Discussion Papers In Economics
And Business

Asymmetric International Transmission in the Conditional
Mean and Volatility to the JapaneseMarket from the U.S.:EGARCH vs. SV Models

Junji Shimada, Yoshihiko Tsukuda and Tatsuyoshi Miyakoshi

Discussion Paper 07-23

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANAsymmetric International Transmission in the Conditional
Mean and Volatility to the JapaneseMarket from the U.S.:EGARCH vs. SV Models

Junji Shimada, Yoshihiko Tsukuda and Tatsuyoshi Miyakoshi

Discussion Paper 07-23
June 2007
この研究は「大学院経済学研究科・経済学部記念事業」
基金より援助を受けた、記して感謝する。
Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANAsymmetric International Transmission in the Conditional
Mean and Volatility to the JapaneseMarket from the U.S.:EGARCH vs. SV Models
byJunji Shimada*
Yoshihiko Tsukuda**
andTatsuyoshi Miyakoshi ***June, 2007 (revised)

Keywords:

asymmetric transmission; conditional mean and volatility; Japanand the U.S. stock markets; EGARCH and SV models;JEL Classification Number: G14; G15*

School of Management, Aoyama Gakuin University**

Graduate School of Economics, Tohoku University*** Graduate School of Economics and Osaka School of International Public Policy (OSIPP),
Osaka University
Correspondence: Tatsuyoshi Miyakoshi, Graduate School of Economics and Osaka School ofInternational Public Policy (OSIPP), Osaka University, 1-31, Machikaneyama-machi,
Toyonaka, Osaka 560-0043, JAPAN
Tel: +81-6-6850-5638, Fax:+81-6-6850-5656, E-mail: miyakoshi@osipp.osaka-u. ac.jp

Abstract:
This paper investigates whether the upturns and downturns of the U.S. market exert
asymmetric influence on the conditional mean and volatility of the Japanese market
using the daily returns on stock price indices. Using both the EGARCH and SV models,
which simultaneously allow two kinds of asymmetric international transmissions acrossthe markets, the result reconfirms the symmetric transmission in the conditional meanobtained by Bahng and Shin (2003) and the asymmetric transmission in the conditional
volatility obtained by Koutmos and Booth (1995) although each of them analyzed theonly one spillover effect separately. Although the EGARCH and SV models lead tosimilar results about the spillover effects, the SV model is preferred to the EGARCH
model in terms of the Lagrange Multiplier test of the EGARCH against the SV models.
The shock to volatility in the U.S. market with the SV model is asymmetricallytransmitted to the volatility in the Japanese market.

11. Introduction
This paper studies asymmetric transmissions of return and volatility in the stock
price index of the U.S. stock market into the Japanese stock market. Numerous
researchers found significant contemporaneous return correlations. In addition, dynamic
market interdependences which indicate causal relationships were also investigated bymany researchers who report significant price volatility spillovers between advanced
markets. ( Hamao et al (1990), Bae and Karolyi (1994), Karolyi (1995) and Karolyi andStulz (1996), Ng (2000), Miyakoshi (2003), Kim (2005) among others). Furthermore,some researchers considered asymmetric international transmission effects. By simply
using a vector autoregressive (VAR) framework, Pagan and Soydemir (2001) and Bahng
and Shin (2003) found that the returns of the domestic market were more sensitive todownturns than uptowns in the foreign markets. Using the ARCH-type models, Booth,
Martikainen and Tse (1997), and Koutmos and Booth (1995) investigated theasymmetric international transmission of volatility amongst the Scandinavian stock
markets and the Japanese, UK, and US markets, respectively. However, there is noresearch simultaneously dealing with both asymmetric international transmissions inreturn and volatility.1
Most analyses of international transmission in return and volatility of the market
of a country to the other country are conducted using the framework of the ARCH typemodels, and there is no research on the international spillover using the stochastic
volatility (SV) models. The SV model is intuitively appealing since it allows thecontemporaneous shock to the present volatility, unlike the ARCH-type models (Taylor(1994) and Andersen (1994)). In addition, the SV model includes the EGARCH model
as a limiting case when the standard deviation of shocks on volatility goes to zero.
Kobayashi and Shi (2005) proposed a method for testing the hypothesis of the
EGARCH against the SV model. More importantly, the SV model is able to analyze
whether the shock to the volatilities in the foreign market is transmitted into thevolatilities in the domestic market, whilst the EGARCH model is not. Nevertheless, theSV model is not frequently used for the empirical analyses of financial markets2.
The purpose of this paper is to investigate whether the upturns and downturns of1

