An empirical analysis of information transmission mechanism and the trilateral relationshi

Description
With rapid economic development over the last few decades, Mainland China has emerged as a crucial
role in the global markets. One might wonder whether Mainland China could serve as an international
center and exhibit significant influences over the neighboring markets. Particularly, the Hong Kong and
Taiwan markets, being geographically near and culturally close to China, are supposed to be deeply
influenced. Utilizing trivariate BEKK (Baba, Engle, Kraft, and Kroner)-GARCH (Generalized Auto Regressive
Conditional Heteroskedasticity) modes, the study attempts to investigate the trilateral relationship
among these markets during the 2000e2012 period from the perspective of information transmission.
The findings indicate that the Mainland China stock market significantly affected the Hong Kong and
Taiwan markets through volatility spillover effects during the sample period. Accordingly, the Mainland
China stock market is found to play a leading role in information transmission. Moreover, this study
utilizes the BEKK-GARCH model to depict conditional variances and dynamic correlations among these
markets. The evidence implies that these markets are closely linked and gradually integrated.

An empirical analysis of information transmission mechanism and the trilateral
relationship among the Mainland China, Hong Kong, and Taiwan stock markets
Tzu-Lun Huang
*
, Hsiou-Jen Kuo
Department of Finance, National Sun Yat-sen University, Kaohsiung City, Taiwan, R.O.C
a r t i c l e i n f o
Article history:
Received 26 May 2013
Accepted 15 August 2013
Available online 26 March 2015
Keywords:
BEKK GARCH
Causality
Information ?ow
Return transmission
Volatility spillover effect
a b s t r a c t
With rapid economic development over the last few decades, Mainland China has emerged as a crucial
role in the global markets. One might wonder whether Mainland China could serve as an international
center and exhibit signi?cant in?uences over the neighboring markets. Particularly, the Hong Kong and
Taiwan markets, being geographically near and culturally close to China, are supposed to be deeply
in?uenced. Utilizing trivariate BEKK (Baba, Engle, Kraft, and Kroner)-GARCH (Generalized Auto Regres-
sive Conditional Heteroskedasticity) modes, the study attempts to investigate the trilateral relationship
among these markets during the 2000e2012 period from the perspective of information transmission.
The ?ndings indicate that the Mainland China stock market signi?cantly affected the Hong Kong and
Taiwan markets through volatility spillover effects during the sample period. Accordingly, the Mainland
China stock market is found to play a leading role in information transmission. Moreover, this study
utilizes the BEKK-GARCH model to depict conditional variances and dynamic correlations among these
markets. The evidence implies that these markets are closely linked and gradually integrated.
© 2015, College of Management, National Cheng Kung University. Production and hosting by Elsevier
Taiwan LLC. All rights reserved.
1. Introduction
With a growing integration of global markets, the interaction of
international capital markets has drawn the attention of numerous
researchers. In view of the importance of information (Allen, 1990;
Grossman &Stiglitz, 1980; Kihlstrom, 1974; Radner &Stiglitz, 1984),
related studies tend to focus on how information is transmitted
between international markets (Engle & Susmel, 1993; Hamao,
Masulis, & Ng, 1990; Karolyi, 1995; Kim & Rui, 1999; Koutmos &
Booth, 1995; Lin, Engle, & Ito, 1994; Wong, Chau, & Yiu, 2007).
The information transmission mechanism mainly consists of two
channels: return transmission (Malkiel & Fama, 1970) and volatility
spillovers (Kyle, 1985; Ross, 1989). Although many empirical studies
have investigated information transmission mechanisms in devel-
oped countries (Hamao et al., 1990; Karolyi, 1995), little attention
has been paid to emerging markets.
This study aims to re-examine the trilateral relationship among
the Mainland China, Hong Kong, and Taiwan stock markets, because
these markets have gone through signi?cant changes in the past
decade. For example, China has experienced amazing economic
growth with annual average growth rates above 9% since 2002
(source: the United Nations Statistics Division). The in?uences of the
?nancial markets in Mainland China should not be ignored. One
might wonder whether the Mainland China market would work as
an international center like the US market. Moreover, these markets
have gone through several global ?nancial crises since 2000,
including the 2007 subprime mortgage crisis, the 2008 ?nancial
tsunami, andthe 2010Europeansovereigndebt crisis. It is interesting
to have a retrospective comparison among these stock markets.
The international center hypothesis suggests that the Mainland
China market should play a leading role in the transmission of in-
formation (Cheung & Mak, 1992; Eun & Shim, 1989). Because
Taiwan and Hong Kong are geographically near and culturally close
to China, both of them are supposed to be in?uenced by Mainland
China. In contrast, the home bias hypothesis implies that the
market information primarily ?ows from a domestic market to the
external markets. As such, in?uences of domestic markets should
dominate those of foreign markets. The home bias effect might
come fromthe superior information of domestic investors over that
of foreign investors. Accordingly, the Taiwan or Hong Kong stock
market should be in?uenced more signi?cantly by domestic market
information than by information from Mainland China.
* Corresponding author. National Sun Yat-sen University, No.70, Lien-Hai, Rd,
Kaohsiung City 80424 , Taiwan, R.O.C.
E-mail address: [email protected] (T.-L. Huang).
Peer review under responsibility of College of Management, National Cheng
Kung University.
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Asia Paci?c Management Review 20 (2015) 65e78
The geographic proximity and homogenous culture among the
Taiwan, Hong Kong, and Mainland China stock markets help infor-
mation?owsmoothlyamong these markets. Therefore, information
transmission among these markets should work more ef?ciently.
However, prior studies have documented controversial evidence.
For example, Chakravarty, Sarkar, and Wu (1998) found that there is
little relation between the China and Hong Kong stock markets.
Likewise, using a restricted VAR (Vector autoregression) model as
well as the Bernanke-Sims decomposition to compute the impulse
response, Wu and Lin (2003) found that Chinese stock markets are
weakly linked to the markets in Taiwan and Hong Kong. In contrast,
Lamand Qiao (2009) used nonlinear Granger causality tests to study
information transmission among the stock markets of Greater
China, showing that information transmissions have recently been
strengthened and that China's stock markets are well connected
with their neighbor markets, Taiwan and Hong Kong.
In this context, we adopt multivariate BEKK (Baba, Engle, Kraft,
and Kroner)-GARCH (Generalized Auto Regressive Conditional
Heteroskedasticity) models to investigate the information trans-
mission mechanism among the Mainland China [Shanghai Stock
Exchange Composite Index (SSEC)], Hong Kong [Hang Seng Index
(HSI)], and Taiwan [TSEC (Taiwan Stock Exchange Corporation)
Weighted Index (TWII)] stock markets. Using VAR(1)-BEKK(1, 1) and
VECM(1)-BEKK(1, 1) models, we endeavor to identify the volatility
spillover effect, and examine the trilateral relationship among these
markets. Previous studies tend to apply bivariate models, which
only can explore bilateral relationships. Using these trivariate
models, we can analyze how these stock markets simultaneously
interact with one another and capture the cross-market in?uences
concurrently. Moreover, our analysis allows for a notable asymme-
try feature. Speci?cally, we classify unexpected events into positive
and negative ones, so as to examine whether market volatility in-
creases with bad news. We also plot conditional variances to
observe how market volatilities grow and decline through the
sample period that coincides with several ?nancial crises. Finally,
we utilize the BEKK-GARCH model to generate conditional corre-
lation coef?cients so as to capture the dynamic volatility linkages.
We ?nd that the function of return transmission seems to be
insigni?cant among these markets. Only the lagged returns on HSI
can predict market returns onTWII. This link between HSI and TWII
is also supported by the Granger causality test. By contrast, parts of
the empirical results indicate that SSEC can signi?cantly in?uence
HSI and TWII through the volatility spillover effects. These spillover
effects are unidirectional, implying that Mainland China might play
a role of international center just like the US. However, these cross-
market in?uences are relatively small in comparison with the do-
mestic in?uences from the home markets. Therefore, our ?nding
also supports the home bias hypothesis.
The rest of this paper is organized as follows. The next section
provides some backgrounds and literature review. Section 3 pre-
sents the econometric methodology, focusing on the symmetric and
asymmetric BEKK-GARCH models. Section 4 provides descriptive
statistics of the sample data. Section 5 presents the empirical re-
sults, which will be discussed in Section 6. Section 7 concludes.
2. Backgrounds and literature review
As mentioned above, return transmission and volatility spill-
overs are two main channels of the information transmission
mechanism, both of which are essential characteristics of ?nancial
assets. On the one hand, the ef?cient market hypothesis (Malkiel &
Fama, 1970) suggests that asset prices have revealed all available
information in an ef?cient market. Accordingly, changes in asset
prices indicate incorporation of new information. Since assets are
so intertwined, assets can affect one another through price
changes. The in?uence may even pass beyond borders in an inte-
grated market system. On the other hand, asset prices might exhibit
volatility, especially when information comes unexpectedly in
clusters. Kyle (1985) argued that information would be revealed in
the volatility of stock prices rather than the price itself. Using the
