Discussion Papers In Economics
And Business

Return and Volatility Spillovers between Japanese andChinese Stock Markets：An Analysis of Overlapping
Trading Hours with High-frequency Data
Yusaku Nishimura, Yoshiro Tsutsui and Kenjiro Hirayama

Discussion Paper 12-01

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANReturn and Volatility Spillovers between Japanese andChinese Stock Markets：An Analysis of Overlapping
Trading Hours with High-frequency Data
Yusaku Nishimura, Yoshiro Tsutsui and Kenjiro Hirayama

Discussion Paper 12-01
February 2012

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANReturn and Volatility Spillovers between Japanese andChinese Stock Markets：An Analysis of Overlapping
Trading Hours with High-frequency Data*
Yusaku Nishimura a (University of International Business and Economics)
Yoshiro Tsutsui b (Osaka University)
Kenjiro Hirayama c (Kwansei Gakuin University)

Abstract
In this paper we analyze return and volatility spillovers during overlapping trading hours
between China (Shanghai Composite Index) and Japan (Nikkei 225 Index) using intraday
high-frequency data. We first adjusted the 5-min. returns for intraday periodicity with
Flexible Fourier Form (FFF). Then these data are used to estimate a FIAPARCH model thestandard residuals of which are then employed to test for causality in mean and in variancewith a cross-correlation function (CCF) approach. The results indicate a unidirectional
influence from China to Japan both in terms of return and volatility. Further, volatility
spillover arises with some delay after a return spillover.

JEL Classification Number: G10, G14, G15
Key words: intraday return and volatility spillover effects, high-frequency data, intraday
periodicity, CCF approach, Flexible Fourier Form*

This research was in part supported by Program for Innovative Research Team and 211 Program in
UIBE for which we express our gratitude.
aInstitute of International Economy, University of International Business and Economics, 10 East
Huixin Street, Chaoyang District, Beijing, 100029, China, e-mail: yusaku.nishimura@gmail.combGraduate School of Economics, Osaka University, 1-7 Machikane-yama, Toyonaka, 560-0043 Japan,
Phone: +81-6-6850-5223, Fax: +81-6-6850-5274, e-mail: tsutsui@econ.osaka-u.ac.jpcSchool of Economics, Kwansei Gakuin University, Uegahara, Nishinomiya-shi 662-8501 Japan, Phone:+81-798-54-6438, Fax: +81-798-54-6438, e-mail: hiraken@kwansei.ac.jp

11．Introduction
The purpose of this paper is to shed light on the intraday return and volatility spillovers
between Chinese 1 and Japanese stock markets. 2 China’s real GDP has overtaken that ofJapan in 2011 and it seems worthwhile to explore the interactions between these twomarkets.
There are a large number of studies on international stock market interdependence.
Many report the existence of return and/or volatility spillover effects between countries ora unidirectional effect from a larger market (such as the U.S.) to a smaller market (Hamao,
Masulis and Ng (1990), Jeon and von Furstenberg (1990), Cheung and Mak (1992), Masih
and Masih (1999), Darrat and Zhong (2005), Mukherjee and Mishra (2010), among others).
However, there exist many papers which point out that the Chinese stock market is not
influenced by price movements in other international markets, such as the U.S., the U.K.,
German, or Japanese markets (Huang, Yang and Hu (2000), Groenewold, Tang and Wu(2004), Chen and Liu (2008), Hirayama and Tsutsui (2009), Nishimura and Men (2010),
etc.). This result of China’s relative independence despite its economic size is aninteresting puzzle which we will explore in this paper using a new dataset andmethodology.
In the first place, most empirical analyses of international stock price interactions havethus far utilized daily data, but this paper employs stock price data observed at a 5-minutefrequency 3 . Technological innovations in communication and computers have led to everfaster transmission of information and execution of financial transactions. Stock markets
that are efficient should reflect new information from abroad very rapidly. Thus, it isimportant to analyze high-frequency data to explore how fast the spillover occurs.
In the second place, since we are focusing on China and Japan, it is crucial to use
high-frequency data because these two markets have overlapping trading hours. The timedifference between the two countries is a mere one hour which implies a daily span is too
1

By ‘China’ we mean the mainland China in this paper. Thus, Hong Kong, Macao and Taiwan are
excluded from the analysis.
2
The share of market capitalization of the Shanghai Stock Exchange in the world total as reported by
the World Federation of Exchanges (WFE) rose from 0.66% in 2005 to 4.94% in 2010. If Shenzhen
Stock Exchange is added to Shanghai, the combined share rose from 0.93% in 2005 to 7.33% in 2010. At
the end of 2010, the market capitalization of the Tokyo Stock Exchange, the single largest in Asia, stoodat 3.83 trillion US dollars with a 6.97% share in the world total.The data source is WFE Annual Report.
3
Studies exploring return and/or volatility spillover with high-frequency data have focused on
European and American markets with overlapping trading hours are: Jeong (1999)， Égert and Kočenda
(2007)， Černy and Koblas (2008)， and Harju and Hussain (2008).

