independent variables in the conditional volatility equation. A similar procedure is also applied to the other three indices Theodossiou, 1994.
4. Discussion of empirical results
4
.
1
. Return and 6olatility beha6ior analysis Table 5 reports the results for the return behavior and the volatility of the
HSCEI, HSCCI, SHI, and SZI by EGARCH-M model. We employ the iterative procedure by Berndt et al. 1994 to maximize the log-likelihood function L
T
and determine the lag lengths for the conditional mean and variance on the basis of the
Schwarz criterion SC and Ljung – Box Q and Q
2
statistics [LB Q
and LB Q
2
].
12
Ljung – Box statistics are not significant at the 5 level, indicating that the model does not have autocorrelation and heteroscedasticity error. In all cases, an AR1-
EGARCH1,1-mean process appears to provide an adequate representation of the time-series properties of each index return.
13
The parameters a, a
†
, a , a
are statistically insignificant, indicating no relationship between the conditional variance and conditional mean of the index
returns. The findings suggest that volatility does not have any significant impact on the future movement of the four index returns. These results are not surprising
given the mixed results in the literature Chan et al., 1992; Glosten et al., 1993; Whitelaw, 1994. The day-of-the-week effects in the mean equations vary among
different indices. Monday and Thursday dummies have a negative effect on the HSCEI return. Wednesday and Friday dummies have a positive effect on the SHI
and Monday and Friday dummies have a positive effect on the SZI. There is no day-of-the-week effect in the HSCCI mean equations. It is interesting to note that
all day-of-the-week dummy variables in all volatility equations are negative and significant, suggesting that day-of-the-week has a significant negative impact on the
volatility of all index returns. Cheung and Ng 1992b find day-of-the-week effects in 251 AMEX-NYSE stock returns. We find that there are day-of-the-week effects
in the HSCEI, HSCCI, SHI and SZI volatility.
There is evidence that past returns influence current and future returns with the exception of the SZI since f
1
, f
1 †
and f
1
are significant for the HSCEI, HSCCI, and SHI, respectively.
The coefficients for past volatility shocks g
1
, g
1 †
, g
1
, g
1
and past conditional variances d
1
, d
1 †
, d
1
, d
1
are statistically significant, indicating that volatility terms of all index returns are predictable using past information. The asymmetry parame-
12
The Schwarz criterion used is defined as: SC = − max Lx − 12k logn, where max Lx is the sample log-likelihood function evaluated at its maximum, k is the number of estimated parameters and
n is the sample size Schwarz, 1978.
13
Also an ARMA1,1-EGARCH1,1-M model was estimated. The results are less significant after inclusion of the MA1 term.
W .P
.H .
Poon ,
H .-
G .
Fung J
. of
Multi .
Fin .
Manag .
10 2000
315 –
343
337 Table 6
Multivariate EGARCH-M model-return and volatility with spillover effect The conditional return and conditional variance for R
t
, R
t †
, R
t
and R
t
are: R
t
=
i = 1 5
l
i
D
i
+ f
1
R
t−1
+ f
2
R
t−1 †
+ f