no-arbitrage martingale approach, Ross (1989) also con?rmed a
positive relation of volatility to the rate of information ?ow. The
phenomenon of volatility spillover is a type of comovement among
asset prices, suggesting that the volatility of one market might in-
?uence the volatility of another market.
Volatility spillover has been extensively studied because of its
important role in managing risk and assessing market stability.
Many studies found evidence of volatility spillovers across inter-
national markets. For example, Kim, In, and Viney (2001) identi?ed
the volatility spillover effect in the Australian stock, bond, and
money markets. Yoon and Kang (2004) reported a unidirectional
volatility spillover effect from the stock market to the bond market
of Korea, while Kim, Moshirian, and Wu (2006) found unidirec-
tional volatility spillovers from the bond market to stock market in
European countries. Therefore, studies on volatility spillover can
help us to understand how information is transmitted across assets
and markets. There were also studies on volatility spillovers be-
tween spot and futures markets, stock indices (Booth & So, 2003;
Chan, Chan, & Karolyi, 1991), interest rates (Crain & Lee, 1995),
re?ned petroleum (Ng & Pirrong, 1996), wheat (Crain & Lee, 1996),
and foreign exchange (Wang & Wang, 2001). Following these pio-
neering studies, mechanisms of information transmission among
?nancial markets have become the focus of recent studies.
In addition, volatility has been believed to be larger in a bear
market than in a bull market (Cappiello, Engle, & Sheppard, 2006;
French, Schwert, & Stambaugh, 1987; Nelson, 1991; Schwert, 1989).
Black (1976) and Christie (1982) explain the phenomenon with the
leverage effect, suggesting that upsurge in ?nancial leverage due to
falling stock prices might increase volatility. Alternative explana-
tions include a positive feedback effect of volatility (Bekaert & Wu,
2000; Campbell & Hentschel, 1992), short selling restrictions
(Jayasuriya, Shambora, & Rossiter, 2009), behavioral preferences
(Hens & Steude, 2006), and expected risk premium (Cho & Engle,
1999). For an overview see Talpsepp and Rieger (2010).
3. Methodology
In the context, two multivariate GARCH models, VAR(1)-
BEKK(1,1) and VECM(1)-BEKK(1, 1), are employed to examine the
trilateral relationship among the Mainland China (SSEC), Hong
Kong (HSI), and Taiwan stock markets (TWII). Prior studies tend to
investigate the ?rst-moment return relationship among interna-
tional markets, but ignore the second-moment effectsevolatility.
Since information affects both the ?rst- and the second-moment
returns, models without taking volatility into account may be
misspeci?ed, and produce incorrect inferences (Chan et al., 1991;
Wong et al., 2007). As result, the multivariate GARCH models,
which consider both mean returns and return volatility, provide an
appropriate approach to exploring the information transmission
mechanism. The present study focus on two channels of informa-
tion transmission: return transmission and volatility spillovers.
Speci?cally, the mean equations of these models are designed to
explore return transmission, while their variance equations, set in
the form of BEKK(1,1) GARCH, aim to investigate the volatility
spillovers among these markets.
3.1. Return transmission
When examining the return transmission among these stock
markets, each return series is modeled as a function of its own
T.-L. Huang, H.-J. Kuo / Asia Paci?c Management Review 20 (2015) 65e78 66
domestic market return lags and the cross market return lags.
Econometrically speaking, the domestic market return lags serve as
autoregressive (AR) terms that can remove linear dependency in
the series. The cross market return lags capture the ?rst moment
information transmission between markets. The lag structures for
SSEC, HSI, and TWII are identical because these stock markets have
overlapping trading hours. Fig. 1 illustrates the opening and closing
time of each market in terms of Universal Time code.
3.1.1. VECM(1)-BEKK(1, 1)
If SSEC, HSI, and TWII have a long-run equilibrium, at least one
cointegrated vector should exist among these index series. AVECM
model can describe the relationship, which can be modelled as:
DP
t
¼ PP
tÀ1
þGDP
tÀ1
þ ?
t
;
?
t
jU
tÀ1
Nð0; H
t
Þ;
(1)
where P
t
and ?
t
are 3X1 vectors. The former stands for a vector of
the logarithm of the SSEC, HSI, and TWII price indices at time t,
while the latter are random errors which represent innovation.
P¼ab', a is an adjustment coef?cient vector, b a cointegrating
vector, and G a short-term adjustment coef?cient matrix. Specif-
ically, a describes the speed of adjustment towards the long run
equilibrium, while b allows for the cointegrated relations among
these markets.
3.1.2. VAR(1)-BEKK(1,1)
The mean equations of the VAR(1)-BEKK(1,1) model can explore
the casual relationships among SSEC, HSI, and TWII, which can be
expressed as:
r
t
¼ DP
t
¼ m þgr
tÀ1
þ ?
t
;
?
t
jU
tÀ1
Nð0; H
t
Þ;
(2)
where m, r
t
and ?
t
are 3X1 vectors. Speci?cally, m is a vector of
constants, r
t
a vector of stock index returns at time t, and ?
t
rep-
resents random errors that are assumed to follow a normal distri-
bution conditional on the information set U
tÀ1
. The squares and
cross products of innovation ?
t
determine the 3X3 conditional
variance-covariance matrix H
t
in the BEKK model [see Eq. (3)], and
g is a 3X3 matrix of estimated coef?cients.
The ef?cient market theory (Malkiel &Fama, 1970) suggests that
all available information has been already re?ected in asset prices.
In other words, asset price at time t has incorporated all informa-
tion at that time, including a variety of possible factors that affect
the price movements. Therefore, we use raw returns at lag one to
predict their future changes. Consequently, shocks or unpredicted
changes, caused by news or unexpected events, are re?ected in the
disturbances ?
t
.
3.2. Volatility spillovers
To investigate the volatility linkage among SSEC, HSI, and TWII,
we specify the variance equations in the formof multivariate BEKK-
GARCH models. The BEKK model, proposed by Engle and Kroner
(1995), is an extension of univariate GARCH model (Bollerslev,
1986) that allows markets to affect one another through spillover
effects. In comparison, a univariate GARCH model fails to consider
conditional variances and covariances across equations due to its
oversimplifying speci?cation. As a result, when investigating the
volatility linkage between markets, a multivariate GARCHapproach
is preferred over the univariate setting.
However, the original BEKK model involves too many parame-
ters to estimate, leading to dif?culty in estimation. Speci?cally, A
full BEKK(p, q) model with n assets involves (p þq)kn
2
þn(n þ1)/2
parameters to estimate, leading to dif?culty in estimation, so it is
typically assumed p ¼ q ¼ k ¼ 1 in applications (Silvennoinen &
Ter€ asvirta, 2009). Accordingly, we also limit the length of lag pe-
riods by setting p ¼ 1 and q ¼ 1. This yields a trivariate BEKK(1, 1)
GARCH model, which can be expressed as:
H
t
¼ C
0
C þA
0
?
tÀ1
?
0
tÀ1
A þB
0
H
tÀ1
B; (3)
where H
t
, A, and B are square matrices of dimension 3X3 and C is an
upper triangular matrix. Matrix H
t
, a conditional variance-
covariance matrix at time t, can model time-varying volatilities in
these market indices. The diagonal elements in H
t
denote the
conditional variances of returns on these market indices, while the
off-diagonal elements stand for the covariances between the mar-
ket index returns. We use A to measure the impacts of unexpected
events, and B to analyze the volatility linkage. Technically speaking,
the off-diagonal elements in matrices A and B reveal the features of
shock and volatility spillovers, respectively.
3.3. Asymmetry effects
In addition, to capture the asymmetric response, we apply a
model of Kroner and Ng (1998), which can be written as:
H
t
¼ C
0
C þA
0
?
tÀ1
?
0
tÀ1
A þB
0
H
tÀ1
B þD
0
h
tÀ1
h
0
tÀ1
D; (4)
where:
h
tÀ1
¼
2
4
max
À
0; À?
1;tÀ1
Á
max
À
0; À?
2;tÀ1
Á
max
À
0; À?
3;tÀ1
Á
3
5
; (5)
and D is a 3X3 square matrix designed to model asymmetry in
variances and covariance through h
tÀ1
. If any coef?cient in D is
positive and signi?cant, then an asymmetric effect exists and bad
news will cause a larger volatility in markets than good news will.
Otherwise, insigni?cance suggests the effect of bad news may be
similar to that of good news; a negative value implies an opposite
effect, which may bring less (or even reduce) volatility in another
market.
3.4. Hypothesis testing
To determine whether the information transmission mecha-
nism among SSEC, HSI, and TWII supports the international center
hypothesis or the home bias hypothesis, the coef?cients in matrices
g, G, A, B, and D will be compared. Diagonal coef?cients in these
matrices represent domestic market effects, while off-diagonal
ones denote the cross-market in?uences. If the cross-market in-
?uences dominate the domestic market effects, the trilateral
Fig. 1. Trading hours for the Mainland China [Shanghai Stock Exchange Composite
Index (SSEC)], Hong Kong [Hang Seng Index (HSI)], and Taiwan [TSEC Weighted Index
(TWII)] stock markets.
T.-L. Huang, H.-J. Kuo / Asia Paci?c Management Review 20 (2015) 65e78 67
relationship among SSEC, HSI, and TWII supports the international
center hypothesis. Otherwise, the home bias hypothesis provides a
proper explanation for the information transmission mechanism.
Take b
ii
for example. Coef?cient b
ii
represents the impact of vola-
tility in market i on its own market i, while coef?cient b
ji
denotes
the Std. error ¼ standard error impact of volatility in market j on
market i, a type of cross-market in?uences. The summation of b
ji
(i sj) terms represents the aggregate volatility effect. Accordingly,
the following mathematical representations can describe the hy-
pothesis testing in the context:
International Center Hypothesis H
0
: jb
ii
j <
X
isj

b
ji

(6a)
Home Bias Hypothesis H
1
: jb
ii
j >
X
isj

b
ji

(6b)
3.5. Conditional variances
Expanding matrix H
t
in Eq. (4), we can see the howthe volatility
of each market is in?uenced more clearly:
h
11;t
¼ C
2
11
þ
À
a
11
?
1;tÀ1
þa
21
?
2;tÀ1
þa
31
?
3;tÀ1
Á
2
þ

b
2
11
h
11;tÀ1
þ b
2
21
h
22;tÀ1
þ b
2
31
h
33;tÀ1
þ2b
11
b
21
h
12;tÀ1
þ2b
11
b
31
h
13;tÀ1
þ2b
21
b
31
h
23;tÀ1