2

long to capture mutual influences. If we use daily closing prices from these markets 4 , wecan probably measure the effect of Tokyo on Shanghai, but the reverse effect from
Shanghai to Tokyo is based on a 23-hour lag which would include effects from theintervening markets such as European and American markets. Consequently, it would benatural and appropriate to utilize intraday high-frequency data during overlapping trading
hours to capture the spillovers between China and Japan.
Hirayama and Tsutsui (2009) also use high-frequency (minute-by-minute) data to
analyze interactions between Chinese and Japanese stock markets. Compared with theirwork, this paper has two merits. The first is that this paper analyzes both return andvolatility spillovers, while Hirayama and Tsutsui (2009) only focus on the former.
Volatility is a very important concept in modern financial markets and it has become astandard practice to estimate volatility spillovers in studying co-movements between
international stock markets (Hamao, Masulis, and Ng (1990)). 5 Whether volatility
spillover effects can be verified as in the case of return spillovers is an interesting question
to answer. 6
Secondly, while Hirayama and Tsutsui (2009) conduct empirical analyses without
dealing with intraday periodicity in stock prices, this paper attempts to purge the data of
intraday periodic patterns by applying Flexible Fourier Form (FFF) to intraday data as
proposed by Gallant (1981). Andersen and Bollerslev (1997, 1998b) also employ thismethod to treat intraday periodicity. As Andersen and Bollerslev (1997, 1998b) and manyothers have shown, estimating volatility without seasonally adjusted intraday data issubject to a statistical bias in estimation. Thus, it is interesting to compare our result withthat of Hirayama and Tsutsui (2009) regarding the return spillover effects.
This paper is organized as follows. In the next section the data to be used is explained
and its intraday characteristics are summarized. Then, the intraday periodicity is removed
by applying the FFF. The third section estimates FIAPARCH (Fractionally Integrated
APARCH) model to characterize the volatility generating mechanism. We derive4

In fact Shanghai closes exactly one hour after Tokyo’s closing.
The stock investors are paying increasing attention to volatility as well as returns. This is probably the
background for Nikkei, Inc., the publisher of the Nikkei Stock Average Index, to introduce a new Nikkei
Stock Average Volatility Index on Nov. 19, 2010 and to start updating this Index every 15 seconds fromJanuary 2012.
6
Another important issue is whether the speed of transmission may differ between the two. To
investigate this problem, we explicitly test for the lags in spillovers by using cross-correlation function(CCF) approach proposed by Cheung and Ng (1996).
5

3

standardized residuals from this model and then compute cross-correlation functions withthese residuals. The fourth section concludes the paper.

