting for the long memory (when d<0.5) feature of the disequilibrium error, the true relations among cointegrated variables may well be distorted. Therefore, this paper employs a Fractionally Integrated methods to conclude that there are no common stochastic trends in stock prices across selected countries.Forbes and Rigobon (2002) claim that after correcting for one theoretical flaw which engenders overestimation of correlation coefficients, recent currency crises (starting from the U.S. market crash in 1987) have not resulted in contagion, although there is a high level of market co-movement which they call interdependence. 7 One of the earliest applications of causality detection on money-income data was done in Hsiao (1981), see also bivariate causality modeling by Granger, et al (2000). Another major theoretical contributor to vector cointegration is Johansen (1988a, 1988b). 8 Fractionally integrated processes and long memory processes were pioneered by Granger (1981) and Geweke and Porter-Hudak (1983), see Booth and Tse (1995) and Breitung and Hassler (2002).for more detailed discussion. 6
  7. 7. VECM (see, e.g. Bailllie and Bollerslev, 1994; Baillie, 1996) to study the co-movement of the pairs of markets. Furthermore, since conditional heteroskedasticity is often observed in high-frequency time series, this paper augments the FIVECM model with a bivariate GARCH representation of the volatility process to capture the second moment autocorrelations in the return series. 9 In particular, we employ the BEKK (1,1) model proposed by Engle and Kroner (1995) to model the evolution of conditional variances. Since there are no restrictions imposed on the coefficient matrices of the conditional mean and variance, lead-lag relations in the first as well as second moments are simultaneously revealed in this model. 10 Of course, the benefits of a FIVECM-BEKK model come at the cost of more complicated computations. We propose a multi-step procedure to estimate this complex model, the details of which are discussed in the next section. III. DATA AND METHODOLOGY 3.1 Data description This paper uses weekly stock index data from January 2, 1991 through December 29, 2004. 11 We use the Bombay Stock Exchange National index for the Indian stock market, the All Shares Index from the Shanghai Stock Exchange for China, and the S&P 500 index for the U.S. market. All data are from Datastream. We use weekly data in order to alleviate the effects of noise characterizing daily or higher frequency data. Further, to avoid the so called day-of-the-week effect, we use Wednesday-close indices, since stock markets are said to be more volatile on Monday and Friday (Lo and MacKinlay, 1988). The total number of 9 Although White (1980) provides a heteroskedasticity-robust covariance estimator, direct modeling of conditional heteroskedasticity by GARCH type models is currently preferred especially in time series studies. 10 Long memory time series models augmented by GARCH have been adopted in the literature to model a variety of economic and financial issues, see, for example, Cheung and Lai (1993), Baillie et al (1996), Lien and Tse (1999) and Gil-Alana (2003). 11 We only report the results for the indices expressed in local currencies. The results for data denominated in U.S. dollars draw similar conclusions and thus we skip reporting these results. The reason these results are similar is that during the study period, the Chinese Renminbi (RMB) was strictly pegged to US dollar and the Indian Rupee was flexible within a narrow band. 7