þ
À
d
11
h
1;tÀ1
þd
21
h
2;tÀ1
þd
31
h
3;tÀ1
Á
2
(7a)
h
22;t
¼

C
2
21
þ C
2
22

þ
À
a
12
?
1;tÀ1
þa
22
?
2;tÀ1
þa
32
?
3;tÀ1
Á
2
þ

b
2
12
h
11;tÀ1
þ b
2
22
h
22;tÀ1
þ b
2
32
h
33;tÀ1
þ2b
12
b
22
h
12;tÀ1
þ2b
12
b
32
h
13;tÀ1
þ2b
22
b
32
h
23;tÀ1

þ
À
d
12
h
1;tÀ1
þd
22
h
2;tÀ1
þd
32
h
3;tÀ1
Á
2
(7b)
h
33;t
¼

C
2
31
þ C
2
23
þ C
2
33

þ
À
a
13
?
1;tÀ1
þa
23
?
2;tÀ1
þa
33
?
3;tÀ1
Á
2
þ

b
2
13
h
11;tÀ1
þ b
2
23
h
22;tÀ1
þ b
2
33
h
33;tÀ1
þ2b
13
b
23
h
12;tÀ1
þ2b
13
b
33
h
13;tÀ1
þ2b
23
b
33
h
23;tÀ1

þ
À
d
13
h
1;tÀ1
þd
23
h
2;tÀ1
þd
33
h
3;tÀ1
Á
2
(7c)
The sample period ranges from January 2000, through
December 2012, coinciding with the 2007 subprime mortgage
crisis, the 2008 ?nancial tsunami, and the 2010 European sovereign
debt crisis. To observe how volatilities grow and decline through
these ?nancial crises, we plot conditional variances using the
estimated H
t
as in Eqs. (7a), (7b), and (7c).
3.6. Dynamic correlations
Moreover, we utilize the conditional variances and covariances
in H
t
to generate dynamic correlation coef?cients so as to capture
the time-varying relationships among the aggregate market. The
dynamic correlation coef?cient s
ij,t
between markets i and j can be
written as:
s
ij;t
¼
h
ij;t
????????
h
ii;t
q ????????
h
jj;t
q (8)
3.7. Estimation method
The trivariate GARCH model can be estimated using an iterative
MaximumLikelihood Estimation method applying the Berndt, Hall,
Hall and Hausman (BHHH) algorithm. The conditional log likeli-
hood function L with T observations can be expressed as:
L ¼ À0:5
X
T
t¼1

nlogð2pÞ þlogjH
t
j þlog

?
0
t
H
À1
t
?
t

(9)
As a robustness check, we alternatively apply the BHHH algo-
rithm and the Broyden, Fletcher, Goldfarb, and Shanno method in
the estimation procedure. To examine whether the estimation re-
sults are consistent under different distribution assumptions, we
further conduct the experiment repeatedly with normal distribu-
tion and student t distribution. To save space, only reliable results
with the maximum likelihood are presented in this study.
4. Data and descriptive statistics
As the asymmetric phenomenon tends to be more apparent
in daily data than in other low frequency data, we use daily data
on the SSEC, HSI and TWIIfrom January 2000, through December
2012. Data with days when any of these stock markets is closed
are removed, yielding a sample containing 3096 observations.
Table 1 displays the summary of descriptive statistics of these
return series. All the mean returns are close to zero and the
standard deviation estimates indicate that the Taiwan stock
market is relatively stable in comparison to the other two mar-
kets. All of these markets are skewed to the left and display
excess kurtosis, suggesting they are leptokurtic and have fat tails.
The results of the Jarque-Bera normality test also indicate
that the distributions of the returns on SSEC, HSI, and TWII are
not normally distributed. This justi?es the use of student t
distribution.
Table 1
Descriptive statistics of sample returns.
Series Obs Obs ¼ number of observations Mean Std error Minimum Maximum Skewness Kurtosis Jarque-Bera
SSEC 3096 0.0149 1.6474 À9.2562 9.4008 À0.0889 4.2416 2324.92
***
HSI 3096 0.0092 1.6311 À13.5820 13.4068 À0.0156 7.3073 6888.36
***
TWII 3096 -0.0042 1.5789 À9.9360 7.0550 À0.2455 2.8483 1077.65
***
***
indicates signi?cance at the 1% level.
HSI ¼ Hang Seng Index; Obs ¼ number of observations; SSEC ¼ Shanghai Stock Exchange Composite Index; Std. error ¼ standard error; TWII ¼ TSEC Weighted Index.
T.-L. Huang, H.-J. Kuo / Asia Paci?c Management Review 20 (2015) 65e78 68
Fig. 2A presents an overview of the overall stock price move-
ments during the sample period. (The series fromtop to bottomare
SSEC, TWII, and HSI, respectively.) For comparison purposes, we
also standardized these price movements with the ?rst day as a
base day and present themin Fig. 2B. (The series fromtop to bottom
are HSI, SSEC, and TWII, respectively.) The corresponding return
series of SSEC, HSI, and TWII are shown in Fig. 3, where we can
observe that market returns exhibited volatility clustering. Such
phenomenon con?rms the appropriateness of using the GARCH
model.
5. Empirical results
5.1. Estimation results of the VECM(1)-BEKK(1, 1) model
Before building the VECM model, we consider the unit root and
cointegration tests for SSEC, HSI, and TWII.
5.1.1. Unit root tests
In order to test the stationary property for each market index,
we carry out the unit roots tests with the Augmented Dickey-Fuller
(A) Stock price movements in TWII, HSI, and SSEC from 2000 through 2012
Year
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
0
5000
10000
15000
20000
25000
30000
35000
(B) Standardized Stock price movements in TWII, HSI, and SSEC from 2000 through 2012
TWII SSEC HSI
Year
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
0.0
1.0
2.0
3.0
4.0
Fig. 2. Stock price movements in Shanghai Stock Exchange Composite Index (SSEC), Hang Seng Index (HSI), and TSEC Weighted Index (TWII) from 2000 through 2012.
(A) Daily returns on SSEC
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
-0.100
-0.075
-0.050
-0.025
-0.000
0.025
0.050
0.075
0.100
(B) Daily returns on HSI
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
(C) Daily returns on TWII
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
-0.100
-0.075
-0.050
-0.025
-0.000
0.025
0.050
0.075
Fig. 3. Daily returns on Shanghai Stock Exchange Composite (SSEC) Index, Hang Seng Index (HSI), and TSEC Weighted Index (TWII) from 2000, through 2012.
T.-L. Huang, H.-J. Kuo / Asia Paci?c Management Review 20 (2015) 65e78 69
test (ADF) and the Phillips and Perron's nonparametric procedure
(PP). Table 2 presents the results for log index prices and return
series in panels A and B, respectively. As for the log price, both tests
fail to reject the null hypothesis of a unit root at the 5% signi?cance
level for all indices. Therefore, these market indices are nonsta-
tionary. Nevertheless, these return series are proved to be sta-
tionary, as shown in panel B.
5.1.2. Cointegration tests
Table 3 presents the results of the Johansen cointegration test
for these market indices. Since the trace and Max-Eigen statistics
exceed their critical values at the 5% signi?cance level, the null
hypothesis that these series are not cointegrated (r ¼ 0) is rejected,
con?rming a cointegration relationship among SSEC, HSI, and TWII.
In other words, a long-run relationship is found among these stock
markets. Thus, we can build the VECM model.
5.1.3. Return transmission in the VECM(1)-BEKK(1, 1) model
Table 4 shows parts of the estimation results of the VECM(1)-
BEKK(1, 1) model, where we can see that all adjustment co-
ef?cients are signi?cant at 1% level. Coef?cients a
1
and a
2
are
negative, implying that both SSEC and HSI would revert towards
the long run equilibrium. Moreover, the speed of adjustments is
slightly faster in the HSI (ja
1
j ¼ 1.2849) than in the SSEC
(ja
2
j ¼ 0.5333). In contrast, the positive coef?cients a
3
suggest that
TWII might move in a different direction.
Table 5 shows the results of mean equations of the VECM(1)-
BEKK(1, 1) model. Almost all coef?cients are insigni?cant (except
coef?cient G
23
), suggesting that no informational correlation exists
among these stock markets. In other words, past information among
thesemarkets couldnot beexploitedtopredict futurepricedynamics.
The ?nding might support the weak-form ef?cient market hypothe-
sis. However, due to insigni?cance, return transmission seems to be
absent in the trilateral relationships among SSEC, HSI, and TWII. One
exception appears in the in?uence of HSI on TWII (i.e., coef?cient
G
23
¼0.0961), where we can see that Dr
2,t-1
is signi?cantly related to
Dr
3,t
at 1%level. Basedonthis lead-lagrelationship, HSI canbe usedto
predict TWII. We can say information ?ows from HSI to TWII in the
short run in terms of information transmission. In contrast, the in-
?uence of Dr
3,t-1
on Dr
2,t-1
(i.e., coef?cient G
32
¼ À0.025) is insignif-
icant, so the information ?ow is unidirectional.
Table 5 also provides several diagnostic tests on the standard-
ized residuals and squared residuals in Panel B. The Ljung-Box
statistic for squared standardized residuals of HSI and TWII in-
dicates that there is no autocorrelation left in these series. However,
the signi?cant value of Z
1
[Q(30) ¼ 49.5636 (0.0138)] indicates that
there is still autocorrelation left in the residual series of SSEC. These
tests are mainly applied to each series separately. To check the
appropriateness of the VECM(1)-BEKK(1, 1) model, the multivariate
extension of the univariate Ljung-Box test e a multivariate port-
manteau test eis conducted. The results are presented in Panel B of
Table 6, which are found to be 288.43525 (0.21056) and 295.84964
(0.13410) under the symmetric and asymmetric speci?cations,
respectively. These signi?cant values of the multivariate test sta-
tistics suggest that both models are properly speci?ed.
5.1.4. Volatility spillovers in the VECM(1)-BEKK(1, 1) model
The estimation results of variance equations of the VECM(1)-
BEKK(1, 1) model are shown in Table 6. All diagonal elements in
matrices A and B are signi?cant at the 1% level, implying that the
volatility of each market is in?uenced by its own past volatility and
shocks.
5.1.4.1. In?uence of volatility spillover
This subsection focuses on matrix B, which is used to capture the
spillover effects among stock markets. Speci?cally, the elements b
ij
in matrix B measure volatility spillover from market i to market j.
With i ¼ j, the diagonal elements in matrix B (i.e., b
11
, b
22
, and b
33
)
refer to the effect of its own lagged volatility on the present vola-
tility, which is a kind of autocorrelation in conditional variances.
With i sj, the off-diagonal elements in matrix B indicate the cross-
Table 2
Results of the unit root tests.
Panel A. Unit root test for log price
ADF PP
Price index t Statistic T Statistic
SSEC 0.20979 À1.55848
HSI 0.29636 À1.33807
TWII À0.29018 À2.30580
Panel B. Unit root test for index returns
ADF PP
Return series t Statistic t Statistic
SSEC À9.11873** À55.8479**
HSI À9.53888** À56.8969**
TWII À9.16950** À53.7335**
Both tests were performed using 30 lags. ** indicates signi?cance at the 5% level.
ADF ¼ Augmented Dickey-Fuller test; HSI ¼ Hang Seng Index; PP ¼ Phillips and
Perron's nonparametric procedure; SSEC ¼ Shanghai Stock Exchange Composite
Index; TWII ¼ TSEC Weighted Index.
Table 3
Results of the Johansen cointegration test.
Null hypothesis Trace statistic p Max-Eigen statistic p
None 30.6034 0.0403 23.1670 0.0255
At most 1 7.4364 0.5275 5.3462 0.6977
At most 2 2.0902 0.1482 2.0902 0.1482
The Johansen cointegration test was performed using 30 lags for the logarithm of
the Shanghai Stock Exchange Composite Index (SSEC), Hang Seng Index (his), and
TSEC Weighted Index (TWII) price indices.
Table 4
Estimation results of the VECM(1)-BEKK(1, 1) modeleadjustment coef?cients.
The table shows the results of the VECM(1)-BEKK(1, 1) model:
DPt ¼ PP
tÀ1
þGDP
tÀ1
þ ?t ;
Ht ¼ C
0
C þA
0
?
tÀ1
?
0
tÀ1
A þB
0
H
tÀ1
B
where P
t
and ?
t
are 3X1 vectors. The former stands for the logarithm of the SSEC, HSI, and TWII price indices at time t, while the latter are random errors which
represent innovation. P ¼ ab
0
, a is an adjustment coef?cient vector, b a cointegrating vector, and G a short-term adjustment coef?cient matrix.
SSEC (a
1
) HSI (a
2
) TWII (a
3
)
Adjustment Coef?cients (a) À0.5333*** (0.0407) À1.2849*** (0.0348) 0.3469*** (0.0389)
SSEC (b1) HSI (b2) TWII (b3) Constant
Cointegrating Vector (b) 0.061236 0.679433 À0.455889 À0.010716
Standard errors are in parenthesis.
** and *** indicate signi?cance at the 5% and 1% levels, respectively.
HSI ¼ Hang Seng Index; SSEC ¼ Shanghai Stock Exchange Composite Index; TWII ¼ TSEC Weighted Index.
T.-L. Huang, H.-J. Kuo / Asia Paci?c Management Review 20 (2015) 65e78 70
market in?uences in terms of volatility spillovers. For ease of un-
derstanding, we express h
11,t
, h
22,t
, and h
33,t
in the form of Eqs. (7a),
(7b), and (7c), respectively. For clarity, we show only relevant parts
as in the following expressions:
h
11;t
¼ /

