Modeling China Stock Markets and
International Linkages
Jin-Lung Lin
Chung-Shu Wu
1Institute of Economics, Academia Sinica
December 2003
1This paper is written for presentation at the Conference on Analysis of High-Frequency Financial Data
and Market Microstructure held during December 15-16, 2003 in Taipei, Taiwan. We would like to thank Miss Yu-Ke Huang for excellent research assistance. The authors gracefully acknowledge financial support from Institute of Economics, Academia Sinica under the project Econometric Analysis of High Frequency Financial Data
Abstract
In this paper we analyze the China stock markets and examine their price and volatility linkages with those of Hong Kong, Taiwan and United States. In particular, we analyze the direction of information flow among A-share and B-share stocks of Shanghai and Shenzhen Stock Exchanges as well as Hong Kong H-share and Red-Chip markets. We employ two methods. The first ap-proach employs direct graph theory to determine the contemporaneous causal order of the residual vectors obtained from restricted VAR model and then use the Bernanke-Sims decomposition to compute the impulse response. The second approach involves estimating the multivariate GARCH models of several market returns to investigate the directions of spillover in mean level as well as in volatility level.
We analyze close-to-open, open-to-close, and close-to-close returns to differentiate foreign and own market effects. We also carefully model the day-of-the-week effect and the impact of the event of opening B-share market to domestic investors on February 28, 2001 to avoid misspeci-fication of the model. Using the data from January 5, 2000 to May 30, 2003, we conclude that Chinese stock markets have a weak linkage with Hong Kong, Taiwan and US markets. As for the four domestic markets, spillover in mean returns goes unidirectionally from A-share market to B-share market but spillover in volatility is bidirectional. Further, Shanghai stock market seems to play a dominating role over Shenzhen stock market.
1
Introduction
China stock markets have attracted a lot of attention of investors and finance analysts for their fast growth and their unique feature of market segmentation. Shanghai Stock Exchange and Shenzhen Stock Exchange were established in November and December of 1990 respectively. In 2002, there are 759 stocks traded in Shanghai Stock Exchange with annual trade volume of 205.6 billion USD while 551 listed securities are traded in Shenzhen Stock Exchange with annual trade volume of 141 billion USD. Both markets have completely segmented trading between domestic investors and domestic investors. An A-share market is open only to Chinese domestic investors and a B-share market only to foreign investors. Shanghai B-B-share market is denominated and traded in US Dollars while Shenzhen B-share market in Hong-Kong dollars. A-share markets are traded, of course, in Renminbi (RMB), the legal currency of China.
A few stocks are listed in both markets for which Bailey(1994) notes the big price discounts of B-share relative to A-share. However, the gap has significantly shrunk since the February 28, 2001. At this important date, the restriction was lifted and domestic investors are legally allowed to trade in both B-share markets but the trade currencies remain to be US Dollars and Hong Kong Dollars respectively. A-share markets remain only open to domestic investors. As of 2002, there are only 59 and 57 B-shares stocks out of 759 and 551 stocks traded in Shanghai and Shenzhen markets respectively. Trade volume of B-share stocks account only about 3% of total trade volume in both markets.
Beyond explaining the price discount of B-share stocks, information asymmetry pattern among segmented markets is an important issue. It is typically assumed that domestic investors are better informed than foreign investors about the value of local assets. However, some researchers argue that foreign investors can be better informed than domestic investors for advanced ability to ana-lyze information and more stringent requirement for corporate information disclosure in B-share market. What is more important, A-share markets are filled with individual investors while B-share market are mostly institutional investors. Previous researches find mixed results for information asymmetry. Chui and Kwok (1998) and Mok and Hui (1998) find B-share investors to be better informed while Chakravarty, Sarkar and Wu (1998) and Su and Fleisher (1999) support the other direction. Chen, Lee and Rui (2001) argues no information asymmetry.
This paper addresses the following questions. First, how strong are the linkages of China stock markets with those in Hong Kong, Taiwan and US? Secondly, within the four China domes-tic markets, what are the causal chain between A-share and B-share markets as well as Shanghai and Shenzhen stock markets? To answer these questions, we employ two methods. For the first approach, we carefully build a VAR models for the returns under investigation. We emphasize that instead of estimating the unrestricted VAR, we should remove the insignificant parameters and
es-timate the restricted model. The reduction of number of parameters and improvement of estimation precision are substantial. Then, we employ direct graphs theory to determine the contemporaneous causal order of the residual vectors obtained from restricted VAR model. See Pearl (1995), Spirtes, Glymour, and Scheines for details on graphs analysis. The causal ordering is transformed into restrictions in the Bernanke-Sims decomposition and the impulse response is computed to study the spillover across markets. The second approach involves estimating the multivariate GARCH models of several market returns to investigate the directions of spillover in mean level as well as in volatility level. To double check our empirical results, we examine simple cross correlations among stock returns of China stock markets, Hong Kong, Taiwan, and US markets.