3
R
t−1
+ f
4
R
t−1
+ a
h
t
+ o
t
4a h
t
= exp
i = 1 5
c
i
D
i
+ d
lnh
t−1
+g
1
gz
t−1
+g
2
gz
t−1 †
+g
3
gz
t−1
+g
4
gz
t−1
} 4b
R
t †
=
i = 1 5
l
i †
D
i †
+ f
1 †
R
t-1
+ f
2 †
R
t−1 †
+ f
3 †
R
t−1
+ f
4 †
R
t−1
+ a
†
h
t †
+ o
t †
4c h
t †
= exp
i = 1 5
c
i †
D
i †
+ d
†
lnh
t−1 †
+g
1 †
gz
t−1
+g
2 †
gz
t−1 †
+g
3 †
gz
t−1
+g
4 †
gz
t−1
} 4d
R
t
=
i = 1 5
l
i
D
i
+ f
1
R
t-1
+ f
2
R
t−1
+ f
3
R
t−1
+ f
4
R
t−1
+ a
h
t
+ o
t
4e h
t
= exp
i = 1 5
c
i
D
i
+ d
lnh
t−1
+g
1
gz
t−1
+g
2
gz
t−1
+g
3
gz
t−1
+g
4
gz
t−1
} 4f
R
t
=
i = 1 5
l
i
D
i
+ f
1
R
t-1
+ f
2
R
t−1 †
+ f
3
R
t−1
+ f
4
R
t−1
+ a
h
t
+ o
t
4g h
t
= exp
i = 1 5
c
i
D
i
+ d
lnh
t−1
+g
1
gz
t−1
+g
2
gz
t−1 †
+g
3
gz
t−1
+g
4
gz
t−1
} 4h
where R
t
, R
t †
, R
t
, R
t
, return of HSCEI, HSCCI, SHI, and SZI at day t, respectively; D
i
, D
i †
, D
i
, D
i
, dummy variable representing the day of the week i i.e., i = 1, 2, 3, 4, 5 for return of HSCEI, HSCCI, SHI, and SZI; u, u
†
, u
, u , asymmetry parameters of HSCEI, HSCCI, SHI, and SZI, respectively;
6 , 6
†
, 6
, 6 , tail thickness parameters. When 6 = 2, the GED becomes the normal distribution. When 6B2, the distribution of o
t
has thicker tails than a normal distribution. When 6\2, the distribution of o
t
has thinner tails than a normal distribution. o
t
, o
t †
, o
t
, o
t
, conditional error term of HSCEI, HSCCI, SHI, and SZI at day t, respectively; z
t
, z
t †
, z
t
, z
t
, standardized residuals HSCEI, HSCCI, SHI, and SZI at day t, respectively; h
t
, h
t †
, h
t
, h
t
, conditional variance HSCEI, HSCCI, SHI, and SZI at day t, respectively.
Coefficient Shanghai composite
H-share index Coefficient
Coefficient Red chip index
Shenzhen composite Coefficient
index SHI HSCEI
HSCCI index SZI
Return equation
:
l
1
0.0015 l
1
0.0043 l
1 †
l
1
0.0003 −
0.0025 l
2
− 0.0010
− 0.0019
− 0.0007
l
2
l
2
− 0.0007
l
2 †
W .P
.H .
Poon ,
H .-
G .
Fung J
. of
Multi .
Fin .
Manag .
10 2000
315 –
343
338 Table 6 Continued
l
3
0.0023 l
3
− 0.0005
l
3
l
3 †
0.0006 0.0010
l
4
l
4
− 0.0021
− 0.0011
l
4 †
− 0.0001
l
4
− 0.0016
l
5
0.0044 0.0016
l
5
− 0.0011
l
5
0.0008 l
5 †
0.0046 0.1764
f
1
0.0079 f
1 †
0.0130 f
1
f
1
f
2
0.0496 f
2
0.0520 f
2 †
0.1966 f
2
0.0388
f
3
− 0.0204
0.0057 f
3 †
0.0553 f
3
0.0183
f
3
− 0.1050
− 0.0263
f
4
− 0.0208
f
4 †
− 0.0063
f
4
f
4
a 0.1182
a −
0.1044 0.2349
a a
†
− 0.0604
Variance equation
:
c
1
− 0.9509
− 0.8196
c
1
− 1.7460
c
1
− 0.8918
c
1 †
− 1.6898
− 1.8454
c
2
− 1.6611
c
2 †
− 1.3690
c
2
c
2
c
3
c
3
− 1.1938
− 2.4750
c
3 †
− 1.4142
c
3
− 0.8055
c
4
− 1.0905
− 1.3035
− 1.9475
c
4 †
c
4
c
4
− 1.2018
− 1.1820
− 2.3833
c
5
− 1.5268
c
5 †
− 1.4909
c
5
c
5
d
0.8401 d
0.8239 d
0.7412 d
†
0.8448 0.2938
0.2476 g
1
− 0.1561
g
1 †
− 0.1028
g
1
g
1
g
2
0.0881 −
0.2487 g
2
0.2946 g
2
0.5268 g
2 †
0.1740 0.2089
g
3
− 0.9105
g
3 †
0.0832 g
3
g
3
g
4
0.2273 g
4
1.3580 g
4 †
g
4
0.0238 −
0.1489 u
− 0.1035
− 0.4176
u
0.1002 u
0.0749 u
†
0.9307 1.1041
6 0.9958
6
†
1.0937 6
V LB
Q 10
LB Q
10 7.8581
7.7220 LB
Q 10
13.3038 LB
Q 10
6.4682 LB Q
2
10 3.3651
12.9814 2.2999
8.9716 LB Q
2
10 LB Q
2
10 LB Q
2
10 Denotes significance at the 10 levels.
Denotes significance at the 5 levels. Denote significance at the 1 levels.