Koutmos (1998), Nam et al. (2003) and many others found that the returns and volatility react
more to the previous downturns of their own market than to the previous upturns. But, they did
not investigate the asymmetric international transmissions in return and volatility.
2
Although it had been computationally difficult to estimate the SV model, estimation of the SVmodel is no more burdensome as before since various efficient methods of estimation have been
extensively developed in recent years. Shimada and Tsukuda (2005) proposed a new estimation
method. See Broto and Ruiz (2004) for reviewing estimation methods.
2the U.S. market exert an asymmetric influence on the conditional mean and volatility of
the Japanese market using the daily returns on stock price indices. We use both the
EGARCH and SV models, which allow the simultaneous treatment of two kinds ofasymmetric international transmissions in the conditional mean and volatility across themarket. First, we examine whether the previous return on the US markets affects thepresent return on the Japanese market, and whether the magnitudes of effects are thesame for both positive and negative returns. Second, we investigate whether theprevious negative shock (bad news) on the return in the US market differently affects
the present volatility in the Japanese market from when the previous positive shock(good news) on the return in the US market does. We also examine the performance of
the EGARCH model and the SV model using the method of Kobayashi and Shi (2005).
The empirical results reveal that (i) the returns in the Japanese market react
symmetrically to the previous upturns and downturns of the U.S. market, (ii) the
previous negative shock (bad news) in the U.S. market increases current volatility in theJapanese market, while the previous positive shock (good news) in the U.S. market does
not significantly increase current volatility in the Japanese market (asymmetrictransmission in the conditional volatility). Our simultaneous treatment reconfirms thesymmetric transmission in the conditional mean obtained by Bahng and Shin (2003) andthe asymmetric transmission in the conditional variance obtained by by Koutmos andBooth (1995), whilst each of them analyzed the only one spillover effect separately.
Although the SV analysis leads to results that are similar to those of the EGARCH
analysis, the SV model is preferred to the EGARCH model based on the hypothesis
testing. Moreover, the shock to the volatility in the U.S. market is asymmetricallytransmitted to the volatility in the Japanese market. However, the EGARCH modelcannot describe this kind of shock to the volatility. Thus, the SV model incorporatingsuch features of the U.S. market is useful for analyzing the Japanese stock market.
The organization of the paper is as follows. Section 2 explains the EGARCH
model with spillover effects and discusses the estimation results of asymmetrictransmission effects on the conditional means and variances. Section 3 employs the SVmodel with international transmission effects, tests the EGARCH against the SV, andcompares the results with those by the EGARCH model. Section 4 gives someconcluding remarks.

3

2. Data and the EGARCH model analysis
2.1 Data and summary statistics
We use the daily closing prices of TOPIX for the Japanese market and the S&P 500
for the U.S. market; both are measured in local currency over a twelve-year period
beginning from January 1, 1993 to December 31, 2004. The number of observations is2861.3 The stock price indices and returns for the whole period are illustrated in Figure
1. Both the stock price indices and returns exhibit large fluctuations over the period.
However, the reason for the changes of movement in the price indices and returns is notapparent from Figure 1.
Table 1 indicates the number of observations, mean, standard deviation, skewness,
excess kurtosis, the first order autocorrelation for the returns, and the first order
autocorrelation for the squared returns of each country. The asterisks in columns 4–7
denote that the values are significant from zero at the 5% level. The typical features ofstock returns, such as fat tail, spiked peak, and the persistence of variance are observedin both the Japanese and U.S. stock markets. The first order autocorrelation of the
returns is significant for the Japanese markets but not for the U.S. markets at the 5%
level. Therefore, the ARCH-type model incorporating the above facts is appropriate foranalyzing the return series.
[ Insert Figure 1 and Table 1 ]2.2 The EGARCH model with asymmetric international transmission
We first provide the nested EGARCH model to examine the asymmetricinternational transmission in returns and volatilities. The stock return on the Japanesestock market is assumed to have a first-order autoregressive (AR) model with possibly
asymmetric effects of the lagged variable.