  8. 8. observations is 731. Logarithms of the stock indices for the Indian, Chinese and U.S. markets at time t are denoted INDt , CHNt and USt respectively. The features of corresponding return series ΔINDt , ΔCHNt and ΔUSt are summarized in Table 1, in which the unconditional correlation coefficients between pair of return series are also exhibited. 3.2 Methodology Firstly, to establish the cointegration relation between stock indices, we employ a Granger two-step procedure. Put briefly, in the first step, we fit the following dynamic ordinary least squares model (DOLS) to each pair of stock indices: p y1t = α + β y 2t + ∑ ω ′ Δy j =− p j 2t − j + ηt (1) where y1t and y2t are a pair of stock indices involving INDt , CHNt and USt ; the estimate βˆ shown by Stock and Watson (1993), unlike the usual OLS estimates, is super-consistent as well as efficient. Then the estimated cointegrating residual is constructed as follows: ˆ ˆ z t = y1t − β y 2t . (2) In the second step, examining the long memory property for each pair of series, we ˆ utilize an R/S statistic on the zt series. If the cointegrating residual is confirmed to follow a long memory ( I (d ) , −0.5 < d < 0.5 ) process, then the series y1t and y2t are said to be fractionally cointegrated with each other 12 , and we proceed to fit an autoregressive fractionally integrated moving average (ARFIMA) model 13 to each residual series in the following form to estimate the order of fractional integration as ARFIMA model is more flexible to capture both long memory and short run dynamics in time series: 12 Otherwise, if the residual series is tested to be I(0) process, the underlying stock index series are cointegrated in the usual sense. See, for example, Baillie and Bollerslev (1994) and Breitung and Hassler (2002) for more discussions on the long memory properties. 13 See, for example, Baillie and Bollerslev (1994) and Breitung and Hassler (2002) for more discussions on the model. 8
  9. 9. Ψ (B ) Φ(B )(1 − B) d z t = at −1 ˆ (3) where, Ψ(B) and Φ(B) are MA and AR polynomials respectively, B is a backward shift operator, at is an i.i.d. noise interpreted as the disequilibrium error in the error correction model to follow. Once the cointegration relations among variables are established, Engle and Granger (1987) show that cointegration leads to the Vector Error Correction Model (VECM) which is extremely powerful in modeling the long-run as well as short-run dynamics among the cointegrated variables. We incorporate the VECM with the FIVECM by accounting for the ˆ fractional integration property in z t series which presents persistent impact on the cointegration relations of underlying series. Following Granger (1986), the bivariate FIVECM can be depicted in the following form: m m Δy1t = c1 + α 1 [(1 − B ) d − (1 − B )]z t + ∑ φ11 Δy1t −i + ∑ φ12 Δy 2t −i + ε 1t ˆ i i i =1 i =1 m m (4) Δy 2t = c 2 + α 2 [(1 − B ) − (1 − B )]z t + ∑ φ Δy1t −i + ∑ φ Δy 2t −i + ε 2t d ˆ i 21 i 22 i =1 i =1 ′ where Δy t = (Δy1t , Δy 2t ) is the differenced index series vector or return vector of (ΔINDt , ΔUS t )′ or (ΔCHN t , ΔUS t )′ or (ΔINDt , ΔCHN t )′ , z t −1 is estimated from Equation ˆ ˆ (2) using estimate of β from regression model (1) fitted to respective stock index vectors and d is obtained from model (3). It is noteworthy that we employ a VAR(m) structure for ′ the FIVECM model with m=1 in this paper in which ε t = (ε 1t , ε 2t ) is the error vector ′ assumed to follow a bivariate t-distribution; the coefficients α = (α 1 , α 2 ) capture the reaction of the series when they deviate from the long-run equilibrium; the magnitudes of the α i ' s represent the speeds of the adjustment; and the lag terms in (4) account for the AR structure of the Δy t series, while their coefficients ( φij ) reflect the return transmissions between different markets. 9