2． Statistical Methodology and Intraday Periodicity
2.1 Data
We have collected data on Nikkei 225 Index (abbreviated as NKY) for Japan and on
Shanghai Composite Index (henceforth referred to as SHCOMP) for China for the period
from Jan. 2, 2008 to Nov. 30, 2010. 7 We retrieved stock prices at 5-minute intervals andcomputed a logged difference multiplied by 100. As one uses higher-frequency data, one
obtains more data points, but it comes at a cost of increased market microstructure noisesuch as the bid-ask bounces. Taking this tradeoff into account, Andersen et al. (2001),
Koopman, Jungbacker, and Hol (2005), and Watanabe (2007) recommend using 5-min.
observations. 8 In the case of NKY, furthermore, there is a peculiar system of updating
special quotes 9 at 5-min. intervals which was first reported by Tsutsui et al. (2007). If one
were working with minute-by-minute data, this would appear as a spike in auto-correlation
functions at 5-min intervals. With 5-min. intervals, this problem becomes irrelevant.
The trading hours of the Tokyo Stock Exchange is 09:00-11:00 for the morning session
and 12:30-15:00 for the afternoon session. Those of Shanghai are, in Japanese Standard
Time, 10:30-12:30 for the morning session and 14:00-16:00 for the afternoon session (Fig.
1). Therefore, there are two overlapping periods (windows) during which the two stock
exchanges are open simultaneously: 30 min. period for 10:30-11:00 in the morning and
60-min. period for 14:00-15:00 in the afternoon every day. We use observations during
these two windows in the computation of cross-correlation functions below. In this casethere are 11,988 observations on 5-min. returns. When either Tokyo or Shanghai Stock
7
China has two major stock exchanges: one in Shanghai and the other in Shenzhen. The Shenzhen
Composite Index is also available to us. The market capitalization of the main board of Shanghai at theend of 2010 stands at 18.5 trillion RMB which is far greater than that of Shenzhen at 4.4 trillion RMB.
The volume and value of market turnover for 2010 is 3.4 trillion shares and 34.7 trillion RMB for
Shanghai and is 1.2 trillion shares and 14.0 trillion RMB for Shenzhen. Since Shanghai is a muchgreater market than Shenzhen, we chose Shanghai to represent the entire Chinese market. In addition,
the simple correlation coefficient between the two market indexes is extremely high (0.94 even using
min.-by-min. returns according to Hirayama and Tsutsui (2009)), implying that it is not necessary totake Shenzhen into account. The data source for the above is the respective website of the two
exchanges and their Fact Books. The figures are total for A and B shares.
8
See also fn. 19.
9
When the next transaction price is likely to exceed a certain pre-set band, a special quote is invoked
and the order matching is temporarily suspended. This constitutes an announcement to inform themarket participants of a large price jump.

4

Exchange is closed due to a national holiday, we excluded this date from the analysis.
However, when we deseasonalize the intraday data and when we estimate volatility
measures by a FIAPARCH model in Section 3, we use all the available observations during
the entire trading hours. Overnight returns and returns during the lunch break are notincluded in the analysis. Consequently, there are 54 observations per day for Tokyo and 48
for Shanghai. With 712 trading days in Tokyo and 707 in Shanghai, the total sample sizeamounts to 38,358 and 33,936 respectively. The data source is Nikkei, Inc. for NKY and
TickData.com for SHCOMP.
===== Figure 1 =====

2.2 Properties of Intraday Data
We characterize the properties of the intraday 5-min. returns in this subsection.
Specifically, we focus on means of 54 or 48 5-min absolute returns ( rt ( i ) ) 10 , averaged
across 712 or 707 days of trading, in order to capture the intraday patterns in volatility(Fig. 2). The graph for NKY exhibits a slightly W-shaped pattern which is not as stark as
those described by Andersen, Bollerslev, and Cai (2000), because we omit returns during
the lunch break. 11 The intraday volatility for SHCOMP, however, does not display a
W-shaped pattern at all. The volatility diminishes unambiguously toward the closing ofeach session in Shanghai.

===== Figure 2 =====The lines in Figure 3 indicate autocorrelation functions up to 10-day lags (namely, 540
lags for NKY, and 480 lags for SHCOMP). These charts clearly exhibit a regular intraday
periodicity which is quite stable over the past several days. Within a day the volatility
pattern is U-shaped in Shanghai, but is somewhat W-shaped in Tokyo. One should note thatthese autocorrelations are all highly statistically significant (the 5% critical value isdepicted in these charts by a dotted line). Another feature is that ACFs decline very
gradually over the 10-day period, suggesting that the volatility follows a long-memory
10

Following Andersen and Bollerslev (1997, 1998b)， Andersen, Bollerslev and Cai (2000) and manyothers, we compute mean absolute returns as a proxy for intraday volatility.
11
If the return over a lunch break is included in the analysis, the spike in the middle of the day becomesmuch higher, giving rise to a much clearer W-shaped pattern.

5

process.

===== Figure 3 =====

2.3 Removing Intraday Periodicity
As Andersen and Bollerslev (1997, 1998b) and others have shown, applying empiricalanalyses to high-frequency intraday data without treating the periodicity properly resultsin biases in estimated volatility. Thus, we apply a Flexible Fourier Form (FFF) proposed
by Gallant (1981) to the raw data as Andersen and Bollerslev (1997, 1998b) have adopted.
Details are relegated to the Appendix. Henceforth, the raw intraday return is denoted byrt (i ) and the adjusted return by rt (i ) .
Figure 4 plots the mean intraday volatility of the adjusted series. The results exhibit no
intraday cyclical patterns, indicating that the adjusted returns, rt (i ) , via FFF are suitablefor estimation. We should be wary, however, of high autocorrelations which dampen very
slowly (Fig. 5). This is a typical symptom of a long-memory process, thus we consider afractional integration when we estimate a volatility model in the next section.