0:9725
2
h
11;tÀ1
þ0:002
2
h
22;tÀ1
þ0:000
2
h
33;tÀ1
þ2*0:9725Ã0:002h
12;tÀ1
þ2*0:9725Ã0:000h
13;tÀ1
þ2Ã0:002Ã0:000h
23;tÀ1

/
h
22;t
¼ /

0:001
2
h
11;tÀ1
þ0:9735
2
h
22;tÀ1
þ0:004
2
h
33;tÀ1
þ2Ã0:001Ã0:9735h
12;tÀ1
þ2Ã0:001Ã0:004h
13;tÀ1
þ2Ã0:9735Ã0:004h
23;tÀ1

/
h
33;t
¼ /

0:007
2
h
11;tÀ1
þ ðÀ0:0103Þ
2
h
22;tÀ1
þ0:9862
2
h
33;tÀ1
þ2Ã0:007ÃðÀ0:0103Þh
12;tÀ1
þ2Ã0:007Ã0:9862h
13;tÀ1
þ2ÃðÀ0:0103ÞÃ0:9862h
23;tÀ1

/
All diagonal coef?cients are statistically signi?cant at 1% level,
implying that the conditional variances are strongly linked to the
past conditional variances. Moreover, these diagonal coef?cients
are close to 1 (i.e., b
11
¼0.9725, b
22
¼ 0.9735, and b
33
¼ 0.9862), so
the evolution of conditional variances is highly linked with the past
conditional variances. In other words, return volatility in SSEC, HSI,
and TWII exhibits high persistence.
As for the off-diagonal elements, only b
13
and b
23
are statistically
signi?cant at the 5% level in the symmetric model. These coef?cients
identify unidirectional volatility spillover effects from SSEC to TWII
and from HSI to TWII. However, the small magnitude of b
13
(0.007),
and b
23
(À0.0103) suggests that the cross-market in?uences of
volatility spillovers, if any, was minimal. The insigni?cance of b
21
, b
31
,
b
12
, and b
32
indicate that return volatility of SSEC and HSI are hardly
affected by external in?uences. Accordingly, variation in the condi-
tional variance is mostly explained by its own past conditional
variance. The ?ndings support the home bias hypothesis.
Under the asymmetric speci?cation, coef?cients b
12
and b
32
become signi?cant, implying that market volatility of HSI would be
affected by volatility spillover effects fromSSEC and TWII. However,
the in?uences are tiny (b
12
¼ 0.008, and b
32
¼ 0.009). Accordingly,
the results of the asymmetric model are generally consistent with
those of the symmetric model.
5.1.4.2. In?uence of shocks
Under the symmetric speci?cation, matrix A mainly explores the
in?uences of shocks (i.e., news, surprises, or unexpected events) on
volatility. The subscript i (¼ 1, 2, 3) refers to each stock market
(corresponding to SSEC, HSI, TWII, respectively). The coef?cients a
ij
in matrix A indicate the impact of shocks arising from market i on
market j. Moreover, just like in matrix B, the diagonal coef?cients a
ii
quantify the effect of its own past shocks (i.e., the lagged value of
squared residual term) on the present volatility, while the off-
diagonal ones capture cross-market impacts of shocks. Regarding
the effects of shocks, relevant parts of Eqs. (7a), (7b), and (7c) can be
expressed as follows:
h
11;t
¼ /
À
0:2065?
1;tÀ1
þ0:003?
2;tÀ1
þ0:001?
3;tÀ1
Á
2
/
h
22;t
¼ /
À
0:008?
1;tÀ1
þ ðÀ0:2132Þ?
2;tÀ1
þ ðÀ0:0002Þ?
3;tÀ1
Á
2
/
h
33;t
¼ /
À
0:022?
1;tÀ1
þ ðÀ0:034Þ?
2;tÀ1
þ ðÀ0:1666Þ?
3;tÀ1
Á
2
/
Since coef?cients a
21
and a
31
(a
12
and a
32
) in Eqs. (7a) and (7b)
are insigni?cant, h
11,t
(h
22,t
) are mainly attributable to the in-
?uences of ?
1,tÀ1
(?
2,tÀ1
). That is, the volatility of SSEC (HSI) is
Table 5
Estimation results of the VECM(1)-BEKK(1, 1) modelemean equations.
The table shows the results of mean equations of the VECM(1)-BEKK(1, 1) model:
DPt ¼ PP
tÀ1
þGDP
tÀ1
þ ?t ;
Ht ¼ C
0
C þA
0
?
tÀ1
?
0
tÀ1
A þ B
0
H
tÀ1
B;
where P
t
and ?
t
are 3X1 vectors. The former stands for the logarithm of the SSEC, HSI, and TWII price indices at time t, while the latter are random errors which
represent innovation. Being a conditional variance-covariance matrix at time t, H
t
can model time-varying volatilities in the stock market. We use A to measure the
extents to which unexpected events affect stability, and B to analyze the volatility linkage. Technically speaking, the off-diagonal elements in matrices A and B
reveal the features of shock and volatility spillovers, respectively. Under the asymmetric speci?cation, Ht ¼ C
0
C þA
0
?
tÀ1
?
0
tÀ1
A þB
0
H
tÀ1
B þD
0
h
tÀ1
h
0
tÀ1
D.
Panel A. Mean equation estimates
(a) Symmetric (b) Asymmetric
Variables SSEC (DP
1,t-1
) HSI (DP
2,t-1
) TWII (DP
3,t-1
) Variables SSEC (DP
1,t-1
) HSI (DP
2,t-1
) TWII (DP
3,t-1
)
SSEC Coeff 0.014 0.031 À0.007 SSEC Coeff 0.007 0.032 0.001
(DP
1,t
) S.E. (0.0176) (0.0178) (0.0168) (DP
1,t
) S.E. (0.0184) (0.0178) (0.0177)
HSI Coeff À0.020 0.022 À0.025 HSI Coeff À0.002 0.021 À0.016
(DP
2,t
) S.E. (0.0135) (0.0203) (0.0166) (DP
2,t
) S.E. (0.0128) (0.0205) (0.0183)
TWII Coeff À0.019 0.0961*** À0.011 TWII Coeff À0.001 0.0890*** 0.009
(DP
3,t
) S.E. (0.0137) (0.0196) (0.0198) (DP
3,t
) S.E. (0.0140) (0.0210) (0.0213)
Panel B. Diagnostic tests for each residual series
(a) Symmetric (b) Asymmetric
Test Ljung-Box Q(30) McLeod-Li(30) Turning points Difference sign Test Ljung-Box Q(30) McLeod-Li(30) Turning points Difference
sign
Z
1
Statistic 49.5636 14.9136 À0.3838 À4.4203 Statistic 52.6198 8.9851 À0.5544 À4.2335
p value 0.0138 0.9902 0.7011 0.0000 p value 0.0065 0.9999 0.5793 0.0000
Z
2
Statistic 31.1723 35.0876 1.4925 À3.1129 Statistic 32.4643 21.6636 1.4073 À3.0506
p value 0.4070 0.2395 0.1356 0.0019 p value 0.3463 0.8660 0.1594 0.0023
Z
3
Statistic 19.7550 63.8663 0.3838 À3.6109 Statistic 21.4887 47.1626 0.6397 À3.2996
p value 0.9228 0.0003 0.7011 0.0003 p value 0.8720 0.0240 0.5224 0.0010
Z
1
, Z
2
, and Z
3
are standardized residuals for Shanghai Stock Exchange Composite (SSEC), Hang Seng Index (HIS), and TSEC Weighted Index (TWII), respectively. Standard errors
are in parenthesis.
** and *** indicate signi?cance at the 5% and 1% levels, respectively.
T.-L. Huang, H.-J. Kuo / Asia Paci?c Management Review 20 (2015) 65e78 71
affected by shocks fromits own market rather than external shocks.
Therefore, the home bias hypothesis is supported by the SSEC and
HSI return series. In contrast, coef?cients a
13
, a
23
and a
33
are sta-
tistically signi?cant at the 5% level in Eq. (7c), implying that the
volatility of TWII is affected by shocks from its own market and