  10. 10. Because it is often observed that the conditional volatilities of financial return series exhibit time varying characteristics, we employ a multivariate GARCH (MGARCH) model to capture the heteroskedasticity in the return series (Brooks, et al, 2003). In other words, we model the conditional mean and conditional variance of the return series simultaneously. ⎛ σ 11 σ t12 ⎞ Particularly, let ∑ t ≡ cov t −1 (ε t ) ≡ ⎜ t21 ⎜σ ⎟ denote the variance-covariance matrix of ε t ⎝ t σ t22 ⎟ ⎠ conditioning on past information, we employ the most general and flexible MGARCH model, namely the BEKK model (Engle and Kroner, 1995) in the following form: p q ∑ t = A0 A0 + ∑ Ai (ε t −i ε t′−i )Ai′ + ∑ B j ∑ t − j B′j ′ (5) i =1 j =1 where A0 is a lower triangular matrix, Ai ' s and B j ' s are unrestricted coefficient matrices, and ∑ t is symmetric and positive semi-definite. Usually, p = 1 and q = 1 suffice for modeling volatility in financial time series. With this formulation, the dynamics of ∑ t are fully displayed in the sense that the dynamics of the conditional variance as well as the conditional covariance are modeled directly, thereby allowing for volatility spillovers across series to be observed. The volatility spillover effect is indicated by the off-diagonal entries of coefficient matrices A1 and B1 . This can be seen from the expansion of BEKK(1,1) into individual dynamic equations: σ t11 = ( A0 ) + ⎡ A111ε1t −1 + A112ε 2t −1 ⎤ + ⎡( B111 ) σ t111 + 2 B112 B111σ t121 + ( B112 ) σ t221 ⎤ , 11 2 2 2 2 ⎣ ⎦ ⎢ ⎣ − − − ⎥ ⎦ σ t22 = ( A021 ) + ( A022 ) + ⎡ A121ε1t −1 + A122ε 2t −1 ⎤ + ⎡( B121 ) σ t111 + 2 B121 B122σ t211 + ( B122 ) σ t221 ⎤ , 2 2 2 2 2 ⎣ ⎦ ⎢ ⎣ − − − ⎥ ⎦ σ t = A0 A0 + A1 A1 ε 1t −1 + ( A1 A1 + A1 A1 )ε1t −1ε 2t −1 + A1 A1 ε 2t −1 + B1 B1 σ t −1 + 12 11 21 11 21 2 11 22 12 21 12 22 2 11 21 11 (B 12 1 B121 + B1 B122 ) σ t121 + B112 B122σ t221 . 11 − − (6) The system of the above equations is much more complicated than a univariate GARCH model because of interactions among the two conditional variances and residuals. The time-varying correlation coefficient can be obtained from the conditional variances and covariances after the model is estimated. Since there are no restrictions on the coefficients, estimation of the BEKK model involves more computation than other MGARCH models. The stationarity condition for the volatility series in a BEKK (1,1) model is that the 10
  11. 11. eigenvalues of matrix A1 ⊗ A1 + B1 ⊗ B1 are less than unity in modulus, where ⊗ stands for Kronecker product of matrices 14 . By jointly estimating the FIVECM-BEKK model (i.e. systems (4) and (6)), the coefficient estimates are expected to be more efficient 15 . The time-varying correlation coefficient between two return series can be obtained from the conditional variances and covariances after the model is estimated. IV. Empirical Results 4.1 Cointegration setup The first necessary step in a cointegration study is to test the non-stationarity of the involved series. To achieve this, we test for non-stationarity by applying the ADF 16 and PP 17 unit root tests, to the logarithms of INDt, USt and CHNt. Consistent with previous findings in the finance literature, the results displayed in Table 2 show that all the indices are found to be I(1) processes under both tests. Next, we test the possible cointegrating relation for each pair of stock indices: ( INDt ,US t )′ , (CHN t , US t )′ and ( INDt , CHN t )′ , by fitting the DOLS model in (1) with lag length p = 2 . The estimated model coefficients exhibited in Table 3 show that all the estimated βˆ for the three regressions are highly significant. In order to confirm the cointegration relation between series in each pair, we test the stationarity of the cointegration ˆ residuals by first constructing the zt series according to (2) for each pair of series using the estimated cointegrating coefficient βˆ obtained from the corresponding DOLS model. These constructed disequilibrium error series are denoted z us , z us and z chn , respectively ind chn ind (where the superscript indicates the endogenous variable, and the subscript denotes the exogenous variable). Thereafter, the R/S test for long memory is applied to these three residual series. The results, presented in Table 4, confirm that all the three residual series 14 For conditions of the general BEKK model, see Proposition 2.7 in Engle and Kroner (1995). 15 Dittmann (2004) provides an estimation procedure in similar spirit. 16 ADF refers to Augmented Dickey - Fuller test, related references include Dickey and Fuller (1979,1981). 17 PP refers to the unit root test developed by Phillips and Perron (1988). 11