===== Figure 4 ========== Figure 5 =====The basic statistical properties of the adjusted returns are displayed in Table 1. The
means of intraday returns are both negative, which imply a declining market in the twostock markets. However, they are not significantly different from zero. The standard
deviation of SHCOMP is greater than that of NKY at 1% significance, indicating a higher
riskiness in Shanghai than in Tokyo during this period. The skewness and kurtosis bothdiffer significantly from the values implied by a normal distribution (0 and 3 respectively).
A large value for kurtosis means the distribution of intraday returns have fatter tails than
the normal distribution.
LB(10) is a test for the absence of serial correlation from the first order through tenthorder lag which was proposed by Ljung and Box (1978). The two volatility measures haveboth very high values of LB(10). LB(500), not shown here, is also highly significant at 1%
level, implying that the intraday volatility has a long-memory property.
6

===== Table 1 =====

3. A Causality-in-mean and Causality-in-variance Test Using the CCF Approach
3.1 The Empirical Methods
In this section, we apply a two-step procedure developed by Cheung and Ng (1996).
Step one: we estimate appropriate volatility model for each univariate time series to obtain
their standardized residuals. Step two: the CCF of standardized residuals and squared
standardized residuals are used to detect causality in mean and causality in variance
between Japanese and Chinese stock markets.

3.1.1 Volatility Model
Models to analyze volatility in economic/financial time series are broadly divided into
two groups. The first is the ARCH (Autoregressive Conditional Heteroskedasticity) model
first proposed by Engle (1982). The second is the SV (Stochastic Volatility) model. 12 Due
to its ease of estimation, the ARCH model has been extended in many directions. We adopt,in this paper, a FIAPARCH（Fractionally Integrated APARCH）model proposed by Chung(1999) which is an extension of APARCH (Asymmetric Power ARCH) model suggested byDing, Granger and Engle (1993). The APARCH model is suited to capture asymmetriceffects in a volatility process. Fractional integration describes a long-memory process,which is often the case with many volatility measures. 13
The AR(k)-FIAPARCH(1,d,1) model to be used in estimation is written as follows:krt (i )  c   h rt ( i  h )   t ( i ) ， t ( i )   t ( i ) zt ( i ) ，zt ( i ) ~ i.i.d . E ( zt (i ) )  0 Var ( zt ( i ) )  1(1)

 t( i )   2 (1   )  (1   L  (1   L )(1  L ) d )((|  t (i ) |  t ( i ) )   2 )   t(i 1)

(2)

h 1

Equation (1) is a return equation which is specified as an AutoRegressive (AR) model. 
12The ARCH-type models are explained in detail by Bollerslev, Engle and Nelson (1994) and Xekalaki
and Degiannakis (2010). The SV models are treated by Shephard (2005).
13
Chung (1999) improves structural problems inherent in a FIGARCH model of Baillie, Bollerslev, andMikkelsen (1996) and in a FIAPARCH model of Tse (1998). The reader is referred to Laurent and Perets(2002) and Xekalaki and Degiannakis (2010) for details. Note in passing that Xekalaki and Degiannakis(2010) label Chung’s model FIAPARCHC in order to distinguish it from Tse’s model.

7are parameters of the autoregressive terms,  t (i ) is an error term, zt ( i ) is an i.i.d. randomvariable with mean 0 and variance 1. 14 Equation (2) is a variance equation which is a
FIAPARCH model as formulated by Chung (1999).  2 is the unconditional variance of t (i ) , and L is the lag operator such that Lk yt  yt  k (k  0,1,) . The notable feature of thismodel is parameter d, which critically determines whether the variable in question has along-memory property. If d  0 , the volatility follows a short-memory process, and if
0  d  1 , it follows a long-memory process. With d  0.5 , it is a stationary, and withd  0.5 , it is a non-stationary long-memory process.