The empirical results support the hypothesis of information advantage of domestic investors in A-share market over B-share markets. Also, we found no linkages of China stock markets with Hong Kong, Taiwan, and US stock markets.
By this empirical application, this paper attempts to bring together restricted VAR modeling, direct graph theory, Bernanke-Sims decomposition and impulse response analysis. Though we are not the first one to combine direct graph method with VAR modeling (Yang (2003), Bessler and Yang (2003), and Reale and Wilson (2000)), we strongly believe that the proposed procedure could become a powerful tool in analyzing dynamic relationship among variables.
In addition to this introduction, Section 2 discusses the econometric methods and data are described in Section 3. Section 4 summarizes empirical findings and conclusions are put in Section 5.
2
Econometric Methods
In this section, we shall discuss the details of building restricted VAR models, direct graph theory and multivariate GARCH models.
2.1
Estimating restricted VAR models
We select lag,p, of VAR model by examining the AIC, partial autocorrelation coefficient matrix
and their associated chi-square test statistics. The essential criterion is to choose the model with minimalp such that there are no remaining autocorrelation among residuals and coefficient matrix
for lagp are significantly different from zero. See Tiao and Box (1981) and Tiao (2001) for details.
Next, the VAR(p) model is estimated using exact maximum likelihood estimate method with
the parameter estimates of conditional maximum likelihood estimates as initial values. Typically, a lot of parameters are insignificant. As insignificancy might arise due to multi-collinearity among variables, removing all insignificant parameters simultaneously might cause the residuals to deviate
from white noise vector and induce more insignificant parameters. Lin(2003) proposes to first remove all parameters with t-value less than 1 and then remove the insignificant parameter with smallest t-value sequently. Finally, re-estimate the restricted model with exact MLE and apply a Wald-test for the imposed zero restrictions. Of course, one has to examine the residuals to make sure that they behave like vector white noise.
2.2
Impulse response and causal ordering
It is well known that residuals from a VAR model are generally correlated and applying the Choleski decomposition is equivalent to assuming recursive causal ordering from the top variable to the bottom variable. Changing the order of the variables will change the result of impulse re-sponse analysis. Bernanke (1986) provided a framework allowing for nonrecursive contemporary causal structure. More specifically, let ut be the vector residuals from VAR models with mean 0
and covarianceΣ. Bernanke decomposition writes utasAut= vtwhereA is a square matrix with
conforming dimension andVtis a vector of orthogonal shocks with diagonal covariance matrix. In
other words,Σ is factored into A−1∗ D ∗ A−10 whereD is diagonal with the variances of V . A has
unit diagonals, but allows for the researchers to force certainA(i, j) = 0, i 6= j. These restrictions
can be tested. Choleski decomposition restrictsA to be lower triangular matrix.
Drawing on work in the area of causal modeling by Glymour and Spirtes (1988) and Spirtes, Glymour and Scheines (1993), Swanson and Granger (1997) proposes a two-step search procedure to determineA. The procedure uses economic information and examines first order partial
corre-lations of VAR residuals in the first step and then test the implying restrictions in the second step. In this study, we rely on direct graphs theory to draw inference on causal ordering as the latter involves less subjective insights and use partial correlations up toN − 2 where N is the number
of returns under investigation. Further, priori knowledge about partial causal ordering of variables can be easily incorporated in the direct graphs analysis, which we shall turn to in next section.
2.3
Directed graphs theory
A direct graph assigns contemporaneous causal flow among a set of variables based on correlations and partial correlations. To illustrate the main idea, letX, Y, Z be three variables under
investiga-tion. Y ← X → Z represents the fact that X is the common cause of Y and Z. Unconditional
correlation betweenY and Z is nonzero but conditional correlation between Y and Z given X is
zero. On the other hand,Y → X ← Z says both Y and Z causes X. Thus, unconditional
corre-lation betweenY and Z is zero but conditional correlation between Y and Z given X is nonzero.
X, Y is uncorrelated with Z. The direction of arrow is then transformed into the zero constraints of A(i, j), i 6= j. Let ut= (Xt, Yt, Zt)0and then the correspondingA matrix for three cases discussed
above denoted asA1, A2andA3are:
A1 = 1 0 0 a21 1 0 a31 0 1 ; A2 = 1 a12 a13 0 1 0 0 0 1 ; A3 = 1 a12 0 0 1 0 a31 0 1
The edge relation of each pair of variables characterizes the causal relation between them. No edge indicates (conditional) independence between two variables whereas an undirected edge (X − Y ) signifies a correlation with no particular causal interpretation. A directed edge (Y → X)
means Y causes X but X does not cause Y conditional on other variables. A bidirected edge
(X ↔ Y ) indicates bidirection causal between these two variables. In other words, there are
contemporaneous feedback betweenX and Y .