  12. 12. have long memory. Therefore, we proceed to fit an ARFIMA model to each of the series. The choice of ARFIMA order is based on the ACF and PACF of the residual series. 18 The fitted results are shown in Table 5. It is noteworthy that all the estimated values of d in the three ARFIMA models fall into the range − 0.5 < d < 0.5 , and estimated coefficients for the AR terms produce three stationary series, although the serial correlations of the three series are persistent. In particular, the three d-values are all positive and less than 0.5, confirming that the cointegrating variables follow long memory stationary processes. Thus, we conclude that the three stock markets are fractionally cointegrated with each other. Next, we proceed to fit a FIVECM-MGARCH model to the return series data. Specifically, we fit the FIVECM-BEKK(1,1) model to the three pairs of log-differenced index series, i.e. (ΔINDt , ΔUS t )′ , (ΔCHN t , ΔUS t )′ and (ΔINDt , ΔCHN t )′ , with the first variable in each pair being the endogenous variable. The AR(1) structure chosen in the FIVECM conditional mean equations is based on an examination of the ACF and PACF of the series. The error structure in each model follows a bivariate student t-distribution because the normality test applied to the return series shows strong non-normality in the series. 4.2 India-U.S. stock market results The estimates of parameters for the bivariate FIVECM in (4) for the Indian and U.S. stock markets are presented in Panel A of Table 6. To interpret the results of the FIVECM model in (4), we first focus on the conditional mean estimates. Note that ci (i=1,2) are the constant terms in the conditional mean equations, φ ij ,k (i=1, j=1,2, k=1,2) are the AR coefficients, and α i (i=1,2) are the adjustment speed parameters. Both c1 and c2 are statistically significant, implying that the long-run unconditional means of both the Indian BSE index return, ΔINDt , and S&P 500 index return, ΔUS t , are positive. The significance of both φ11 and φ 22 terms verifies the serial dependence in the index returns. The 1 1 18 Details are available upon request. 12
  13. 13. nonsignificance of both φ12 and φ 21 terms indicates that there is no return transmission 1 1 from the U.S. market to the Indian market, and vice versa. In other words, the U.S. stock market does not Granger-cause or lead the Indian stock market, and vice versa. In addition, α1 is significantly negative, indicating that the Indian market adjusts when it drifts away from long-run equilibrium. However, α 2 is not statistically significant. This suggests that the cointegrating relation between the two markets does impose certain restrictions on the movement of the Indian stock market, but not on the U.S. stock market. Secondly, the estimates for the conditional variance equations in (5) reveal further relationship between the two markets. { A(i, j )} are the elements of the constant matrix A0 in the variance equation (5). The statistical significance of the diagonal elements of the constant matrix shows that the unconditional variances of the two index return series are positive. The first-order ARCH(i,j) and GARCH(i,j) terms are the elements of the ARCH and GARCH coefficient matrices A1 and B1 , respectively. The diagonal elements of the ARCH and GARCH matrices are highly significant, indicating that the ARCH and GARCH effects are substantial in both index return series, supporting the notion that GARCH modeling is appropriate for our dataset. The significance of the off-diagonal elements ARCH(1,2) and GARCH(1,2) indicates that there is unidirectional information transmission from the U.S. stock market to the Indian stock market. In short, our results point to unidirectional volatility spillover from the U.S. to the Indian market. The strong influence of the U.S. stock market on the Indian stock market is expected, since the former is the largest stock market