There might arise an asymmetric effect on volatility, depending upon whether the stock
price rises or falls. In our FIAPARCH model, this asymmetry can be captured by  . If  0 , there is no asymmetric effect, and if   0 , an unexpected decline in stock price (anegative  t (i ) ) increases volatility.
While the variance is specified as  t2(i ) in most ARCH models, in our APARCH
specification above,  t(i ) is formulated. The power  of this term is also estimated as
one of the parameters. 15
3.1.2 The CCF approach
The residuals of an estimated FIAPARCH model are standardized by zˆt ( i )  ˆt ( i ) / ˆ t (i )which are then applied to the CCF approach of Cheung and Ng (1996). The CCF approachenables us to obtain information on the lag structure in causal relationships as well as on
the causality in mean and causality in variance. Namely, return and volatility spillover
effects can be tested at the same time. This approach does not require a normality
assumption, because the test statistics are known to follow a standard normal distribution
asymptotically (Hamori 2003, p. 2).
For the sake of exposition let us denote the standard residuals for Japan as zˆ Jpn ,t ( i ) andthose for China as zˆChn,t ( i ) . The sample cross-correlation function at a k-th lag betweenzˆ Jpn ,t ( i ) and zˆChn,t ( i ) is defined as follows:

14

Since the standardized residuals of equation (1) do not follow a normal distribution, we used
Quasi-Maximum Likelihood (QML) method to estimate parameters of the AR-FIAPARCH model. See
Sec. 2.2 of Xekalaki and Degiannakis (2010) for details of QML.
15
An APARCH model incorporates seven special cases of an ARCH-type model which helps us to
identify one of them by restricting certain parameters. For example, if   2,   0 , the APARCH modelis reduced to a conventional GARCH model. See Appendix A of Ding, Granger and Engle (1993)
for details.

8 JpnChn ( k )  CovJpnChn ( k )VarJpn  VarChn(3)

where VarJpn and VarChn is the variance of zˆJpn ,t (i ) and zˆChn,t ( i ) respectively and Covuv (k )is a sample cross-covariance with a k-th lag.
Now we can define a test statistic, CCF (k ) , at lag k:

CCF (k )  T  n  xy (k ) .

（4）

Cheung and Ng (1996) proved that the test statistic of (4) follows an asymptoticallystandard normal distribution as the sample size, T, approaches infinity. By testing the null
hypothesis, H 0 :CCF(k)=0 (no causality) against the alternative hypothesis, H 1 :CCF (k)≠0(causality exists), we can infer the presence or absence of causality at lag k between two
return series. To be specific, when we cannot reject the null for k>0, we infer causality
from Japan to China. In the case of k<0, non-rejection of the null implies causality from
China to Japan.
The above is a test of causality in mean. The causality in variance is tested by first22
ˆChnsquaring the two standardized residuals, zˆ Jpn, t ( i ) and z, t ( i ) , and then by applying thesame procedures as above to these squared residuals.

3.2 Empirical Results
3.2.1 Estimation Results of the AR-FIAPARCH Model
The estimation results of AR-FIAPARCH model are summarized in Table 2. 16 The
parameter, d, is greater than 0 and less than 0.5 at a 1% significance level in both China
and Japan, which implies that the two intraday volatility measures follow a stationary
long-memory process.
The parameter,  , to capture the asymmetric response of volatility is positive at a 1%
significance level. Volatility tends to increase more in the case of stock price declines.
This result is consistent with past research on Chinese and Japanese stock markets such as
Watanabe (2007), Men, Nishimura and Li (2007), among others. The null of   2 cannot
be rejected either in China or Japan .
16

The lag order of the AR part was determined by the minimum AIC achieved by k=24 for both NKY
and SHCOMP after varying the parameter between 1 and 30. However, these 24 coefficients on thelagged independent variables in the AR part are not shown in the Table to save space.

9We examine the appropriateness of our specification by focusing on the serial
correlation of standardized residuals, zˆt (i )  ˆt (i ) / ˆ t (i ) , and their squares, zˆt2(i ) . The
Ljung-Box statistics, LB(10) and LB(30) in Table 2, test the null hypothesis that the
autocorrelation coefficients from lag 1 to 10 or 30 are all zero. The results indicate thatthe null cannot be rejected at a 10% level, justifying our model specification.

===== Table 2 =====

3.2.2 Causality Tests by the CCF Approach
We now proceed to test causality in mean and causality in variance by using thestandardized residuals obtained above in the FIAPARCH model. We can shed light on the
return and volatility spillover effects between China and Japan.
The estimation results are shown in Table 3. Since the common trading hours is 30 min.
in the morning and 60 min. in the afternoon, we tested lags up to sixth order (30 min.).
Tests on causality in mean are displayed on the left-hand side of Table 3. The results
indicate there is no causality from past values of NKY to SHCOMP. However, SHCOMP
has a significant effect on NKY with 1- or 2- period lag at a 1% or a 10% significance level
respectively. The 5-min return in Tokyo responds to a return in Shanghai with a 5- to
10-min. delay. Utilizing min.-by-min. returns of Shanghai and Tokyo, Hirayama andTsutsui (2009) found that Tokyo completes responding to Shanghai within about 10
minutes. Our result is quite consistent with their finding.
The tests on causality in variance are exhibited on the right-hand side of Table 3. As in
the case of causality tests in mean, NKY has no discernible effect on SHCOMP, but
SHCOMP has a slight, albeit with a three-period lag (15 min.), effect on NKY at a 5%
level. Thus, volatility spillover also runs from China to Japan as in the return spillover
effects.
Finally, we should note that the spillover effects are both positive: a rise in return orvolatility in China leads to a similar rise in Japan.