Several search algorithms are available and PC algorithm seems to be the most popular one. See Pearl (2000), and Spirtes, Glymour and Scheines (1993) for details. In this paper, we adopt PC algorithm and outline the main algorithm as below. First, start with a graph in which each variable is connected by an edge with every other variables. Compute the unconditional correlation between every pair of variables and remove the edge for the insignificant pairs. Compute the
1-th order conditional correlation between every pair of variables and eliminate 1-the edge between
insignificant ones. Repeat the procedure for computing i-th order conditional correlation until i = N − 2, where N is the number of variables under investigation. Fisher’s z statistics is used in
the significance test:
z(i, j|K) = 1/2(n − |K| − 3)(1/2)ln{(|1 + r[i, j|K]|) |1 − r[i, j|K]| }
where r([i, j|K]) denotes conditional correlation between variables, i and j conditional upon K
variables, and|K| number of series for K.
Under some regularity conditions,z approximates standard normal distribution. Next, for each
pair of variables(Y, Z) that are unconnected by a direct edge but connected through an undirected
edge through a third variableX. Assign Y → X ← Z if and only if conditional correlation of Y and Z conditioning on all possible variables combinations with the presence of X variable are
nonzero. Repeat the process above until all possible cases are exhausted. IfX → Z, Z − Y and X and Y are not directly connected, the assign Z → Y . If there is a directed path between X and Y (say X → Z → Y ) and there is an undirected edge between X and Y , then assign X → Y .
Pearl(2000) and Spirtes, Glymour, and Scheines (1993) provide detailed account of this ap-proach. Demiralp and Hoover (2003) present simulation results to show how the efficacy of PC
algorithm varies with signal strength. In general, they find direct graphs method to be an useful tool in structural causal analysis.
2.4
Multivariate GARCH models
The mean and variance equations in a system are:
yt = B + D ∗ dummyt+ P yt−1+ t (1)
Ht = E(0tt|It−1) (2)
Ht = C + B00t−1t−1B + A0Ht−1A (3)
where It−1 contains information up to t − 1, and dummyt measures Monday dummy . This is
the M-GARCH(1,1) model. Previous research has shown that this model could capture the fun-damental features of the financial markets. While higher order is feasible, the increase in number parameters often create problem for convergence in estimation. See Chou, Lin, and Wu (1999) for an example.
Denoting n as the number of endogenous variables, which is 2 in our case, Ω, A and B are
symmetric nxn parameter matrices whileA is a general nxn parameter matrices. This is the BEKK
model of Engle and Kroner (1995). The BEKK has the advantage of being parsimonious in param-eters which is due to the restrictions imposed on across and within equations. Also, it guarantee the positive definiteness of the covariance matrix.
For a nonsignificant matrixΓ the residuals from the structural equations and from the reduced
form have the same GARCH structures. The likelihood function can be written as:
L = T X t=1 Lt (4) Lt = n 2ln(2π) − ln|Γ| − 1 2ln|Ht| − 1 2 0 tHt−1t (5)
The maximum likelihood estimate is then applied to obtain the estimate of unknown parameters that uses the updating algorithm:
θi+1= θi+ ρ
∂2L
∂θ∂θ0
∂L ∂θ
whereθ contains all the parameters and ρ is a scalar step length. Simplex algorithm is first used
to obtain initial estimates and BFGS (Broyden, Fletcher, Goldfarb, and Shanno) scent methods follows as updating algorithm.
Bai, Russell and Tiao (2003) constructs analytical representations for the precision of vari-ance estimates in the presence of volatility clustering, leptokurtosis, deterministic patterns in the
volatility structure and serial correlation of the returns. However, it is unclear how the presence of ARCH error will affect the finite sample efficiency of the estimate of conditional correlation and direct graphs analysis.
3
Data and Preliminary Analysis
The data used consists of daily stock returns of Shanghai A-share (SA), Shanghai B-share (SB), Shenzhen A-share (ZA), Shenzhen B-share (ZB), Hong Kong H-share (HH), Hong Kong Red Chip (HR), Hong Kong Hang Seng Index (HS), Taiwan Stock Exchange Weighted Index (TAIEX), SP500, NASDAQ and Dow Jones indexes. HH and HR are all China based companies with HH registering in China and HR in Hong Kong respectively. Cross listing of the same company in two markets is not allowed.