ters u, u
†
, u
1
, u
1
are different in signs for the different index returns, implying that unexpected positive positive shocks and unexpected negative return negative
shocks of all indices have asymmetric effects on volatility. These results indicate that the EGARCH model is reasonably well specified in this study. In addition,
given g
1
, g
1 †
, g
1
and g
1
parameters are positive and significant, the positive values for u, u
†
imply that positive shocks have a larger impact on future volatility of the HSCEI and HSCCI returns than negative shocks and the contrary result applies to
the SHI and SZI returns, u , u
. These findings suggest that stocks listed in the Hong Kong market H shares and red chips are more sensitive to ‘good’ news than
‘bad’ news, while stocks listed in the China market are more sensitive to ‘bad’ news than ‘good’ news. Hong Kong investors appear to be optimistic to news while
Chinese investors i.e. investors in China are more pessimistic because returns on Chinese stocks are affected more frequently by negative rumors economic or
political. The difference in attitude can have a substantial impact on the stock market. It is usual to observe the negative innovations bad news inciting bigger
response in the literature. It is interesting to note the opposite results reported for the Hong Kong market. One possible explanation is when good news are released
by Chinese companies, they tend to be highly inflated, as a result, Hong Kong investors are somewhat skeptical of these good news from the Chinese market.
Therefore, we observe a greater sensitivity of the Hong Kong market to the good news from the Chinese market.
The estimated values of the scale parameter 6 for all index returns are 1.0841, 1.0282, 0.9093 and 0.9803 and they are significant at the 1 level. Because the
estimated parameter, 6 is B 2, the distribution of o
t
will have a thicker tail than the normal distribution. These results suggest that the distributions of the all index
returns are significantly thicker-tailed than the normal distribution. Alternatively, we can interpret that these distributions are beyond the range permitted by the
normal distribution. Therefore, the empirical results support the use of GED assumption in this study.
4
.
2
. Spillo6er effect analysis Table 6 presents the results of return and volatility spillover of the four markets
using the multivariate EGARCH-M analysis. Past returns in the HSCEI and HSCCI have a positive impact on their own current and future returns. The past
red chips HSCCI return has a positive impact on the current SZI return while the past SZI return has a negative impact on the current SHI return. The past SHI
return, on the other hand, has a positive impact on the current H shares HSCEI return. These results are indicative of significant mean spillovers from the red-chip
market to the Shenzhen stock market, then from the Shenzhen stock market to the Shanghai stock market, and finally from the Shanghai stock market to the H share
market. The results imply that the red chips impact directly or indirectly on all other China-backed markets.
Results of the conditional variance equations depict the presence of significant conditional heteroscedasticity in the raw data series of all returns. That is, the
coefficients for one-lag conditional variance d
1
, d
1 †
, d
1
, d
1
and own past volatility shock g
1
, g
2 †
, g
4
are statistically significant, and the conditional volatility of both index returns are predictable using past information. The only exception is the
coefficient of the one-lag conditional variance for the SHI return, which is statisti- cally insignificant.
Past volatility shock in the red chips HSCCI return has a negative impact on current volatility in the SHI return and has a positive influence on current volatility
in the HSCEI return. The past volatility shocks in the HSCEI and SZI have a positive impact on current volatility in the SHI return. Moreover, past volatility
shock in the HSCEI return has a negative influence on current volatility in the SZI return. The negative spillover is likely due to a possible overreaction in one market
followed by an underreaction in another market De Bondt and Thaler, 1985. In addition, if the Chinese stock markets are partially segmented Poon et al., 1998,
information may not spread to other markets rapidly. That is, a big change in volatility in one market may result a small change in volatility in another market.
Our findings indicate there is volatility spillover from the red chip market to the H share market and the Shanghai stock market; then from the H share market to
the Shenzhen stock market and Shanghai stock market; and finally from the Shenzhen stock market to the Shanghai stock market. These results also suggest
that 1 Shanghai stock market is the only market that responds to the lagged information of other stock markets, and 2 red chips are initiating information for
all the other China-backed securities.
5. Conclusions