===== Table 3 =====

4. Conclusions
10

Despite ample evidence on mutual return/volatility spillovers between major economies,
the Chinese market has been an exception in that it is not affected by other markets.
Therefore, we regard this finding an important and interesting issue worth investigating in
depth. Even more importantly, we would like to explore its underlying causes. One of our
new contributions to the literature is the use of high-frequency (5-min.) data to focus on
this issue. Since China and Japan are geographically close, they share one and a half hours
of simultaneous trading on a given day. It is natural as well as appropriate to examine
real-time interactions between China and Japan during these overlapping trading hours.
Considering the fact that investors are now obtaining information very rapidly thanks torecent advances in information and communication technology, this use of high-frequency
data is expected to shed more light on the informational efficiency of international stock
markets.
Hirayama and Tsutsui (2009) is one of the few studies on interactions between Chineseand Japanese stock markets using high-frequency data, but they focus only on return
spillovers. They do not adjust for the intraday periodicity of the data, but we have adjusted
the data for this periodicity. While they compute conventional linear regressions, we haveapplied cross-correlation functions to test for causality in both mean and variance.
We compiled stock price data sets at a 5-min. frequency for Shanghai and Tokyo markets
for the period from Jan. 2, 2008 through Nov. 30, 2010. The empirical analyses revealed
both return and volatility one-way spillover effects running from Shanghai to Tokyo. The
return spillover effect is observed with a 1- to 2-period (5- to 10-min.) lag, but thevolatility spillover occurs with a three-period (15-min.) lag. Volatility spillover is found tooccur more slowly relative to return spillovers.
The first result (China not being affected by Japan) is consistent with past studies which
also report China’s independence of other markets. The cause for this would be found in
the fact that the scope of foreign investors’ activity is strictly regulated in China and that
Chinese individual investors’ portfolios are not diversified internationally. In principle,
foreign investors can buy only B shares of Shanghai Stock Exchange. The market
capitalization of B shares represents only 0.96% of the entire market capitalization (A+B)

11

at the end of 2010. Thus, foreign influence on Shanghai is quite limited. 17
China’s stock market participation abroad started in 2006 when it was legalized with asmall group of institutional investors who were approved as Qualified Domestic
Institutional Investors (QDII). 18 Excluding this group of investors, most other Chinese
institutional investors’ portfolio does not contain foreign stocks. Thus, they have no
incentive to collect and analyze information on foreign markets.
Why, then, do we have a lagged response in volatility spillovers? We interpret thisphenomenon as follows: A rise or fall in returns is easy to interpret, but changes involatility are difficult to disentangle. When a stock return rises, it contains a good news
about the prospect of a firm or an economy, and vice versa. When volatility rises, it cannot
be immediately interpreted as a good news or a bad news. It would take investors someeffort and time to infer what lies behind the volatility rise or fall. Ross (1989) hypothesizes
a close relationship between information flows and volatility. An increase in information
flow leads to a rise in volatility, but it would be difficult to determine the implications ofsuch an increase.
Some may argue that a rise in volatility implies a rise in uncertainty and that its effects
on other markets are clear-cut. However, one needs to have a sufficient number ofobservations to conclude a rise in volatility. The volatility measure estimated in this paper
is an ex post proxy for the underlying uncertainty. In reality some time is required torecognize a rise in uncertainty. This is another interpretation for the delayed volatility
spillover reported in this paper.

17

To be precise, foreign investors can also buy A shares if they become eligible as Qualified Foreign
Institutional Investors (QFII). The QFII status is accorded to only 97 institutions with up to 19.7 billion
US dollars in investible assets as of end 2010. And their share of stock holdings in China is a mere
0.57%. Thus, it would be fair to conclude that their influence on Chinese stock market is almost
negligible.
18
Foreign assets that QDII can hold are also subject to many regulations. Risky investments
particularly in stocks are restricted such that the share of stocks in their foreign portfolio is still verysmall.