We distinguish three returns: Close at time t-1 to Open at time t (CTO), Open at time t to
close at timet (OTC), and Close at time t-1 (CTC) to close to time t. To be precise, three returns
are defined as:
CT Ot = (Ot− Ct−1)/Ct−1∗ 100
OT Ct = (Ct− Ot)/Ot∗ 100
CT Ct = (Ct− Ct−1)/Ct−1∗ 100
In Taiwan stock market, there is a price limit for each stock. Price of each stock is only allowed to fluctuate within the band of 7% with closing price of previous trading day. See Cho, Russell, Tiao and Tsay (2002) for an analysis of the effect of these price limits.
All data are taken from database of Taiwan Economic Journal ranging from January 5, 2000 to May 30, 2003 with 794 observations. When US stock markets are included, number of observa-tions reduces to 731.
The close prices of all 11 markets mentioned above are put in Figure 1. From the figure, we make the following observations. First, judging from the co-movement, we can divide 11 close prices into three groups. Group 1 consists of Dow Jones Index, NASDAQ, SP500, TAIEX, HS, and HR. SA and ZA make up the second group while the third group includes SB, ZB, and HH. Second, While group A exhibits a long-term declining trend, the second and the third groups actually display a growing trend prior to May 30, 2001. This might be explained by the fact that on February 28, 2001 the restriction of B-share to foreign traders is lifted in both Shanghai and Shenzhen markets that significantly shrank the discount of B-share market to A-share market. Two B-share markets had been shutdown for one week prior to February 28, 2001. When the B-share market is re-opened, daily return jumped up by over 9.7% for 5 (4) consecutive days in Shenzhen
(Shanghai) market. These are essentially level shifts for the daily close price for SB, ZB and HH. Third, the declining speed for China stock markets after May 30, 20001 are slightly slower that of US, Taiwan and Hong Kong market.
The descriptive statistics for 11 daily CTC returns as well as CTO and OTC returns for China stock markets are put in Table 1. The fifth column of the table is excess kurtosis. From the table, we observe the following. First, SB and ZB have the highest CTC returns followed by HH. This is due to the effect of the event of opening B-share markets to domestic investors on February 28, 2001. In our analysis, we subtract the CTC return during the period between February 28, 2001 to May 31, 2001 from the mean of this subperiod and keep observations in other subperiod unchanged. We have also tried to control the impact by adding dummy and found the results similar. Second, except for HR, all China stock returns are positive while other returns are negative during the same sample period. Third, as is obvious from the second and third panels of the table, CTO is much higher than OTC for China stock market, indicating the pattern of opening high and staying high until closing. Fourth, from the standard deviation and kurtosis, we find that A-share markets are much more volatile than B-share markets which latter are more volatile than US, Hong Kong and Taiwan stock markets. The kurtosis for the CTO of four China markets are all higher than 50 with both ZA and SA greater than 100. Fitting GARCH models or any other time series models for such high kurtosis seems impossible.
4
Empirical results
In additional to the impulse response analysis and multivariate GARCH models, we also perform simple cross correlation analysis as a preliminary analysis of the spillover effect between China stock markets, Hong Kong, Taiwan and US markets. We shall discuss the empirical results in the sequel.
4.1
Empirical results of cross correlation analysis
The cross correlation of the returns of Hong Kong, China and Taiwan stock markets with those of SP500, Dow Jones and NASDAQ are reported in Table 2. To account for different time zone, returns at timet − 1 in US markets are paired with returns at time t for three Asian stock markets.
To explore possible lead-lag relationship, we compute cross correlation for lagl = −1, 0, 1, where rxy(l) = Corr(xt, yt+l). As is clear from the table, HS has the strongest correlation with US
market with correlation coefficients all higher than 0.4. The correlations of HR and HH with US markets are also high with correlation coefficient higher than 0.3 for the former and around 0.2 for the latter. The correlation coefficients for Taiwan are all higher than 0.25. As for China stock
markets, the correlation coefficients are all less than 0.1. We further compute the correlation of stock markets of China with Hong Kong and Taiwan and summarize the results in Table 3. From the tables we find that the correlations between stock markets of China an Taiwan are low with correlation coefficients all less than 0.08. As for the correlation between Hong Kong and China stock markets, the linkage between B-share and HS are stronger than that between A-share and HS.
To explore the possibility that spillover effects only occur when the market opens, we further compute the correlation between CTO of China stock market with US and Hong Kong markets. The results are reported in Table 4. Again, all correlations coefficients are very small with almost all less than 0.05.
Lastly, we examine the cross correlation among four China stock markets and report the results in Table 5. From the table, we find strongest linkages among two A-share markets, ZA, and SA, followed by two B-share markets, ZB and SB. Correlation between SA and SB, ZA and ZB, SA and ZB, as well as ZA and SB are about the same with value around 0.63. As for the cross-correlation between CTO and OTC as reported in the bottom panel of Table 5, we find that within the same market, the linkage is weak. In other words, opening price today is not influential of closing price today. On the contrary, OCT att-1 has an impact of CTO at time t and the effect is across markets.