3 If either the TOPIX or S&P 500 is not open on a particular day, we have excluded the data forthat day from the observation. Hence, the two markets have the same number of observations.
The URL of TOPIX historical prices is http://table.yahoo.co.jp/t?s=998405.t&g=dand of S&P 500 historical prices is http://finance.yahoo.com/q/hp?s=%5EGSPC.

4

RJP, t = a0 + a1R+JP, t-1 + a 2R−JP, t-1 + b1R+US,t-1 + b2R−US,t-1 + ε JP, t ,(1)where R +JP, t -1 = max{ R JP, t -1 ,0} , and R −JP, t -1 = min{R JP, t -1 ,0}. The disturbance term hasheteroscedasticity,

ε JP, t = σ JP , t z t ,z t ~ i.i.d. N( 0 , 1 ).

(2)

The EGARCH model proposed by Nelson (1991) specifies the log-volatility process as+−+−
ln σ JP2 , t = φ0 + φ1 ln σ JP2 , t-1 + φ2 z JP
, t-1 + φ3 z JP , t -1 + δ 1z US , t-1 + δ 2 z US , t -1

(3)

+
+
−
−
+
−
where zJP
, t-1 =εJP, t-1 /σJP, t-1 , zJP, t-1 = ε JP, t-1 /σJP, t-1 , and ε JP, t-1 (ε JP, t-1 ) are similarly defined
+
−
+
−
ε US
to R JP+ , t -1 ( R JP− , t -1 ) . The R US,, t-1 (ε US, t-1 ) for the U.S. are defined tot -1 ( R US, t -1 ) andthe corresponding Japanese ones. The present volatility of the EGARCH model isdetermined completely by the past observations on the returns. The EGARCH model of(1), (2), and (3) for the Japanese market has a corresponding model for the U.S. market,
although we do not explicitly state it here.
+−+−
We note that z JP , t -1 , z JP , t -1 , z US , t -1 , and z US , t -1 are treated as the observableshocks. The data for these variables are the residuals calculated from equations (1), (2),and (3) without the international transmission for the Japanese and U.S. stock markets.4
Thus, this model is not a bivariate EGARCH model consisting of both the Japanese andthe U.S. markets.
The return generating processes incorporate either the symmetric or asymmetrictransmission of the returns of the previous U.S. market. On the other hand, thelog-volatility processes incorporate the symmetric (or asymmetric) transmission of the+−shocks on the previous returns in the U.S. market ( z US
, t -1 and z US , t -1 ).
Second, we provide hypotheses to examine whether the asymmetric internationaltransmission exists in the Japanese market. The null hypothesis of the symmetricinternational transmission can be expressed using (1), (2), and (3):H 1 :b1 = b2 and δ1 = −δ2 vs. H 1a : b1 ≠ b2 or δ1 ≠ −δ2 ,4 For the Japanese market, these data are the residuals calculated from the equations:
+
−
+
−
2
2
R JP, t = a 0 + a 1 R JP,
t -1 + a 2 R JP, t -1 + ε JP, t , and ln σ JP , t = φ0 + φ1 ln σ JP , t-1 + φ2 z JP , t-1 + φ3z JP , t-1 .

5

H 2 :b1 = b2 vs. H 2a :b1 ≠ b2 ,H3 : δ1 =− δ2 vs. H3a : δ1 ≠− δ2 .

(4)

We note that the null hypothesis H1 encompasses the hypotheses H2 and H3. If we
reject the null hypothesis H1, we must acknowledge the existence of the asymmetricinternational transmission and use the general model proposed in this paper. Moreover,
we must analyze whether the asymmetric transmission of the returns or the volatility
exists by testing H2 and H3. The null hypothesis H2 was examined by Pagan andSoydemir (2001) and Bahng and Shin (2003) in the model with only asymmetricinternational transmission in returns. The H3 was tested by Booth, Martikainen, and Tse(1997) and Koutmos and Booth (1995) in the model with only asymmetric internationaltransmission in volatilities. The intuition behind this comparison between H2 and H3 isshown in Figure 2 (a) and (b).
[ Insert Figure 2 ]2.3 Estimation Results and Testing Hypotheses
We examine the asymmetric international transmission effect on the Japanesemarkets from the U.S. The estimation result in Table 2 is summarized as follows:(i) Adjustments within the domestic market. The previous positive return positively
affects the present return, but the previous negative return does not. The previous shockin the return equation (1) increases the present volatility in the equation (3), but theeffects of negative shock are greater than that of positive shock (leverage effect).
(ii) International Transmission across the markets: The previous positive (negative)
return on the U.S. markets positively (negatively) affects the present return on theJapanese market, and the magnitude of the effects is the same for both the positive andnegative returns (symmetric transmission in the conditional mean). The previous
negative shock (bad news) on the return in the U.S. market increases the present
volatility in the Japanese market, whereas the previous positive shock (good news) doesnot (asymmetric transmission in the conditional variance).
[ Insert Table 2 ]Our simultaneous treatment of the conditional variance and conditional mean