those from the other markets (i.e., from SSEC and HSI). Comparing
their in?uences on the volatility of TWII, we can ?nd that
ja
33
j >ja
23
j >ja
13
j (0.1666>0.034>0.022). Accordingly, the volatility
of TWII is mainly affected by shocks from its own market as well
(0.1666>0.034>0.022), so the home bias hypothesis is also sup-
ported by the TWII return series.
These in?uences are robust even after we classify shocks into
positive ones (good news) and negative ones (bad news). The co-
ef?cients on positive shocks are given as follows:
h
11;t
¼ /
À
0:2170?
1;tÀ1
þ ðÀ0:015Þ?
2;tÀ1
þ ðÀ0:015Þ?
3;tÀ1
Á
2
/
h
22;t
¼ /
À
ðÀ0:011Þ?
1;tÀ1
þ0:041?
2;tÀ1
þ0:0634?
3;tÀ1
Á
2
/
h
33;t
¼ /
À
ðÀ0:0558Þ?
1;tÀ1
þ0:1348?
2;tÀ1
þ ðÀ0:0789Þ?
3;tÀ1
Á
2
/
By contrast, the coef?cients on negative shocks are:
h
11;t
¼ /
À
0:1772h
1;tÀ1
þ0:032h
2;tÀ1
þ ðÀ0:030Þh
3;tÀ1
Á
2
/
h
22;t
¼ /
À
ðÀ0:022Þh
1;tÀ1
þ0:3135h
2;tÀ1
þ ðÀ0:013Þh
3;tÀ1
Á
2
/
h
33;t
¼ /
À
ðÀ0:018Þh
1;tÀ1
þ0:033h
2;tÀ1
þ0:2398h
3;tÀ1
Á
2
/
As shown in the (b) asymmetric speci?cation of Table 6, co-
ef?cients a
13
, a
23
, d
13
, and d
23
are statistically signi?cant at the 5%
level. Therefore, the volatility of the TWII market returns is affected
by external shocks, no matter whether good or bad, from SSEC and
HSI. Meanwhile, since coef?cient a
32
(0.0634) is statistically sig-
ni?cant at the 1% level, good news from TWII is also found to affect
the volatility of HSI market returns. Therefore, a bidirectional in-
formation transmission mechanism exists between HSI and TWII.
However, since the values of all off-diagonal coef?cients in matrices
A and D are relatively small when compared to those of the diag-
onal coef?cients, the cross-market in?uences are tiny. As a result,
the home bias hypothesis obtains supports from the asymmetric
model as well.
As for the asymmetric effects, since all diagonal elements in
matrix D are statistically signi?cant, bad news is found to possess
Table 6
Estimation results of the VECM(1)-BEKK(1, 1) modelevariance equations.
The table shows the results of variance equations of the VECM(1)-BEKK(1, 1) model:
DPt ¼ PP
tÀ1
þGDP
tÀ1
þ ?t ;
Ht ¼ C
0
C þA
0
?
tÀ1
?
0
tÀ1
A þB
0
H
tÀ1
B;
where P
t
and ?
t
are 3X1 vectors. The former stands for the logarithm of the SSEC, HSI, and TWII price indices at time t, while the latter are
random errors which represent innovation. Being a conditional variance-covariance matrix at time t, H
t
can model time-varying
volatilities in the stock market. We use A to measure the extents to which unexpected events affect stability, and B to analyze the
volatility linkage. Technically speaking, the off-diagonal elements in matrices A and B reveal the features of shock and volatility
spillovers, respectively. Under the asymmetric speci?cation, Ht ¼ C
0
C þA
0
?
tÀ1
?
0
tÀ1
A þB
0
H
tÀ1
B þD
0
h
tÀ1
h
0
tÀ1
D.
Panel A: Multivariate GARCH model estimates
(a) Symmetric (b) Asymmetric
Ht ¼ C
0
C þA
0
?
tÀ1
?
0
tÀ1
A þB
0
H
tÀ1
B Ht ¼ C
0
C þA
0
?
tÀ1
?
0
tÀ1
A þB
0
H
tÀ1
B þD
0
h
tÀ1
h
0
tÀ1
D
C ¼
2
6
6
6
6
6
4
0:1594Ã Ã Ã
ð 0:0176Þ
0:022
ð 0:0240Þ
À0:1119Ã Ã Ã
ð 0:0161Þ
À0:006
ð 0:0221Þ
À0:0528Ã Ã Ã
ð 0:0200Þ
À0:0606Ã Ã Ã
ð 0:0162Þ
3
7
7
7
7
7
5
A ¼
2
6
6
6
6
6
4
0:2065Ã Ã Ã
ð 0:0128Þ
0:008
ð 0:0127Þ
0:022Ã Ã
ð 0:0114Þ
0:003
ð0:0171Þ
À0:2132Ã Ã Ã
ð 0:0161Þ
À0:034Ã Ã
ð 0:0149Þ
0:001
ð 0:0139Þ
À0:0002
ð 0:0149Þ
À0:1666Ã Ã Ã
ð 0:0130Þ
3
7
7
7
7
7
5
B ¼
2
6
6
6
6
6
4
0:9725Ã Ã Ã
ð 0:0033Þ
0:001
ð 0:0034Þ
0:007Ã Ã
ð 0:0030Þ
0:002
ð0:0039Þ
0:9735Ã Ã Ã
ð 0:0035Þ
À0:0103Ã Ã Ã
ð 0:0034Þ
0:000
ð 0:0028Þ
0:002
ð 0:0029Þ
0:9862Ã Ã Ã
ð 0:0024Þ
3
7
7
7
7
7
5
C ¼
2
6
6
6
6
6
4
0:1728Ã Ã Ã
ð 0:0144Þ
0:011
ð 0:0245Þ
0:1412Ã Ã Ã
ð 0:0118Þ
0:022
ð 0:0220Þ
0:0818Ã Ã Ã
ð 0:0184Þ
0:0623Ã Ã Ã
ð 0:0182Þ
3
7
7
7
7
7
5
A ¼
2
6
6
6
6
6
4
0:2170Ã Ã Ã
ð 0:0114Þ
À0:011
ð 0:0103Þ
À0:0558Ã Ã Ã
ð 0:0091Þ
À0:015
ð0:0127Þ
0:041Ã Ã Ã
ð 0:0181Þ
0:1348Ã Ã Ã
ð 0:0104Þ
À0:015
ð 0:0113Þ
0:0634Ã Ã Ã
ð 0:0141Þ
À0:0789Ã Ã Ã
ð 0:0162Þ
3
7
7
7
7
7
5
B ¼
2
6
6
6
6
6
4
0:9638Ã Ã Ã
ð 0:0027Þ
0:008Ã Ã
ð 0:0033Þ
0:0145Ã Ã Ã
ð 0:0028Þ
0:001
ð0:0042Þ
0:9613Ã Ã Ã
ð 0:0036Þ
À0:0181Ã Ã Ã
ð 0:0039Þ
À0:002
ð 0:0035Þ
0:009Ã Ã
ð 0:0035Þ
0:9808Ã Ã Ã
ð 0:0025Þ
3
7
7
7
7
7
5
D ¼
2
6
6
6
6
6
4
0:1772Ã Ã Ã
ð 0:0194Þ
À0:022
ð 0:0177Þ
À0:018Ã Ã
ð 0:0166Þ
0:032
ð0:0209Þ
0:3135Ã Ã Ã
ð 0:0184Þ
0:033Ã Ã Ã
ð 0:0194Þ
À0:030
ð 0:0159Þ
À0:013
ð 0:0194Þ
0:2398Ã Ã Ã
ð 0:0154Þ
3
7
7
7
7
7
5
Panel B: Multivariate diagnostic tests for model speci?cation
(a) Symmetric (b) Asymmetric
Log likelihood
À15381.0920
Log likelihood
À15540.6216
Multivariate Q(30) ¼ 288.43525
Signi?cance level as Chi-square(270)¼ 0.21056
Multivariate Q(30) ¼ 295.84964
Signi?cance Level as Chi-square(270)¼ 0.13410
Standard errors are in parenthesis.
** and *** indicate signi?cance at the 5% and 1% levels, respectively.
T.-L. Huang, H.-J. Kuo / Asia Paci?c Management Review 20 (2015) 65e78 72
greater in?uence. Moreover, all off-diagonal elements in matrix D
are insigni?cant. Accordingly, bad news fails to add incremental
effects to the cross-market in?uences.
5.2. Estimation results of the VAR(1)-BEKK(1, 1) model
We then employ the trivariate VAR(1)-BEKK(1, 1) model to
investigate the interaction among SSEC, HSI, and TWII, focusing on
return transmission and volatility spillover effect. To enhance our
understanding of the causality relationship, we ?rst conduct the
Granger causality test.
5.2.1. Granger causality test
The results of the Granger causality test are presented in Table 7,
suggesting that price movements in HSI are useful in forecasting
those in TWII and that SSEC are good predictors of those in HSI, but
not vice versa. The ?ndings are consistent with those of Huang,
Yang, and Hu (2000) and Groenewold, Tang, and Wu (2004), who
documented a unidirectional Granger causality relationship from
HSI to TWII.
5.2.2. Return transmission in the VAR(1)-BEKK(1,1) model
The estimation results of the VAR(1)-BEKK(1, 1) model are re-