built upon the most influential economy in the world and the U.S. is the most important trading partner and export destination for Indian goods and services. The model diagnostics listed in Panel B of Table 6 include the three test statistics and their corresponding p-values applied to the individual residual series separately. Specifically, the Jarque-Bera Normality tests are conducted on the two residual series; Ljung-Box tests of white noise are applied to standardized residuals and squared residual series to test for serial correlation in the first and second moments of residuals. Since all the p-values of Ljung-Box 13
  14. 14. tests for both standardized residuals and squared residual series in Table 6 are larger than conventional levels, we can conclude that the fitted model is adequate and successful in capturing the dynamics in the first as well as second moments of the index return series. ˆ ˆ ˆ ˆ ˆ ˆ Finally, the eigenvalue moduli of A1 ⊗ A1 + B1 ⊗ B1 (where A1 and B1 are estimated ARCH and GARCH coefficient matrices respectively) are 0.988, 0.956, 0.944, 0.927. Since they are all less than unity, we conclude that the conditional volatilities of the two stock return series are stationary. 4.3. China-U.S. stock market results The estimates for the FIVECM-BEKK model fitted on the China-U.S. pair of stock returns are reported in Panel A of Table 7. Firstly, we find that the significance of c2 indicates that the long-run mean of ΔUS t is positive, whereas that of ΔCHN t is not rejected to be zero as shown by the non-significant c1 , which is consistent with the finding in Table 6. The significance of φ11 and φ 22 terms indicates that serial dependence in ΔCHN t 1 1 and ΔUS t is non-trivial. The cross terms in the AR structure reveal an interactive relationship between the two series. In particular, the highly significant φ12 points to return 1 transmission from the U.S. market to the Chinese market. The negative sign indicates that an upward move in the S&P index (positive return) would cause China’s stock market to move down in the following week. In addition, the non-significant φ 21 implies that the return 1 transmission is unidirectional from the U.S. market to the Chinese market. The cointegration between the two markets is indicated by the adjustment speed coefficient α1 which is significantly negative. Its close-to-one magnitude implies that the disequilibrium between the two markets will likely be corrected within one period, namely one week in this paper. The non-significance of α 2 shows that the U.S. market is not bound by the cointegration relationship between the two markets. Secondly, the results for the conditional variance equations confirm existence of a 14
  15. 15. simple relation between the volatilities of the two index return series. Again, the highly significant diagonal elements in the ARCH and GARCH matrices confirm the strong dependence in their conditional volatilities. However, no feedback relation between the conditional variances of series (ΔCHN t , ΔUSt )′ is detected, because none of the off-diagonal terms in the ARCH and GARCH matrices is significant. In other words, there is no information transmission between the two markets. Finally, the positive and significant A(1,1) and A(2,2) coefficients suggest nonzero unconditional variances for the two return series. The diagnostic test statistics for this FIVECM-BEKK model reported in Panel B support ˆ ˆ ˆ ˆ the adequacy of the model used. The moduli of the four eigenvalues of A1 ⊗ A1 + B1 ⊗ B1 for this model are 0.996, 0.977, 0.976 and 0.976, all are less than unity, inferring that the ′ conditional volatilities of the (ΔCHN t , ΔUS t ) series are deemed to be stationary. 