In summary, the linkage between China stock market with US, Taiwan and Hong Kong (HS) stock markets are very weak. Due to relatively small sample size, we can not include too many variables in VAR and GARCH models. Also drawing inference from the results of cross correlation analysis, we focus on 6 China stock returns (CTC), SA, SB, ZA, ZB, HR and HH in the sequel. This assumption is confirmed by applying direct graphs methods to the contemporaneous correlation matrix among these six indexes, three US stock indexes, TAIEX and HS. There are no edge linking US, Taiwan and HS with these 6 returns.
4.2
Empirical results of impulse response analysis
It is somewhat surprising the it takes lag 6 to whiten the residual. For the unrestricted mode, there are 222 parameters to estimate. We follow the proposed procedure above and obtain a restricted model with only 37 parameters. In other words, 185 parameters are restricted to be zero and their associated variables are removed from the model. The significance pattern of the estimates are reported in Table 6, where ’.’ means insignificant, ’+’ positively significant and ’-’ negatively significant. Theχ2 test statistics is 209.0327 which gives p-value 0.1087. Thus, we cannot reject
the null hypothesis that 185 parameters are equal to zero. We further examine the diagnostic checking statistics of residual vector and do not find remaining autocorrelation.
obtain the causal graphs as in 2. The graph read as below. (1) HH and HR are independent of ZA, ZB, SA and SB. (2) HH and HR are related but graphs theory is inclusive about causal order. (3). ZA and SB causes ZB. ZA and ZB are related but causal direction is inconclusive. Similarly for SA and SB. Drawing upon the findings of correlation analysis, we assign the causal order for the three inconclusive cases asSA → ZA, SA → ZB and HR → HH. The pattern matrix in
the Bernanke-Sims decomposition for correspondingA matrix used in impulse response analysis
become A0 = 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1
The impulse response of the effects of one market to other markets are put in Figures 3 to 8. From these graphs, we make the following observations. First, information flow goes from A-share market to B-share market and not the other way around. In other words, shocks to A-share market transmit to B-share market but shocks to B-share market have no significant effect on A-share market. Second, the speed of spillover in Shanghai market is faster than that of Shenzhen market. Shocks in Shanghai A-share market affect instantaneously Shanghai B-share market and Shenzhen share market while shocks in Shenzhen A-share market does not have impact on Shanghai B-share market until 6 days later. Third, shocks in Shanghai A-B-share market have an instantaneous impact on Shenzhen A-share market but it takes 4 days for the impact from the opposition to be effective. This result is no surprising as B-share markets only account for 3% of total stock transaction and volume of transaction in Shanghai market is larger than that of Shenzhen market. In addition, Shanghai has been viewed as the financial center of China and receive more attention than Shenzhen market. Fourth, ZB stays in the bottom of the causal chain by receiving impact from ZA, SA, and SB but does not affect other markets. Fifth, HH behaves like ZB to reflect impact on ZA, SA, SB and HR. Sixth, HH and HR do not have significant effect on China domestic stock markets.
4.3
Empirical results of GARCH modeling
The estimation results of M-GARCH model are reported in Table 7. As is obvious from the table, the multivariate GARCH model basically confirm the findings of previous two methods. The findings for the mean of the returns are: (1) spillover run unidirectionally from A-share market to B-share market within each market and across markets; (2)there exist feedback between SA and
ZA. Similarly, feedback are found for SB and ZB. As for volatility level, each market is affected by other markets. In other words, volatility spillover from any market to other markets.
We shall conclude this section by comparing our findings with those of Yang(2003). Yang (2003) builds an unrestricted VAR(1) for same six returns as ours for the data from January 2, 1995 to December 29, 2000. He also applies direct graphs theory to determine the contemporane-ous causal order followed by a forecast error decomposition. He started with level VAR, test for cointegration, convert the cointegrated model back to level VAR and then perform forecast error decomposition. We analyze three different returns and do not need to worry about cointegration. We choose to perform response analysis and report confidence interval by simulation. We use most recent data from January 5, 2001 to May 30, 2003. Yang concludes causal order from ZB to ZA and SA to SB while we find causal flow from A-share to B-share. The difference might arise from different sample periods but considering the size of B-share markets to A-share markets, we believe that our findings are more reasonable.
