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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 NUS Risk Management Institute and Department of Economics Faculty of Arts and Social Sciences National University of Singapore 21 Lower Kent Ridge Road Singapore 119077 Phone: (65) 65168-974 Email: [email protected]
Wing-Keung Wong NUS Risk Management Institute and Department of Economics National University of Singapore Block S16, Level 5, 6 Science Drive 2 Singapore 117546 Tel: (65) 6516-6014 Fax: (65) 6775-2646 Email: [email protected]
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: [email protected]
* 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).
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
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
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
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
markets. 6 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
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 5.05.0 <<− d .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
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
observations is 731. Logarithms of the stock indices for the Indian, Chinese and U.S. markets
at time are denoted , and respectively. The features of corresponding
return series , and
t tIND tCHN tUS
tINDΔ tCHNΔ tUSΔ 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:
t
p
pjjtjtt yyy ηωβα +Δ′++= ∑
−=−221 (1)
where 1ty and 2ty are a pair of stock indices involving , and ; the
estimate 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:
tIND tCHN tUS
β
ttt yyz 21ˆˆ β−= . (2)
In the second step, examining the long memory property for each pair of series, we
utilize an R/S statistic on the series. If the cointegrating residual is confirmed to follow a
long memory ( ,
tz
( )I d 0.5 0.5d− < < ) process, then the series 1ty and 2ty are said to be
fractionally cointegrated with each other 12 , and we proceed to fit an autoregressive
fractionally integrated moving average (ARFIMA) model13 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
( ) ( ) ttd azBBB =−ΦΨ − ˆ)1(1 (3)
where, Ψ(B) and Φ(B) are MA and AR polynomials respectively, B is a backward shift
operator, is an i.i.d. noise interpreted as the disequilibrium error in the error correction
model to follow.
ta
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
fractional integration property in 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:
tz
t
m
iit
im
iit
it
dt
t
m
iit
im
iit
it
dt
yyzBBcy
yyzBBcy
21
2221
121222
11
2121
111111
ˆ)]1()1[(
ˆ)]1()1[(
εφφα
εφφα
+Δ+Δ+−−−+=Δ
+Δ+Δ+−−−+=Δ
∑∑
∑∑
=−
=−
=−
=−
(4)
where is the differenced index series vector or return vector of
or or
( ′ΔΔ=Δ ttt yyy 2,1 )
),( ′ΔΔ tt USIND ),( ′ΔΔ tt USCHN ),( ′ΔΔ tt CHNIND , is estimated from Equation
(2) using estimate of from regression model (1) fitted to respective stock index vectors
and 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
1ˆ −tz
β
d
( )′= ttt 21 ,εεε is the error vector
assumed to follow a bivariate t-distribution; the coefficients capture the
reaction of the series when they deviate from the long-run equilibrium; the magnitudes of the
( ′= 21,ααα )
si 'α represent the speeds of the adjustment; and the lag terms in (4) account for the AR
structure of the series, while their coefficients (tyΔ ijφ ) reflect the return transmissions
between different markets.
9
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.