6

reconfirms the asymmetric transmission in the conditional variance obtained from aseparate treatment by Koutmos and Booth (1995), and the symmetric transmission in
the conditional mean by Bahng and Shin (2003).
We also reconfirm these results by testing hypotheses H1, H2, and H3. As shownin the first column of Table 3, we can reject the null hypothesis of H1 even at the 1%
level, supporting “asymmetric international transmission in returns and volatilities” inour generalized model. On detailed inspection, we can not reject the null hypothesis of
H1 (symmetric international transmission in returns) at the 10% level, supporting theresults by Bahng and Shin (2003). However, we can reject the null hypothesis of H2(symmetric international transmission in volatilities) at the 1% level, supporting theresults by Koutmos and Booth (1995).
[ Insert Table 3 ]3.

Analysis by the SV model in comparison with the EGARCH modelThis section first specifies the SV model and then shows that the SV model ispreferable to the EGARCH model for describing the return processes on both theJapanese and U.S. stock price indices based upon the Lagrange Multiplier specification
test proposed by Kobayashi and Shi (2005).
3.1 The SV model with international transmission effects
The SV model with international transmission effects is described by+−ln σ JP2 , t = φ0 + φ1 ln σ JP2 , t -1 + φ 2 z JP
, t -1 + φ 3 z JP , t -1+−
+ δ 1z +US , t -1 + δ 2 z −US , t -1 + λ1η US, t -1 + λ2η US , t -1 + η JP , t .

(5)where ηJP, t ~ i.i.d.N(0 , σ η2 ) , in addition to (1) and (2). The present volatility of the SVmodel is not completely determined but depends on the present shocks. The SV modelof (1), (2), and (5) for the Japanese market has the corresponding model for the U.S.
±±±
market.5 We note that R JP± , t -1 , R US
, z JP± , t -1 , z USand η USin (1) and (5) are, t -1, t -1, t -1
treated in an analogous manner to the variables in (1)–(3). Unlike the EGARCH model,
the volatilities are unobservable stochastic variables. Therefore, we use the smoothing
5 We apply the non-linear maximum likelihood method (MLE) proposed by Watanabe (1999)

for estimating the SV models throughout this paper. This method is applicable for many types of
SV models. The number of grids for the numerical integration is set to 50 in this paper asrecommended by Watanabe (1999).
7

±±estimates of z USand η USas the spillover variable. The equation (5) expresses, t -1, t -1the transmission effects of the previous volatility shocks in the U.S. ( η US , t -1 ), which do
not appear in the analysis using the EGARCH model.