5
Conclusions
We have combined directed graphs theory with impulse response to study the linkage of China stock markets with US, Hong Kong and Taiwan stock markets. We also employ multivariate GARCH models to analyze the mean and volatility spillover among China stock market. The empirical analysis find weak linkage between China stock market with US and Taiwan stock mar-kets. It seems that China stock markets do not synchronize with these stock marmar-kets. As for the four domestic markets, spillover in mean returns goes unidirectionally from A-share market to B-share market but spillover in volatility is bidirectional. Further, Shanghai stock market seems to play a dominating role over Shenzhen stock market.
Table 1: Descriptive Statistics for 11 stock returns
Stock Mean SD Skewness Kurtosis
Close-to-Close return DJ -0.00612 1.41092 0.22089 1.45811 NASDAQ -0.05763 2.60803 0.45478 1.80180 SP500 -0.02632 1.47399 0.27820 1.06206 TX -0.02466 1.89690 0.23023 0.60562 HS -0.04417 1.59629 -0.06570 1.82112 HR -0.01955 2.29318 0.25197 2.87506 HH 0.11891 2.06231 0.58156 3.06123 SA 0.06253 1.42137 1.13759 9.23670 SB 0.23601 2.42950 0.65727 3.67997 ZA 0.05802 1.48472 0.89229 7.87250 ZB 0.22115 2.51285 0.75152 3.84218 Close-to-Open return SA 0.06550 0.62910 8.86420 109.27130 SB 0.13004 1.02210 6.35959 53.12769 ZA 0.04632 0.60453 8.95247 110.01810 ZB 0.16490 0.92401 7.63606 70.44921 Open-to-Close return SA -0.00277 1.28681 0.12750 3.82135 SB 0.01908 2.14690 0.16884 4.08185 ZA 0.01184 1.36452 0.10340 3.85243 ZB 0.05838 2.42293 0.25318 3.93920
Table 2: Cross-Correlation of HongKong, Taiwan and China Stock Markets with US Stock Market
Stock DJ NASDAQ SP500
Hong Kong Stock Market
HS -1 0.0544 0.0235 0.0547 0 0.4216 0.463 0.4651 1 0.0946 0.1233 0.1092 HR -1 0.0094 0.0051 0.0117 0 0.3042 0.3325 0.3385 1 0.1283 0.1118 0.1257 HH -1 -0.035 -0.0713 -0.0447 0 0.1865 0.2031 0.2082 1 0.0547 0.0802 0.0631
Taiwan Stock Market
TX -1 0.0205 0.1026 0.0453 0 0.2513 0.2595 0.2672 1 0.1024 0.1295 0.1082
China Stock Market
SA -1 0.0065 -0.0151 0.0002 0 0.0175 0.0186 0.0137 1 -0.0475 -0.0449 -0.0482 SB -1 -0.0099 -0.0721 -0.0333 0 0.0828 0.0485 0.0698 1 -0.021 -0.0453 -0.0343 ZA -1 0.0128 -0.0168 0.0032 0 0.0173 0.0234 0.0147 1 -0.0502 -0.0479 -0.0521 ZB -1 -0.0141 -0.058 -0.0296 0 0.0936 0.0844 0.092 1 -0.024 -0.0249 -0.0279
Table 3: Cross-Correlation of China Stock Markets with Taiwan and Hong Kong Stock Markets Stock TX HS HR HH SA -1 0.0792 0.024 0.0351 -0.0132 0 -0.0179 0.0868 0.0928 0.1249 1 0.0012 -0.0665 -0.0299 -0.0737 SB -1 0.0399 0.0064 0.0007 0.0054 0 0.047 0.1342 0.1121 0.1429 1 -0.0316 -0.0525 -0.0389 -0.0944 ZA -1 0.0771 0.0218 0.0383 -0.0173 0 -0.0148 0.0796 0.0824 0.1172 1 -0.0041 -0.0653 -0.0296 -0.0804 ZB -1 0.0715 -0.0024 -0.0113 -0.027 0 0.0599 0.1485 0.1119 0.1152 1 -0.0112 -0.0344 -0.0216 -0.0697
Table 4: Cross-Correlation of China, US and Hong Kong Stock Markets
Stock DJ NASDAQ SP500 HS HR HH Close-to-Close SA(Close-to-Open) -1 0.0161 0.0063 0.003 0.0904 0.0998 0.0522 0 0.0092 -0.0076 -0.0024 0.0347 0.0635 0.0336 1 0.0246 0.0453 0.0256 -0.0109 0.0183 -0.0016 SB(Close-to-Open) -1 0.0137 -0.0132 -0.0002 0.0203 0.0301 0.0476 0 0.0635 0.031 0.0475 0.0735 0.0968 0.0808 1 0.021 0.0503 0.0237 0.0303 0.0494 -0.0032 ZA(Close-to-Open) -1 0.0138 0.0078 0.0022 0.082 0.0879 0.046 0 0.0087 -0.0107 -0.0067 0.0301 0.0607 0.0356 1 0.0258 0.0381 0.0223 -0.0096 0.0133 -0.0036 ZB(Close-to-Open) -1 0.0033 -0.0149 -0.0127 0.0304 0.0382 0.0364 0 0.0564 0.0412 0.0461 0.0445 0.0709 0.0372 1 0.0142 0.0342 0.0127 0.0168 0.0243 0.0103