Particularly, let denote the variance-covariance matrix of ( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛≡≡∑ − 2221
1211
1covtt
ttttt σσ
σσε tε
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:
( ) ∑∑=
−=
−− ′∑+′′+′=∑q
jjjtj
p
iiititit BBAAAA
1100 εε (5)
where is a lower triangular matrix, and are unrestricted coefficient
matrices, and is symmetric and positive semi-definite. Usually, and
0A sAi ' sB j '
t∑ 1p = 1q =
suffice for modeling volatility in financial time series. With this formulation, the dynamics of
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 and
t∑
1A 1B . This can be seen from the expansion of
BEKK(1,1) into individual dynamic equations:
( ) ( ) ( )
( ) ( ) ( ) ( )
2 2 2211 11 11 12 11 11 12 11 12 12 220 1 1 1 1 2 1 1 1 1 1 1 1 1
2 2 2 2222 21 22 21 22 21 11 21 22 21 22 220 0 1 1 1 1 2 1 1 1 1 1 1 1 1
12 11 21 11 21 20 0 1 1 1 1
2 ,
2 ,
(
t t t t t t
t t t t t
t t
A A A B B B B
A A A A B B B B
A A A A
σ ε ε σ σ σ
σ ε ε σ σ
σ ε
− − − − −
− − − − −
−
⎡ ⎤⎡ ⎤= + + + + +⎣ ⎦ ⎢ ⎥⎣ ⎦⎡ ⎤⎡ ⎤= + + + + + +⎣ ⎦ ⎢ ⎥⎣ ⎦
= + +
( )11 22 12 21 12 22 2 11 21 111 1 1 1 1 1 2 1 1 1 2 1 1 1 1
12 21 11 22 12 12 22 221 1 1 1 1 1 1 1
)
. (t t t t
t t
A A A A A A B B
B B B B B B
ε ε ε σ
σ σ− − − −
− −
+ + + +
+ +
tσ
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
eigenvalues of matrix are less than unity in modulus, where stands for
Kronecker product of matrices
1111 BBAA ⊗+⊗ ⊗
14. By jointly estimating the FIVECM-BEKK model (i.e.
systems (4) and (6)), the coefficient estimates are expected to be more efficient15. 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 ADF16 and PP17 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:
, and ),( ′tt USIND ),( ′tt USCHN ),( ′tt CHNIND , by fitting the DOLS model in (1) with lag
length . The estimated model coefficients exhibited in Table 3 show that all the
estimated 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
residuals by first constructing the series according to (2) for each pair of series using the
estimated cointegrating coefficient obtained from the corresponding DOLS model.
These constructed disequilibrium error series are denoted , and , respectively
(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
2p =
β
tz
β
indusz chn
usz indchnz
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
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 in the three ARFIMA models fall into
the range , 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.
d
5.05.0 <<− d
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. , ),( ′ΔΔ tt USIND ),( ′ΔΔ tt USCHN and ),( ′ΔΔ tt CHNIND , 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 (i=1,2) are the
constant terms in the conditional mean equations, (i=1, j=1,2, k=1,2) are the AR
coefficients, and
ic
ikj ,φ
iα (i=1,2) are the adjustment speed parameters. Both and are
statistically significant, implying that the long-run unconditional means of both the Indian
BSE index return, , and S&P 500 index return,
1c 2c
tINDΔ tUSΔ , are positive. The significance
of both and terms verifies the serial dependence in the index returns. The 111φ 1
22φ
18 Details are available upon request.
12
nonsignificance of both and terms indicates that there is no return transmission
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,
112φ 1
21φ
1α is significantly negative, indicating that the Indian market adjusts when it drifts away
from long-run equilibrium. However, 2α 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
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 and
0A
1A 1B , 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
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.
Finally, the eigenvalue moduli of (where and 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.
1111ˆˆˆˆ BBAA ⊗+⊗ 1A 1B
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
indicates that the long-run mean of
2c
tUSΔ is positive, whereas that of is not
rejected to be zero as shown by the non-significant , which is consistent with the finding in
Table 6. The significance of and terms indicates that serial dependence in
and is non-trivial. The cross terms in the AR structure reveal an interactive
relationship between the two series. In particular, the highly significant points to return
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 implies that the return
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
tCHNΔ
1c
111φ 1
22φ tCHNΔ
tUSΔ
112φ
121φ
1α 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 2α 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
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 ( )′ΔΔ tt USCHN , 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
the adequacy of the model used. The moduli of the four eigenvalues of
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
1111ˆˆˆˆ BBAA ⊗+⊗
( )′ΔΔ tt USCHN , 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 and terms indicates that serial dependence in and
is substantial. It is noteworthy that is marginally significant with a p-value of
0.0675, inferring existence of return transmission from the Chinese market to the Indian
market. This, coupled with the non-significant , implies that the Chinese market
Granger-causes the Indian market, but not vice versa.