4.4 India-China stock market results The estimates for the FIVECM-BEKK model fitted on the India-China pair of stock returns are reported in Panel A of Table 8. The coefficients are notated as in Table 6. The significance of both φ11 and φ 22 terms indicates that serial dependence in ΔINDt and 1 1 ΔCHN t is substantial. It is noteworthy that φ12 is marginally significant with a p-value of 1 0.0675, inferring existence of return transmission from the Chinese market to the Indian market. This, coupled with the non-significant φ 21 , implies that the Chinese market 1 Granger-causes the Indian market, but not vice versa. The adjustment speed parameter α1 is significantly negative, implying that when the relationship between the two markets strays from equilibrium, it will restore to the long-run equilibrium soon. The other adjustment parameter α 2 is not significant, though it has the expected sign. Secondly, the estimates for the conditional variance equations reveal an interesting relationship between the volatilities of the two index return series. In particular, the 15
  16. 16. significance of both ARCH(2,1) and GARCH(2,1) terms indicates that there is volatility spillover from the Indian market to the Chinese market, and the spillover appears to be unidirectional since the other two off-diagonal coefficient estimates are insignificant. In other words, when it comes to the transmission of shocks, it is the Indian market which leads the Chinese market. The highly significant diagonal estimates of the ARCH and GARCH coefficient matrices show that the time varying features of the second moments of the individual series are pronounced. At the same time, the diagonal elements of the constant matrices A(1,1) and A(2,2) are significantly positive, suggesting nonzero unconditional variances for the two return series. In sum, the overall picture revealed by the model estimates suggests that the Chinese market passes return realizations to the Indian market, while the latter leads in the transmission of volatility. Model diagnostics for the FIVECM-BEKK model listed in Panel B indicate the adequacy of our model in capturing the dynamics of the conditional means and variances. Also, the ˆ ˆ ˆ ˆ four eigenvalues of A1 ⊗ A1 + B1 ⊗ B1 for this model are 0.979, 0.940, 0.938 and 0.904 ′ which are all less than unity. Therefore, the conditional volatilities of (ΔINDt , ΔCHN t ) are deemed to be stationary. However, the Ljung-Box test for white noise on ΔCHN t points to the need to further investigate the dynamics of the Chinese market. V. Conclusion This paper employs a fractionally integrated vector error correction (FIVECM) model to investigate the bilateral relations between the Indian, U.S. and Chinese stock markets. By augmenting the FIVECM model with a multivariate GARCH, we reveal simultaneously the cointegrating relations among the index series, and the dynamic dependence and lead-lag relations in the first and second conditional moments of the index return series. The estimation results confirm our conjecture that there is fractional cointegration or long-run equilibrium for each pair of stock markets. In each of the three models, only one market is found to adjust to restore equilibrium. In particular, the Indian market adjusts in 16
  17. 17. response to disequilibrium with both the U.S. and Chinese markets; the Chinese market adjusts to disequilibrium conditions with the U.S. We also find that while the U.S. market does not Granger-cause or lead the Indian market with respect to return (first moment) transmission, it does lead the Chinese market in this respect. However, while there is unidirectional volatility (second moment) transmission from the U.S. market to the Indian market, no such feedback is observed between the U.S. and Chinese markets. The Indian and Chinese markets are found to be more interactive. In addition to being fractionally cointegrated, there are interesting lead-lag relations between the two markets. Specifically, we find that the Chinese market leads the Indian market in return transmission, whereas the latter leads the former in information spillover. The finding that the three markets are pair-wise fractionally cointegrated implies that international investors might be limited in their ability to