ported in Table 8. Among the estimates of the coef?cients in the
mean equations, only lag returns on HSI have signi?cant explana-
tory power for returns on TWII at the 1% level. However, all of the
other coef?cients in these mean equations are insigni?cant at the
5% level, implying that the past information among these markets
could not be exploited to predict future price dynamics, just as the
weak-form ef?cient market hypothesis predicts. The ?nding here is
consistent with the results of the Granger causality test and those of
the VECM(1)-BEKK(1, 1) model.
The right side of Table 8 reports the estimation results of the
asymmetric VAR(1)-BEKK(1, 1) model. Theresults of meanequations
under the asymmetric speci?cation are mostly consistent with the
symmetric speci?cation. All of the coef?cients in the mean equa-
tions are insigni?cant at the 5% level except g
23
. Therefore, the in-
?uence of HSI on TWII seems to be robust. However, as most off-
diagonal coef?cients in matrix g are statistically insigni?cant, re-
turn transmission is absent under the asymmetric speci?cation. On
the basis of the estimation results of the mean equations, we could
infer that these markets seem to be independent of one another in
terms of return transmission.
Panel B of Table 8 also provides several diagnostic tests on the
standardized residuals and squared residuals for each series. The
Ljung-Box statistic for squared standardized residuals of HSI and
TWII indicates that there is no autocorrelation left in these se-
ries. However, the signi?cant value of Z
1
[Q(30) ¼ 49.7053
(0.0133) and Q(30) ¼ 52.5887 (0.0066) under symmetric and
asymmetric speci?cation, respectively], indicates that there is
still autocorrelation left in the residual series of SSEC. The results
of the multivariate portmanteau tests are reported in Panel B of
Table 9, where we can see the test statistics are 288.34163
(0.21167) and 295.05453 (0.14119) under the symmetric and
Table 7
Pairwise Granger causality tests.
Null hypothesis: F-statistic Probability
HSI does not Granger cause SSEC 1.43866 0.0580
SSEC does not Granger cause HSI 2.08179 0.0005
TWII does not Granger cause SSEC 0.94138 0.5577
SSEC does not Granger cause TWII 1.01955 0.4366
TWII does not Granger cause HSI 1.13224 0.2835
HSI does not Granger cause TWII 2.96025 0.0000
The lag length was set to 30.
HSI ¼ Hang Seng Index; SSEC ¼ Shanghai Stock Exchange Composite Index;
TWII ¼ TSEC Weighted Index.
Table 8
Estimation results of the VAR(1)-BEKK(1, 1) modelemean equations.
The table shows the results of mean equations of the VAR(1)-BEKK(1, 1) model:
rt ¼ m þgr
tÀ1
þ ?t;
Ht ¼ C
0
C þA
0
?
tÀ1
?
0
tÀ1
A þ B
0
H
tÀ1
B;
where r
t
and ?
t
are 3X1 vectors. The former stores information about the stock index returns at time t and the latter are random errors which represents innovation.
Being a conditional variance-covariance matrix at time t, H
t
can model time-varying volatilities in the stock market. We use A to measure the extents to which
unexpected events affect stability, and B to analyze the volatility linkage. Technically speaking, the off-diagonal elements in matrices A and B reveal the features of
shock and volatility spillovers, respectively. Under the asymmetric speci?cation, Ht ¼ C
0
C þA
0
?
tÀ1
?
tÀ1
A þB
0
H
tÀ1
B þD
0
h
tÀ1
h
0
tÀ1
D.
Panel A. Mean equation estimates
(a) Symmetric (b) Asymmetric
Lag return (r
tÀ1
) on Lag return (r
tÀ1
) on
Constant SSEC HSI TWII Constant SSEC HSI TWII
SSEC Coeff 0.019 0.014 0.031 À0.007 Coeff À0.003 0.007 0.032 0.001
(r
1,t
) S.E. (0.0218) (0.0176) (0.0178) (0.0168) S.E. (0.0234) (0.0183) (0.0178) (0.0177)
HSI Coeff 0.0667 À0.021 0.020 À0.026 Coeff 0.023 À0.003 0.021 À0.016
(r
2,t
) S.E. (0.0398) (0.0134) (0.0204) (0.0166) S.E. (0.0211) (0.0129) (0.0205) (0.0183)
TWII Coeff 0.0588 À0.020 0.0946*** À0.012 Coeff 0.020 À0.002 0.0892*** 0.008
(r
3,t
) S.E. (0.0305) (0.0136) (0.0196) (0.0198) S.E. (0.0217) (0.0140) (0.0211) (0.0214)
Panel B. Diagnostic tests for each residual series
(a) Symmetric (b) Asymmetric
Test Ljung-Box Q(30) McLeod-Li(30) Turning points Difference sign Test Ljung-Box Q(30) McLeod-Li(30) Turning points Difference sign
Z1 Statistic 49.7053 14.9566 À0.3838 À4.4203 Statistic 52.5887 8.9972 À0.5544 À4.2335
p value 0.0133 0.9900 0.7011 0.0000 p value 0.0066 0.9999 0.5793 0.0000
Z2 Statistic 30.6271 35.0636 1.4925 À3.1129 Statistic 32.0331 21.6409 1.4073 À2.9883
p value 0.4339 0.2403 0.1356 0.0019 p value 0.3660 0.8668 0.1594 0.0028
Z3 Statistic 19.4328 65.0507 0.2985 À3.6109 Statistic 21.1629 46.8126 0.5544 À3.2996
p value 0.9305 0.0002 0.7653 0.0003 p value 0.8827 0.0260 0.5793 0.0010
Z1, Z2, and Z3 are standardized residuals for Shanghai Stock Exchange Composite (SSEC), Hang Seng Index (HIS), and TSEC Weighted Index (TWII), respectively. Standard
errors are in parenthesis.
** and *** indicate signi?cance at the 5% and 1% levels, respectively.
T.-L. Huang, H.-J. Kuo / Asia Paci?c Management Review 20 (2015) 65e78 73
asymmetric speci?cations, respectively. These signi?cant values
of the multivariate test statistics suggest that both models are
properly speci?ed.
5.2.3. Volatility spillovers in the VAR(1)-BEKK(1, 1) model
The estimation results of variance equation of the VAR(1)-
BEKK(1, 1) model are shown in Table 9. All diagonal elements
in matrices A and B are signi?cant at the 1% level, implying that
the volatility of each market is in?uenced by its own past
volatility and shocks. The results also identify unidirectional
volatility spillover effects from SSEC and HSI to TWII. At the
same time, shocks arising from HSI and SSEC also bring signif-
icant impacts on TWII. The estimation results of the VAR(1)-
BEKK(1, 1) model are quite consistent with those of the
VECM(1)-BEKK(1, 1) model.
5.2.3.1. In?uence of past volatility
As in the previous subsection, the effects of past volatility on the
present volatility can be mathematically expressed as follows:
h
11;t
¼ /