12

Appendix: Flexible Fourier Form (FFF)
In this appendix we explain the Flexible Fourier Form (FFF) which removes intraday
periodicity from the raw data. The intraday return observed at time i on day t, rt (i )( t  1, 2,, T ; i  1,2,, n ), is expressed as:
rt (i )  E[rt ( i ) ]   t (i ) st ( i ) zt ( i )

(A1)

,

Where E[rt (i ) ] is the expected return,  t ( i ) is an intraday volatility factor, st ( i ) is an
intraday periodic factor, and zt ( i ) is an i.i.d mean 0 and variance 1, error term. These are
all independent of each other with  t (i ) , st (i )  0 assumed. Equation (A1) is squared andlogged. After rearranging the terms, we get:xt ( i )  2 ln(| rt ( i )  E[ rt (i ) ] |)  ln( t2( i ) )  c  2 ln( st ( i ) )  ut ( i )(A2)where c  E[ln( zt2(i ) )] and ut (i )  ln( zt2(i ) )  E[ln( zt2(i ) )] .
Andersen and Bollerslev (1997, 1998b) have applied the FFF to deseasonalize theperiodic factor and the FFF was originally proposed by Gallant (1981). The FFF is applied
to our periodic factor st (i ) as follows:

J
P


i
i2
2l i
2l i  D   l , j cos
 l , j sin
2ln(st (i) )  f  ; t(i)  tj 0, j  1, j  2, j  k Ik  t(i)  (A3)N1
N2 l 1 nn  k 1j 0where t is the observation date, i the time on the observation date, n the number of intraday
observations, N1  ( n  1) / 2 , N 2  (n  1)( n  2) / 6 , and 0, j , 1, j ,  2, j ,  l , j ,  l , j , k parameters
to be estimated. The second and third terms in the square brackets on the right-hand side of(A3) represent linear and quadratic time trends during one day and the fourth term withtrigonometric functions capture the intraday periodic patterns. I k (t (i )) in the last term isan event dummy with value 1 if a certain event occurs on day t, at time i, and 0 otherwise.
We consider the day-of-the-week effects in this paper, thus the day of the week is the event
we adopt for I k (t (i )) . 19
19

If we set J=0 and P=0 in (A3), it is equivalent to the standard FFF of Gallant (1981). However,Andersen and Bollerslev (1997) assert that it is important to consider the interactions between periodic

13

There are two steps in the actual estimation of (A3). The first step is to determine
E[ rt ( i ) ] and  t2(i ) which will then define xt (i ) of (A2). Andersen and Bollerslev (1997,
1998b) propose that E[ rt ( i ) ] be replaced by rt (i ) which is a sample mean and that  t2(i ) be
replaced by ˆt2(i )  ˆt2 / n where ˆt2 is the one estimated by a GARCH model. In this paper,
however, ˆt2 is replaced by ˆ t2(i )  RVt / n , where RVt is a Realized Volatility which is amore accurate estimator of volatility as proposed by Andersen and Bollerslev (1998a). The
Realized Volatility for day t is simply a sum over squared intraday returns:n

RVt   rt 2( i ) .

(A4)

i 1

If the number of daily observations, n, is sufficiently large, RVt is a consistent estimatorof the true volatility under certain conditions. Its proof is provided by Andersen et al(2001), Barndorff-Nielsen and Shephard (2002), Andersen et al. (2003), and others. 20
The second step is to estimate (A3) by OLS using rt (i ) and ˆt2 . The intraday return
purged of periodicity is computed as rt ( i )  rt ( i ) / sˆt ( i ) .

patterns and  tj with J  1 . Thus we set J  1 and varied P from 1 to 30 and chose appropriate P
that minimizes the AIC.
20
However, Aït-Sahalia, Mykland and Zhang (2005) show that, as the intraday observation frequency
rises, the market microstructure noise contaminates estimation of Realized Volatlity. Consequently, one
has to strike a delicate balance between the observation frequency and the effect of microstructure noise.
An answer to this problem has been proposed by Andersen et al. (2001), Koopman, Jungbacker and Hol(2005), and Watanabe (2007). which is to use a 5-min. frequency. We have also used this frequency inthis paper.