diversify long-run portfolios by investing in the Indian, Chinese and United States stock markets. However, some diversification benefits are likely since the degree of market integration appears to be imperfect. The fact that volatility shocks originating in the U.S. market do not transmit to China’s market may be an indication that the large capital flows from the U.S. to China are still mainly in the form of foreign direct investment. However, the fact that the Indian stock market responds to shocks in U.S. stock markets might be indicative of the fact that the Indian capital market is less restrictive in terms of portfolio flows compared to the Chinese market. The large and growing economic relationship between India and China could be the force driving the spillovers between these two markets. Our study supports the notion that the forces of globalization have contributed to the integration of national stock markets. The domino effect caused by the most recent 9% drop in the Shanghai stock market in February 2007 justifies the motivation and timing of this paper. 17
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  22. 22. Table 1. Descriptive Statistics for the Return Series Statistic ΔINDt ΔCHN t ΔUSt N 730 730 730 Mean 0.0004 0.0005 0.0003 Median 0.0007 0.0001 0.0004 Std Dev. 0.0055 0.0092 0.0032 Skewness 0.2401 2.2566 -0.0860 Kurtosis 3.1796 23.811 1.7700 Correlation ΔINDt 1.0000 ΔCHN t 0.0427 1.0000 ΔUSt 0.0893 -0.0078 1.0000 Note: The indices are the Bombay Stock Exchange National index (INDt), the S&P 500 index (USt), and all Shares Index of Shanghai Stock Exchange (CHNt). The kurtosis, computed with S-PLUS, is the excess kurtosis. Table 2. Unit Root Tests for the Indices Test ADF PP Index t-statistic p-value t-statistic p-value INDt 1.6392 0.9757 1.4371 0.9629 CHN t -2.6150 0.2739 -2.8206 0.1899 2.1153 0.9922 2.2809 0.9950 US t Note: The indices are the Bombay Stock Exchange National index (INDt), the S&P 500 index (USt), and All Shares Index of the Shanghai Stock Exchange (CHNt). The ADF tests applied on the logarithms of INDt and USt are with constant and one lag, the ADF test on logarithm of CHNt is with constant, trend and one lag. The corresponding PP tests have the same structure without lag terms. Table 3. Estimates of the Dynamic OLS Model for Each Pair of Indices Statistic (INDt, USt) (CHNt, USt) (INDt, CHNt) Estimate P-value Estimate P-value Estimate P-value Estimate αˆ 4.2644 0.0000 -0.7179 0.0009 4.9064 0.0000 βˆ 0.4707 0.0000 1.1454 0.0000 0.3605 0.0000 Note: The endogenous variable in each model is marked in bold. For purposes of space, estimates for lead and lag terms are not reported, but are available upon request. 22
  23. 23. Table 4. Stationarity Tests on Cointegration Residuals Test Range Over Standard Deviation (R/S) test Index Test statistic P-value ind z us 4.8760 <0.01 chn z us 5.6635 <0.01 ind z chn 4.4440 <0.01 Note: The residual series are constructed using Equation (2) in the text based on the corresponding DOLS model in Table 3. Table 5. ARFIMA Estimation for the Residuals Estimate ind chn ind z us z us z chn Parameter Value P-value Value P-value Value P-value D 0.1562 0.0291 0.0872 0.0288 0.2007 0.0110 AR(1) 0.8386 0.0000 0.9696 0.0000 0.8249 0.000 AR(2) 0.1235 0.0497 NA NA 0.1251 0.0510 ind chn ind Note: The series z us , z us and z chn are constructed with equation (2). The superscript denotes the endogenous variable, while the subscript denotes the exogenous variable. The choice of AR lags is based on an examination of the ACF and PACF. ARFIMA model is defined in (3). 23