0:9727
2
h
11;tÀ1
þ0:002
2
h
22;tÀ1
þ ðÀ0:001Þ
2
h
33;tÀ1
þ2*0:9727*0:002h
12;tÀ1
þ2*0:9727ÃðÀ0:001Þh
13;tÀ1
þ2*0:002ÃðÀ0:001Þh
23;tÀ1

/
h
22;t
¼ /

0:002
2
h
11;tÀ1
þ0:9721
2
h
22;tÀ1
þ0:004
2
h
33;tÀ1
þ2Ã0:002Ã0:9721h
12;tÀ1
þ2Ã0:002Ã0:004h
13;tÀ1
þ2Ã0:9721Ã0:004h
23;tÀ1

/
h
33;t
¼ /

0:007
2
h
11;tÀ1
þ

À0:0116
2

h
22;tÀ1
þ0:9869
2
h
33;tÀ1
þ2Ã0:007ÃðÀ0:0116Þh
12;tÀ1
þ2Ã0:007Ã0:9869h
13;tÀ1
þ2ÃðÀ0:0116ÞÃ0:9869h
23;tÀ1

/
All diagonal coef?cients in matrix B (i.e., b
11
, b
22
, and b
33
) are sta-
tisticallysigni?cant at the1%level, implyingthat conditional variances
are strongly linked to past conditional variances. Moreover, these
Table 9
Estimation results of the VAR(1)-BEKK(1, 1) modelevariance equations.
The table shows the results of variance equations of the VAR(1)-BEKK(1, 1) model:
rt ¼ m þgr
tÀ1
þ ?t;
Ht ¼ C
0
C þA
0
?
tÀ1
?
0
tÀ1
A þB
0
H
tÀ1
B
where r
t
and ?
t
are 3X1 vectors. The former stores information about the stock index returns at time t and the latter are random errors
which represents innovation. Being a conditional variance-covariance matrix at time t, H
t
can model time-varying volatilities in the
stock market. We use A to measure the extents to which unexpected events affect stability, and B to analyze the volatility linkage.
Technically speaking, the off-diagonal elements in matrices A and B reveal the features of shock and volatility spillovers, respectively.
Under the asymmetric speci?cation, Ht ¼ C
0
C þA
0
?
tÀ1
?
0
tÀ1
A þB
0
H
tÀ1
B þD
0
h
tÀ1
h
0
tÀ1
D.
Panel A. Multivariate GARCH model estimates
(a) Symmetric (b) Asymmetric
Ht ¼ C
0
C þA
0
?
tÀ1
?
0
tÀ1
A þB
0
H
tÀ1
B Ht ¼ C
0
C þA
0
?
tÀ1
?
0
tÀ1
A þB
0
H
tÀ1
B þD
0
h
tÀ1
h
0
tÀ1
D
C ¼
2
6
6
6
6
6
4
0:1597Ã Ã Ã
ð 0:0176Þ
0:024
ð 0:0242Þ
0:1120Ã Ã Ã
ð 0:0162Þ
À0:003
ð 0:0221Þ
0:049Ã Ã
ð 0:0201Þ
À0:0603Ã Ã Ã
ð 0:0164Þ
3
7
7
7
7
7
5
A ¼
2
6
6
6
6
6
4
0:2054Ã Ã Ã
ð 0:0129Þ
0:011
ð 0:0128Þ
0:023Ã Ã
ð 0:0114Þ
0:002
ð0:0172Þ
À0:2210Ã Ã Ã
ð 0:006Þ
À0:0407Ã Ã Ã
ð 0:0150Þ
À0:001
ð 0:0139Þ
0:0006
ð 0:0150Þ
À0:1631Ã Ã Ã
ð 0:0131Þ
3
7
7
7
7
7
5
B ¼
2
6
6
6
6
6
4
0:9727Ã Ã Ã
ð 0:0033Þ
0:002
ð 0:0035Þ
0:007Ã Ã
ð 0:0030Þ
0:002
ð0:0039Þ
0:9721Ã Ã Ã
ð 0:0036ÞÞ
À0:0116Ã Ã Ã
ð 0:0034Þ
À0:001
ð 0:0028Þ
0:004
ð 0:0030Þ
0:9869Ã Ã Ã
ð 0:0024Þ
3
7
7
7
7
7
5
C ¼
2
6
6
6
6
6
4
0:1730Ã Ã Ã
ð 0:0144Þ
0:009
ð 0:0245Þ
0:1391Ã Ã Ã
ð 0:0119Þ
0:021
ð 0:0220Þ
0:0799Ã Ã
ð 0:0188Þ
0:0610Ã Ã Ã
ð 0:0187Þ
3
7
7
7
7
7
5
A ¼
2
6
6
6
6
6
4
0:2172Ã Ã Ã
ð 0:0114Þ
À0:012
ð 0:0103Þ
0:0566Ã Ã Ã
ð 0:0091Þ
À0:016
ð0:0128Þ
0:042Ã Ã Ã
ð 0:0182Þ
0:1359Ã Ã Ã
ð 0:0105Þ
À0:014
ð 0:0114Þ
0:0627Ã Ã Ã
ð 0:0142Þ
À0:0795Ã Ã Ã
ð 0:0163Þ
3
7
7
7
7
7
5
B ¼
2
6
6
6
6
6
4
0:9638Ã Ã Ã
ð 0:0027Þ
0:0084Ã Ã Ã
ð 0:0032Þ
0:0147Ã Ã Ã
ð 0:0027Þ
0:001
ð0:0042Þ
0:9611Ã Ã Ã
ð 0:0036Þ
À0:0184Ã Ã Ã
ð 0:0039Þ
À0:002
ð 0:0036Þ
0:009Ã Ã
ð 0:0035Þ
0:9806Ã Ã Ã
ð 0:0025Þ
3
7
7
7
7
7
5
D ¼
2
6
6
6
6
6
4
0:1774Ã Ã Ã
ð 0:0202Þ
À0:023
ð 0:0177Þ
À0:019Ã Ã
ð 0:0166Þ
0:033
ð0:0208Þ
0:3126Ã Ã Ã
ð 0:0183Þ
0:034Ã Ã Ã
ð 0:0193Þ
À0:029
ð 0:0160Þ
À0:014
ð 0:0194Þ
0:2387Ã Ã Ã
ð 0:0153Þ
3
7
7
7
7
7
5
Panel B. Multivariate diagnostic tests for model speci?cation
(a) Symmetric (b) Asymmetric
Log likelihood
À15374.5968
Log likelihood
À15539.8046
Multivariate Q(30) ¼ 288.34163
Signi?cance level as Chi-Square (270)¼ 0.21167
Multivariate Q(30) ¼ 295.05453
Signi?cance Level as Chi-Square(270)¼ 0.14119
Standard errors are in parenthesis.
** and *** indicate signi?cance at the 5% and 1% levels, respectively.
T.-L. Huang, H.-J. Kuo / Asia Paci?c Management Review 20 (2015) 65e78 74
diagonal coef?cients are close to 1 (i.e., b
11
¼0.9727, b
22
¼0.9721, and
b
33
¼ 0.9869), so the evolution of conditional variances exhibits high
persistence. The insigni?cance of b
21
, b
31
, b
12
, and b
32
, and the small
magnitude of b
13
(0.007), and b
23
(À0.0116), suggests that the cross-
market in?uences of volatility spillovers was minimal. Accordingly,
variation in the conditional variance is mostly explained by its own
past conditional variance. The ?nding is consistent under the asym-
metric speci?cationand withthose of the VECM(1)-BEKK(1, 1) model.
5.2.3.2. In?uences of shocks
Under the symmetric speci?cation, the effects of shocks on the
present volatility can be mathematically expressed as follows:
h
11;t
¼ /
À
0:2054?
1;tÀ1
þ0:002?
2;tÀ1
þ ðÀ0:001Þ?
3;tÀ1
Á
2
/
h
22;t
¼ /
À
0:011?
1;tÀ1
þ ðÀ0:2210Þ?
2;tÀ1
þ0:0006?
3;tÀ1
Á
2
/
h
33;t
¼ /
À
0:023?
1;tÀ1
þ ðÀ0:0407Þ?
2;tÀ1
þ ðÀ0:1631Þ?
3;tÀ1
Á
2
/
Since coef?cients a
21
and a
31
(a
12
and a
32
) in Eqs. (7a) and (7b)
are insigni?cant, h
11,t
(h
22,t
) can be attributable to the in?uences
of ?
1,tÀ1
(?
2,tÀ1
). As a result, volatility of SSEC (HSI) is mainly affected
by shocks from its own market rather than external shocks. In
contrast, coef?cients a
13
, a
23
, and a
33
are statistically signi?cant at
the 5% level in Eq. (7c), implying that the volatility of TWII is
affected by shocks fromits own market and fromthe other markets
(SSEC and HSI). Comparing their in?uences on the volatility of
TWII, we can ?nd that ja
33
j >ja
23
j >ja
13
j (0.1631 > 0.0407 > 0.023).
Accordingly, the volatility of TWII is mainly affected by shocks from
its own market as well.
These in?uences are also robust after we classify shocks into
positive and negative ones. The coef?cients on positive shocks are:
h
11;t
¼ /
À
0:2172?
1;tÀ1
þ ðÀ0:016Þ?
2;tÀ1
þ ðÀ0:014Þ?
3;tÀ1
Á
2
/
h
22;t
¼ /
À
ðÀ0:012Þ?
1;tÀ1
þ0:042?
2;tÀ1
þ0:0627?
3;tÀ1
Á
2
/
h
33;t
¼ /
À
ðÀ0:0566Þ?
1;tÀ1
þ0:1359?
2;tÀ1
þ ðÀ0:0795Þ?
3;tÀ1
Á
2
/
while the coef?cients on negative shocks are:
h
11;t
¼ /
À
0:1774h
1;tÀ1
þ0:033h
2;tÀ1
þ ðÀ0:029Þh
3;tÀ1
Á
2
/
h
22;t
¼ /
À
ðÀ0:023Þh
1;tÀ1
þ0:3126h
2;tÀ1
þ ðÀ0:014Þh
3;tÀ1
Á
2
/
h
33;t
¼ /
À
ðÀ0:019Þh
1;tÀ1
þ0:034h
2;tÀ1
þ0:2387h
3;tÀ1
Á
2
…
As shown in the (b) asymmetric speci?cation of Table 9, co-
ef?cients a
13
, a
23
, d
13
, and d
23
are statistically signi?cant at the 5%
level. Accordingly, the return volatility of TWII is also found to be
affected by external shocks from SSEC and HSI in the asymmetric
model. Meanwhile, good news from TWII is found to affect the
volatility of HSI market returns as well, since coef?cient a
32
(0.0627) is also statistically signi?cant at the 1% level. Therefore, a
bidirectional information transmission mechanism exists between
HSI and TWII.
In summary, the estimation results of the VAR(1)-BEKK(1, 1)
model are quite consistent with those of the VECM(1)-BEKK(1, 1)
model. Lagged returns on HSI possess explanatory power for the
present returns on TWII. Without the link, return transmission
would be absent in the trilateral relationship among SSEC, HSI, and
TWII. Nevertheless, volatility spillovers are found ?owing from
(A) Conditional variances of of SSEC
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
0
5
10
15
20
25
30
35
40
(B) Conditional variances of HSI
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
0
5
10
15
20
25
30
35
40
(C) Conditional variances of TWII
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
0
5
10
15
20
25
30
35
40
Fig. 4. Conditional variances of Shanghai Stock Exchange Composite Index (SSEC), Hang Seng Index (HSI), and TSEC Weighted Index (TWII) estimated by the VAR(1)-BEKK model.
T.-L. Huang, H.-J. Kuo / Asia Paci?c Management Review 20 (2015) 65e78 75
SSEC and HSI to TWII, suggesting that return volatility of TWII is
susceptible to information from HSI to SSEC. However, these cross-
market in?uences are relatively small in comparison with the do-
mestic in?uences. Accordingly, both the VECM(1)-BEKK(1, 1) model
and VAR(1)-BEKK(1, 1) model provide evidence supportive of the
home bias hypothesis.
5.3. Conditional variances by the VAR(1)-BEKK(1, 1) model
Fig. 4 plots the conditional variances of SSEC, HSI, and TWII,
estimated by the VAR(1)-BEKK(1,1) model. The most prominent
and common feature of these plots is the surge of volatility around
the year 2008, suggesting that the markets were signi?cantly
affected by the subprime mortgage crisis near the end of 2007 and
became even more volatile due to the 2008 ?nancial crisis. More-
over, among these crisis-affected markets, HSI exhibits a most
volatile state which had never been seen in its own market as well
as in the other two markets, implying that HSI would be extremely
sensitive to ?nancial crisis.
5.4. Dynamic correlations by the VAR(1)-BEKK(1, 1) model
Fig. 5 depicts the time-varying correlation coef?cients between
SSEC, HSI, and TWII, and it provides several features worth noting.
First, TWII and HSI have been maintaining a positive relationship
during the sample period (Fig. 4C). Second, unlike the relationship