Table 5: Cross-Correlation among 4 China stock markets Close-to-Close return SA SB ZA ZB SA -1 0.0071 0.0024 0.0037 0.0029 0 0.6293 0.9837 0.6392 1 -0.051 0.0171 -0.0534 SB -1 0.0711 -0.0481 0.069 0 0.6252 0.8577 1 0.0067 0.067 ZA -1 0.0163 0.0086 0 0.6397 1 -0.05 ZB -1 0.0987 0 1
Close-to-Open return and Open-to-Close return
Open-to-Close return Close-to-Open return SA SB ZA ZB SA -1 0.237 0.1372 0.2505 0.1798 0 -0.0235 -0.0176 -0.0005 -0.0005 1 -0.0497 -0.0686 -0.0578 -0.0809 SB -1 0.1353 0.3169 0.1523 0.3429 0 -0.0331 0.0021 -0.0169 0.0419 1 -0.019 -0.1739 -0.037 -0.1749 ZA -1 0.2422 0.131 0.2598 0.1783 0 -0.0382 -0.0231 -0.0174 -0.0131 1 -0.0544 -0.071 -0.065 -0.0811 ZB -1 0.1088 0.2056 0.1136 0.3082 0 -0.0605 -0.0996 -0.0509 -0.0995 1 0.0095 -0.082 -0.0032 -0.0665
Table 6: Significance Pattern of VAR(6) models for ZA, ZB, SA, SB, HR, and HH C Φ1 Φ2 Φ3 Φ4 Φ6 . . . . + . . . + . - . . . + . - . . + . + - . . . - . . . + . - + . . . . . . + . . . + . - . . . + . - . . + . . . + . . . - . . . + . - . . . . . . - . + . . - . + . . . - . + . . . -The model isyt = c + Φ1yt−1+ . . . + Φ6yt−1+ t
Table 7: Estimation results of M-GARCH Models
Variable Coeff T-Stat Variable Coeff T-Stat
B11 -0.04445112 -0.43331 VAR(1,4) 0.05615391* 9.53496 B21 0.10181669* 4.05090 VAR(2,4) 0.29447625* 3.88106 B31 -0.05478603 -1.26109 VAR(3,4) -0.04826805* -5.08553 B41 0.09497512* 4.03400 VAR(4,4) 0.23577822* 6.68491 P11 -0.28089090 -0.65104 VBR(1,1) 0.14171402 1.42091 P12 8.82740179 0.67691 VBR(2,1) 0.04967372 0.59293 P13 -0.15115793 -0.51755 VBR(3,1) -0.45802221* -4.62600 P14 0.01414863 0.39029 VBR(4,1) 0.08206867 0.97202 P21 -0.29824932* -2.82117 VBR(1,2) -0.00717032 -0.78140 P22 -15.38251335* -4.69848 VBR(2,2) 0.03958990* 4.47419 P23 0.44622415* 6.23518 VBR(3,2) -0.01028988 -1.18250 P24 -0.00369124 -0.40546 VBR(4,2) -0.01107684 -1.25432 P31 -0.41107393* -2.24977 VBR(1,3) -0.14897222* -2.27443 P32 9.70186891 1.75732 VBR(2,3) 0.06011878 1.29799 P33 -0.09785808 -0.79108 VBR(3,3) -0.26872156* -4.31539 P34 0.02119631 1.38132 VBR(4,3) 0.05936620 1.28909 P41 -0.09879660 -0.99764 VBR(1,4) -0.00587779 -0.64042 P42 -15.84666602* -5.18329 VBR(2,4) 0.00062476 0.06941 P43 0.65677240* 9.79800 VBR(3,4) -0.01147905 -1.31997 P44 0.03834491* 4.51190 VBR(4,4) 0.02754570* 3.04940 D11 0.12393901 1.35966 VCR(1,1) -0.27177852* -17.53479 D21 -0.01885947 -0.59523 VCR(2,1) -0.14299456* -6.41426 D31 0.20534747* 2.26987 VCR(3,1) 0.99118882* 63.50114 D41 -0.01863376 -0.58740 VCR(4,1) 0.66324548* 28.09564 VAR(1,1) 0.37132528* 9.96133 VCR(1,2) 0.00000000* 0.00000 VAR(2,1) 3.40155005* 10.83752 VCR(2,2) 0.00036685 1.76877 VAR(3,1) -0.83431218* -16.86891 VCR(3,2) -0.00014395 -1.15624 VAR(4,1) -3.01468282* -9.31696 VCR(4,2) 2.22751027* 185.30643 VAR(1,2) 0.05631398* 9.52214 VCR(1,3) 0.00000000* 0.00000 VAR(2,2) 0.22660018* 3.41087 VCR(2,3) 0.00000000* 0.00000 VAR(3,2) -0.04823599* -5.11427 VCR(3,3) 1.11517483* 91.33073 VAR(4,2) 0.30376753* 8.35691 VCR(4,3) 0.58193455* 23.07853 VAR(1,3) 0.28143830* 10.32185 VCR(1,4) 0.00000000* 0.00000 VAR(2,3) 0.16918025 0.84987 VCR(2,4) 0.00000000* 0.00000 VAR(3,3) -0.82744753* -18.7038816VCR(3,4) 0.00000000* 0.00000