  24. 24. Table 6. FIVECM-BEKK(1,1) Model for India-U.S. Panel A. Model Estimates Parameter Estimate Std. Error t value Pr(>|t|) c1 0.0033 0.0013 2.4884 0.0065 c2 0.0027 0.0006 4.1521 0.0002 φ 1 11 0.5180 0.2515 2.0596 0.0199 -0.0289 0.1266 -0.2288 0.4095 φ12 1 φ 21 1 -0.1085 0.1262 -0.8594 0.1952 φ 1 22 -0.0831 0.0681 -1.2199 0.1115 α1 -0.4602 0.2539 -1.8124 0.0352 α2 0.1068 0.1270 0.8407 0.2004 A(1,1) 0.0105 0.0020 5.1415 0.0000 A(2,1) -0.0004 0.0011 -0.3678 0.3566 A(2,2) 0.0022 0.0007 3.1198 0.0009 ARCH(1,1) 0.3137 0.0430 7.2927 0.0000 ARCH(1,2) -0.1563 0.0732 -2.1342 0.0166 ARCH(2,1) 0.0219 0.0204 1.0733 0.1417 ARCH(2,2) 0.2581 0.0377 6.8400 0.0000 GARCH(1,1) 0.9082 0.0243 37.361 0.0000 GARCH(1,2) 0.0446 0.0286 1.5614 0.0594 GARCH(2,1) -0.0027 0.0115 -0.2369 0.4064 GARCH(2,2) 0.9595 0.0115 83.470 0.0000 Panel B. Model Diagnostics Test Normality test White noise test GARCH effect test (Jarque-Bera) (Ljung-Box) (Ljung-Box) Series statistic p-value statistic p-value statistic p-value ΔINDt 117.7 0.0000 11.3 0.5064 8.7 0.7256 ΔUSt 55.2 0.0000 11.5 0.4840 13.2 0.3556 Note: The estimated model is FIVECM-BEKK(1,1) (Equation systems (4) + (6)); the endogenous variable is ΔINDt ; the error structure is bivariate t-distribution, the estimated degrees of freedom are 9.412 with standard error 1.895. The number of lags in the two Ljung-Box tests is 12 and the test statistic follows a Chi-square distribution with 12 degrees of freedom. 24
  25. 25. Table 7. FIVECM-BEKK(1,1) Model for China-U.S. Panel A. Model Estimates Parameter Estimate Std. Error t value Pr(>|t|) c1 0.0006 0.0012 0.4560 0.3243 c2 0.0031 0.0007 4.8063 0.0000 φ 1 11 1.0259 0.1495 6.8638 0.0000 φ 1 12 -1.0403 0.1850 -5.6223 0.0000 φ 1 21 0.0103 0.0682 0.1515 0.4398 φ 1 22 -0.1403 0.0864 -1.6239 0.0524 α1 -0.9496 0.1535 -6.1877 0.0000 α2 -0.0213 0.0688 -0.3093 0.3786 A(1,1) 0.0074 0.0012 6.0161 0.0000 A(2,1) -0.0001 0.0013 -0.0621 0.4752 A(2,2) 0.0018 0.0006 2.9136 0.0018 ARCH(1,1) 0.3520 0.0316 11.148 0.0000 ARCH(1,2) 0.0612 0.0711 0.8601 0.1950 ARCH(2,1) -0.0043 0.0133 -0.3263 0.3721 ARCH(2,2) 0.2272 0.0322 7.0495 0.0000 GARCH(1,1) 0.9227 0.0125 73.86 0.0000 GARCH(1,2) -0.0071 0.0228 -0.3107 0.3780 GARCH(2,1) 0.0005 0.0052 0.1034 0.4589 GARCH(2,2) 0.9718 0.0077 125.5 0.0000 Panel B. Model Diagnostics Test Normality test White noise test GARCH effect test (Jarque-Bera) (Ljung-Box) (Ljung-Box) Series statistic p-value statistic p-value statistic p-value ΔCHNt 1530.1 0.0000 17.4 0.1351 14.1 0.2963 ΔUSt 79.9 0.0000 11.8 0.4619 14.3 0.2834 Note: The estimated model is FIVECM-BEKK(1,1) (Equation systems (4) + (6)); the endogenous variable is ΔCHNt ; the error structure is bivariate t-distribution, the estimated degrees of freedom are 6.861 with standard error 1.005. The number of lags employed in the two Ljung-Box tests is 12 and the test statistic follows a Chi-square distribution with 12 degrees of freedom. 25
  26. 26. Table 8. FIVECM-BEKK(1,1) Model for India-China Panel A. Model Estimates Parameter Estimate Std. Error t value Pr(>|t|) c1 0.0027 0.0013 2.0835 0.0188 c2 0.0009 0.0013 0.6522 0.2572 φ 1 11 0.4198 0.2278 1.8426 0.0329 φ12 1 -0.1249 0.0835 -1.4961 0.0675 φ 1 21 0.0016 0.2256 0.0070 0.4972 φ 22 1 0.1094 0.0867 1.2615 0.1038 α1 -0.3419 0.2290 -1.4935 0.0679 α2 0.0446 0.2284 0.1953 0.4226 A(1,1) 0.0126 0.0026 4.8700 0.0000 A(2,1) -0.0031 0.0025 -1.2122 0.1129 A(2,2) 0.0064 0.0022 2.8774 0.0021 ARCH(1,1) 0.3310 0.0498 6.6506 0.0000 ARCH(1,2) -0.0138 0.0333 -0.4149 0.3392 ARCH(2,1) -0.0833 0.0432 -1.9263 0.0272 ARCH(2,2) 0.3419 0.0328 10.423 0.0000 GARCH(1,1) 0.8947 0.0326 27.482 0.0000 GARCH(1,2) 0.0146 0.0125 1.1665 0.1219 GARCH(2,1) 0.0465 0.0303 1.5354 0.0626 GARCH(2,2) 0.9241 0.0123 75.223 0.0000 Panel B. Model Diagnostics Normality test White noise test GARCH effect test Test (Jarque-Bera) (Ljung-Box) (Ljung-Box) statistic p-value statistic p-value statistic p-value Series ΔINDt 113.1 0.0000 12.4 0.4123 10.4 0.5827 ΔCHNt 995.3 0.0000 27.9 0.0057 14.7 0.2580 Note: The estimated model is FIVECM-BEKK(1,1) (Equation systems (4) + (6)); the endogenous variable is ΔINDt ; the error structure is bivariate t-distribution, the estimated degrees of freedom are 6.361 with standard error 0.932. The number of lags employed in the two Ljung-Box tests are 12 and the test statistics follow a Chi-square distribution with 12 degrees of freedom. 26

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