14

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18

Table 1. Descriptive Statistics of Intraday Returns rt (i ) after Seasonal Adjustment
Sample period: Jan. 2, 2008 to Nov. 30, 2010
Mean

NKY

SHCOMP-0.0002(0.0009)-0.0005(0.0014)

Standard
Deviation

0.17210.2548

Kurtosis

LB(10)

Skewness

1.511687.997(0.0125)(0.0250)

0.16556.7246(0.0133)(0.0266)

N. Obs.

r|r|

78.006

30453

38358

476.78

16231

33936

Notes: Numbers in parentheses are standard errors. LB(10) is a Ljung-Box statistics with a null that
autocorrelation coefficients on the first to tenth lags are all zero.

19

Table 2 Estimated Results of FIAPARCH Model
Sample period: Jan. 2, 2008 to Nov. 30, 2010
NKY

SHCOMP

0.0399 *(0.0211)0.0358 **(0.0174)d0.3624 ***(0.0182)

0.4267 ***(0.0157)

0.3044 ***(0.0389)

0.1085 ***(0.0155)

0.6205 ***(0.0438)

0.5366 ***(0.0216)

0.1204 ***(0.0316)0.1952 ***(0.0195)



1.8458 ***(0.0674)

1.9245 ***(0.0361)22814.49

3735.84zˆt8.74649.2704zˆt2

8.27506.5865zˆt19.36819.568zˆt2

18.49334.340

38448

33936

L.L.
LB (10)

LB (30)Obs（ 注 ） ***, **, * denotes significance at a 1%， 5%， 10% level respectively． Estimation method is
Quasi-Maximum Likelihood. Numbers in parentheses are standard errors derived from the QML
estimation.  2 is an unconditional variance of  t (i ) . L.L. is log likelihood. LB(k) is a Ljung-Box
test statistic which has a null that autocorrelations from first to the k-th order lags are all zero. zˆtand zˆt2 are standardized residuals and their squares.

20

Table 3. Results of Causality-in-Mean and Causality-in-Variance Tests
Causality in Mean

Causality in Variance

Lag

NKY  SHCOMPSHCOMP  NKY

NKY  SHCOMPSHCOMP  NKY

1-0.9825

7.4413 ***-0.3244-0.06342

0.82921.7504 *-0.2626-0.166930.82500.1155-0.84212.5111 **4-1.2269-0.76280.6492-1.434050.67810.7243-0.56020.7064

6-0.8369-0.9834-0.3192

0.0750（ 注 ） ***， **， * denotes significance at a 1%， 5%， 10% level. The numbers in the table are CCF(k)statistics.

21

10:30

9:00

09:00

10:00

Shanghai

11:00

12:00

13:00

Tokyo
11:00

14:00

12:30

12:30

14:00

Tokyo

Shanghai

15:00

16:00

16:00

15:00

Figure 1. Trading hours of the Tokyo and Shanghai Stock Exchanges.
Hours are according to time in Tokyo (Japan Standard Time, JST). Overlapping hours (windows ofsimultaneous trading) are shaded.

22

.32

.30

NKY

SHCOMP

.28
.25
.24
.20

.20

.16
.15
.12
.08

.10
5 10 15 20 25 30 35 40 45 50

5

10 15 20 25 30 35 40 45

Figure 2. Mean Intraday Volatilities at 5-min. Intervals
Notes: The absolute 5-min. returns | rt ( i ) | is averaged across days in the sample. One period measured
along the horizontal axis is a 5-min. interval. NKY has 54 periods and SHCOMP has 48 periods per day.

.35

.30

NKY

.30

SHCOMP

.25

.25

.20

.20
.15
.15
.10

.10

.05

.05
.00

.00
100

200

300

400

500

100

200

300

400

Figure 3. Autocorrelation Coefficients of Intraday Volatility
Notes: The vertical axis measure autocorrelation coefficients and the horizontal axis measures thenumber of lags (periods). Lags are taken from the first lag through 540 th (10 days in total) for NKY andfrom the first through 480 th (10 days) for SHCOMP.

23

.14

.22

NKY

SHCOMP

.21

.13

.20

.12

.19
.11
.18
.10

.17

.09

.16

.08

.15
5 10 15 20 25 30 35 40 45 50

5

10 15 20 25 30 35 40 45

Figure 4. Mean Volatility at 5-min. Intervals after Seasonal Adjustments
Notes: The adjusted absolute 5-min. returns | rt ( i ) | are averaged across days in the sample. See notes to
Figure 2.

.30

.30

NKY

.25

.25

.20

.20

.15

.15

.10

.10

.05

.05

.00

SHCOMP

.00
100

200

300

400

500

100

200

300

400

Figure 5. Autocorrelation Coefficients of Intraday Volatility after Seasonal
Adjustments
Note: See notes to Figure 3 above.

24