between TWII and HSI, the index movement in SSEC exhibits lowor
even negative correlations with those in HSI and in TWII for the
?rst half of sample period. It was after the middle of 2006 that
increasing positive relationships of SSEC with HSI and with TWII
emerged. In general, upward trends are present in these condi-
tional correlations during the sample period, indicating a growing
integration of these markets.
6. Discussions
Using VECM(1)-BEKK(1, 1) and VAR(1)-BEKK(1, 1) models, the
present study aims to examine the information transmission
mechanism among the Mainland China, Hong Kong, and Taiwan
stock markets. Through mean and variance equations of these
models, the study investigates two channels of information trans-
mission mechanism: return transmission and volatility spillovers.
The estimation results of the VAR(1)-BEKK(1, 1) model and those
of the VECM(1)-BEKK(1, 1) model are quite consistent. A major
?nding is that the function of return transmission seems to be
insigni?cant among these markets. Only the lagged returns on HSI
can predict market returns onTWII. This link between HSI and TWII
is also supported by the Granger causality test. Moreover, the
?nding is consistent with those of Huang et al. (2000) and
Groenewold et al. (2004), who documented a unidirectional
Granger causality relationship from HSI to TWII. Except the link
between HSI and TWII, past return information among these
markets could not be exploited to predict future price dynamics.
Therefore, these markets seemto be independent fromone another
in terms of return transmission. The ?nding might support the
ef?cient market hypothesis (Malkiel & Fama, 1970).
By contrast, volatility spillovers are found ?owing from SSEC
and HSI to TWII. Meanwhile, shocks (or news) of SSEC and HSI are
found to signi?cantly in?uence TWII. These impacts on TWII are
robust even after we classify the shocks into positive and negative
ones. These ?ndings indicate that return volatility of TWII is sus-
ceptible to information from HSI to SSEC.
One possible reason for the signi?cant in?uences of SSEC and
HSI on TWII is the international center hypothesis. The hypothesis
suggests that the Mainland China market, with annual average
growth rates above 9% since 2002, might serve as an international
center just like the US market. The in?uences of this emerging
market cannot be ignored. Therefore, the Mainland China market
(A) Conditional correlation of SSEC with HSI
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
(B) Conditional correlation of SSEC with TWII
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
(C) Conditional correlation of HSI with TWII
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
Fig. 5. Conditional correlations estimated by the VAR(1)-BEKK model.
T.-L. Huang, H.-J. Kuo / Asia Paci?c Management Review 20 (2015) 65e78 76
should play a leading role in the transmission of information
(Cheung & Mak, 1992; Eun & Shim, 1989). Taiwan and Hong Kong,
being geographically near and culturally close to China, are sup-
posed to be in?uenced by Mainland China. The estimation results of
the asymmetric VECM(1)-BEKK(1, 1) and VAR(1)-BEKK(1, 1) models
also identi?ed signi?cant spillover effects from SSEC to HSI and
TWII, implying the Mainland China market might dominate the
other markets in terms of information transmission. The ?nding
here partly supports the international center hypothesis.
Although the Mainland China market is found to possess sig-
ni?cant in?uences on the Hong Kong and Taiwan markets, these
cross-market in?uences are relatively small in comparison with the
domestic in?uences. This evidence indicates that market volatility
is mainly attributed to domestic in?uences rather than external
impacts. Accordingly, both the VECM(1)-BEKK(1, 1) model and
VAR(1)-BEKK(1, 1) model provide evidence supportive of the home
bias hypothesis.
The other possible reason might be asynchronous trading.
Speci?cally, the Taiwan stock market closes earlier than the other
two markets, as shown in Fig. 1. SSEC and HSI have a greater chance
to re?ect the new information because they have longer trading
hours. Consequently, SSEC and HSI might have incorporated some
information that has not yet been re?ected in TWII. Suppose a
global event that might affect all the three markets happens in the
afternoon, when the Taiwan stock market is closed. In this case,
SSEC and HSI will react to the event on the very day due to the later
closing time of these markets. However, TWII cannot re?ect the
new information, because it has stopped transactions on the event
day. TWII will not respond until the next day. In other words, in-
formation about this global event ?ows into SSEC and HSI, and then
?ows into TWII. Therefore, the Taiwan stock market seems to be
sensitive to the shocks from the Hong Kong and Mainland China
markets.
7. Conclusions
To conclude, the present study has investigated the trilateral
relationship among Taiwan (TWII), Hong Kong (HSI) and Mainland
China (SSEC) stock markets in terms of the information trans-
mission mechanism, but its relevance to market integration can also
be seen. When examining the relationship among these markets,
prior studies tendto focus onreturntransmission, but fail toaccount
for the volatility linkage. Moreover, previous studies usually adopt
bivariate models that only can explore a bilateral relationship. To ?ll
the gap, this study adopts the VECM(1)-BEKK(1, 1) and VAR(1)-
BEKK(1, 1) models to identify the volatility spillover effect in addi-
tion to examining the return transmission. In particular, we classify
market innovations into positive shocks (good news) and negative
shocks (bad news), so as to observe the asymmetric response of
these markets to news of different nature. The application of tri-
variate BEKK-GARCH models also enables us to capture the cross-
market in?uences simultaneously. Therefore, a vivid trilateral
relationship among these markets can be precisely described.
On the basis of the Granger causality test and the estimation
results of the VECM(1)-BEKK(1, 1) and VAR(1)-BEKK(1, 1) models,
we ?nd that these markets seem to be nearly insensitive to past
information concerning raw returns, conforming to the weak-form
ef?cient market hypothesis. By contrast, parts of the empirical re-
sults indicate that SSEC can signi?cantly in?uence HSI and TWII
through volatility spillover effects. These spillover effects are uni-
directional, implying that Mainland China might play a role of an
international center just like the US. However, these cross-market
in?uences are relatively small in comparison with the domestic
in?uences fromhome markets. Therefore, our ?nding also supports
the home bias hypothesis.
Our analysis contributes to literature on market interaction in
several aspects. First, the investigation into information trans-
mission mechanisms points out that these markets in?uence one
another more signi?cantly through volatilities than through
changes in asset prices. Second, this study provides a vivid picture
of dynamic interaction among these markets, which offers a deep
insight into the trilateral relationship. Finally, these markets are
found to be closely linked and gradually integrated. Fund managers
and investors who seek international diversi?cation bene?ts need
to consider the market integration. Otherwise, they might over-
estimate the pro?ts of their diversi?ed portfolios and underesti-
mate the underlying risks.
However, much remains to be answered because of several
limitations to this study. As mentioned in the discussion, asyn-
chronous trading may affect when and how information transmits
from one market to another. The availability of daily data allows
only one to investigate the information transmission mechanism in
terms of close-to-close returns. Intraday data permits researchers
to explore the information transmission mechanism during trading
hours and after trading hours. Therefore, researchers can use higher
frequency data to conduct further studies. However, the limited
availability of data should be overcome.
Con?icts of interest
All contributing authors declare no con?icts of interest.
Acknowledgments
The authors are thankful for the reviewer's valuable comments
that strengthen the foundation of the research. Their opinions also
greatly improve the ?ndings in the research and provide better
insights into the information transmission mechanism among
Mainland China, Hong Kong, and Taiwan stock markets.
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