111φ 1
22φ tINDΔ
tCHNΔ 112φ
121φ
The adjustment speed parameter 1α 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 2α 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
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
four eigenvalues of for this model are 0.979, 0.940, 0.938 and 0.904
which are all less than unity. Therefore, the conditional volatilities of
1111ˆˆˆˆ BBAA ⊗+⊗
( )′ΔΔ tt CHNIND , are
deemed to be stationary. However, the Ljung-Box test for white noise on points to
the need to further investigate the dynamics of the Chinese market.
tCHNΔ
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
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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21
Table 1. Descriptive Statistics for the Return Series Statistic tINDΔ tCHNΔ tUSΔ
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
tINDΔ 1.0000
tCHNΔ 0.0427 1.0000 tUSΔ 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
ADF PP Test Index t-statistic p-value t-statistic p-value
tIND 1.6392 0.9757 1.4371 0.9629 tCHN -2.6150 0.2739 -2.8206 0.1899
tUS 2.1153 0.9922 2.2809 0.9950
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 (INDt, USt) (CHNt, USt) (INDt, CHNt) Statistic
Estimate Estimate P-value Estimate P-value Estimate P-value
α 4.2644 0.0000 -0.7179 0.0009 4.9064 0.0000
β 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
Table 4. Stationarity Tests on Cointegration Residuals Range Over Standard Deviation (R/S) test Test
Index Test statistic P-value indusz 4.8760 <0.01 chnusz 5.6635 <0.01 indchnz 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 indusz chn
usz indchnz Estimate
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
Note: The series , and 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).
indusz chn
usz indchnz
23
Table 6. FIVECM-BEKK(1,1) Model for India-U.S.
Panel A. Model Estimates Parameter Estimate Std. Error t value Pr(>|t|)
1c 0.0033 0.0013 2.4884 0.0065
2c 0.0027 0.0006 4.1521 0.0002 111φ 0.5180 0.2515 2.0596 0.0199
1φ12 -0.0289 0.1266 -0.2288 0.4095
121φ -0.1085 0.1262 -0.8594 0.1952 122φ -0.0831 0.0681 -1.2199 0.1115
1α -0.4602 0.2539 -1.8124 0.0352
2α 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 Normality test (Jarque-Bera)
White noise test (Ljung-Box)
GARCH effect test (Ljung-Box)
Test 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
; 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.
tINDΔ
24
Table 7. FIVECM-BEKK(1,1) Model for China-U.S.
Panel A. Model Estimates Parameter Estimate Std. Error t value Pr(>|t|)
1c 0.0006 0.0012 0.4560 0.3243
2c 0.0031 0.0007 4.8063 0.0000 111φ 1.0259 0.1495 6.8638 0.0000 112φ -1.0403 0.1850 -5.6223 0.0000 121φ 0.0103 0.0682 0.1515 0.4398
122φ -0.1403 0.0864 -1.6239 0.0524
1α -0.9496 0.1535 -6.1877 0.0000
2α -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 Normality test (Jarque-Bera)
White noise test (Ljung-Box)
GARCH effect test (Ljung-Box)
Test 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
; 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.
tCHNΔ
25
Table 8. FIVECM-BEKK(1,1) Model for India-China
Panel A. Model Estimates Parameter Estimate Std. Error t value Pr(>|t|)
1c 0.0027 0.0013 2.0835 0.0188
2c 0.0009 0.0013 0.6522 0.2572 111φ 0.4198 0.2278 1.8426 0.0329 112φ -0.1249 0.0835 -1.4961 0.0675 121φ 0.0016 0.2256 0.0070 0.4972
122φ 0.1094 0.0867 1.2615 0.1038
1 α -0.3419 0.2290 -1.4935 0.0679
2α 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 (Jarque-Bera)
White noise test (Ljung-Box)
GARCH effect test (Ljung-Box)
Test Series
statistic p-value statistic p-value statistic p-value
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
; 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.
tINDΔ
26