DJ 250 500 750 7000 8000 9000 10000 11000 12000 SA 500 1280 1440 1600 1760 1920 2080 2240 2400 HS 500 8000 10000 12000 14000 16000 18000 20000 SP500 250 500 750 720 840 960 1080 1200 1320 1440 1560 ZA 500 360 400 440 480 520 560 600 640 680 720 HR 500 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 NASDAQ 250 500 750 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 SB 500 25 50 75 100 125 150 175 200 225 250 HH 500 300 600 900 1200 1500 1800 2100 2400 2700 TWN 250 500 750 3000 4000 5000 6000 7000 8000 9000 10000 11000 ZB 100 200 300 400 500 600 700 50 100 150 200 250 300 350 400 450
HH
SA
HR
ZB
ZA
SB
Effects of a Shock to ZAR
ZAR 0 5 10 15 20 -1.2 -0.8 -0.4 -0.0 0.4 0.8 1.2 1.6 ZBR 0 5 10 15 20 -1.2 -0.8 -0.4 -0.0 0.4 0.8 1.2 1.6 SAR 0 5 10 15 20 -1.2 -0.8 -0.4 -0.0 0.4 0.8 1.2 1.6 SBR 0 5 10 15 20 -1.2 -0.8 -0.4 -0.0 0.4 0.8 1.2 1.6 HR 0 5 10 15 20 -1.2 -0.8 -0.4 -0.0 0.4 0.8 1.2 1.6 HH 0 5 10 15 20 -1.2 -0.8 -0.4 -0.0 0.4 0.8 1.2 1.6Effects of a Shock to ZBR
ZAR 0 5 10 15 20 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 ZBR 0 5 10 15 20 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 SAR 0 5 10 15 20 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 SBR 0 5 10 15 20 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 HR 0 5 10 15 20 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 HH 0 5 10 15 20 -0.2 0.0 0.2 0.4 0.6 0.8 1.0Effects of a Shock to SAR
ZAR 0 5 10 15 20 -0.16 0.00 0.16 0.32 0.48 0.64 0.80 0.96 1.12 1.28 ZBR 0 5 10 15 20 -0.16 0.00 0.16 0.32 0.48 0.64 0.80 0.96 1.12 1.28 SAR 0 5 10 15 20 -0.16 0.00 0.16 0.32 0.48 0.64 0.80 0.96 1.12 1.28 SBR 0 5 10 15 20 -0.16 0.00 0.16 0.32 0.48 0.64 0.80 0.96 1.12 1.28 HR 0 5 10 15 20 -0.16 0.00 0.16 0.32 0.48 0.64 0.80 0.96 1.12 1.28 HH 0 5 10 15 20 -0.16 0.00 0.16 0.32 0.48 0.64 0.80 0.96 1.12 1.28Effects of a Shock to SBR
ZAR 0 5 10 15 20 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 ZBR 0 5 10 15 20 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 SAR 0 5 10 15 20 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 SBR 0 5 10 15 20 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 HR 0 5 10 15 20 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 HH 0 5 10 15 20 -0.2 0.0 0.2 0.4 0.6 0.8 1.0Effects of a Shock to HH
ZAR 0 5 10 15 20 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 ZBR 0 5 10 15 20 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 SAR 0 5 10 15 20 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 SBR 0 5 10 15 20 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 HR 0 5 10 15 20 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 HH 0 5 10 15 20 -0.2 0.0 0.2 0.4 0.6 0.8 1.0Effects of a Shock to HR
ZAR 0 5 10 15 20 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 ZBR 0 5 10 15 20 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 SAR 0 5 10 15 20 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 SBR 0 5 10 15 20 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 HR 0 5 10 15 20 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 HH 0 5 10 15 20 -0.2 0.0 0.2 0.4 0.6 0.8 1.0References
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