3.2 The SV vs. EGARCH Models
The SV model reduces to the EGARCH model if ση = 0. Kobayashi and Shi(2005) proposed the LM statistic for testing the null of the EGARCH model against the
SV model. Their LM test statistic is approximately distributed as N (0, 1) under the null
hypothesis (i.e., ση = 0).
Table 4 indicates that the null of the EGARCH model against the SV model isstrongly rejected in both the Japanese and U.S. markets. The result of this paper isconformable to the evidence Kobayashi and Shi (2005) found for the Japanese stock
market. The result in this section provides a justification for using the SV model toinvestigate the spillover effects from the U.S. stock market to the Japanese stock market±
as an alternative to the EGARCH model. Note that z JP± , t -1 and z US
in both (3) and, t -1±±(5), and η JP , t -1 and η US , t -1 in (5) are the residuals calculated from the equations
without international transmission for the Japanese and U.S. stock markets.
[Insert Table 4]
3.3 Estimation Results and Testing Hypotheses
Table 5 presents the estimates of the SV model of (1), (2), and (5). The estimatesof these parameters are very close to those in Table 2 except for the estimate of φ2 and φ3.
In particular, the estimated value of φ2 is positive and significant in Table 2, while it isnegative and significant in Table 5. In other words, the SV model shows that theprevious positive shock in the return equation decreases the present volatility, but theprevious negative shock in the return equation does not affect the present volatility.
[Insert Table 5]
We can also test the null hypotheses in (4) using the SV model. The log-volatility
process in (5) has two sources of transmission from the U.S. to the Japanese market: the+−first is the standardized shock to the U.S. stock price ( zUS, t-1 , zUS, t-1 ), and the second is+−
the shock to the volatility in the U.S. market ( η US). The second source of, t -1 , η US , t -1
transmission effects does not appear in the EGARCH model. The asymmetry throughthe second source can be tested by the hypothesis8

H 4 : λ1 = λ 2 , H 40 : λ1 ≠ λ 2 .

(6)

The second column of Table 3 presents the testing results. Comparing the second
column with the first column, we recognize that the result using the SV model is thesame as that using the EGARCH model. The null hypothesis of H4 is not rejected.
+
However, as shown in Table 5, the positive shock η US
on the volatility in the U.S.
, t -1market is positively transmitted into the volatility in the Japanese market at the 10%−
level in a one-sided test, while the negative shock η US
, t -1 is not significantly transmitted.
This fact supports the asymmetric transmission. Although this fact is not necessarily
conformable with the result of the hypothesis test of H4, we will perceive a weakevidence for the existence of asymmetric transmission. We generally think that theshock to the volatility transmits into the volatility in the other country, so did a
one-sided test and not a both-sided test. The SV model is preferred to the EGARCH
model based on the Lagrange Multiplier test of Kobayashi and Shi (2005). The SV
analysis leads to the similar results to those of the EGARCH analysis except for one
important point, i.e., the shock to the volatility in the U.S. market is asymmetricallytransmitted into the volatility in the Japanese market. However, the EGARCH modelcannot describe the shock to the volatility.
Hamao et.al (1990) claimed that the daily returns defined by the log-difference
between the openning and closing prices are preferred to the close-to-close returns inorder to examine the spillover effects between the two markets. We carried out all the
calculations in this paper using the open-to-close returns. However, the results arealmost the same as those obtained by the close-to-close daily returns, although we do
not explicitly report this here.

4. Concluding remarks
This paper investigates whether the upturns and downturns of the U.S. market
exert any asymmetric influence on the conditional mean and variance of the Japanesemarket. We use the EGARCH and SV models, which allow the simultaneous treatmentof two kinds of asymmetric transmissions across the markets. Our simultaneous
treatment reconfirms: (i) the symmetric transmission in the conditional mean obtained
from the separate treatment by Bahng and Shin (2003), (ii) the asymmetric transmission
in the conditional volatility obtained by Koutmos and Booth (1995). Although the
EGARCH and SV models analyses lead to empirically similar results, the SV model ispreferred to the EGARCH model in the sense that the EGARCH model is rejectedagainst the SV model based on the Lagrange Multiplier test by Kobayashi and Shi

9(2005). Moreover, one important advantage of the SV model over the EGARCH modelis that the former is able to incorporate the asymmetric transmission of the shock to thevolatility in the U.S. market to the volatility in the Japanese market while the latter is
not.

10

References
Andersen, T.G. (1994), "Stochastic autoregressive volatility : A framework for volatility
modeling", Mathematical Finance, 4, 75-102.
Bahng, J. S. and S. Shin (2003), "Do stock price indices respond asymmetrically?
Evidence from China, Japan, and South Korea", Journal of Asian Economics, 14,
541–563
Bae, K. H. and G. A. Karolyi (1994), "Good news, bad news and international spilloversof stock return volatility between Japan and the U.S.", Pacific Basin Finance
Journal, 2, 405-438.
Booth, G. G., T. Martikainen, and Y. Tse (1997), "Price and volatility spillovers in
Scandinavian stock markets", Journal of Banking and Finance, 21, 811-823.
Broto, C. and E. Ruiz, (2004), "Estimation Methods for Stochastic Volatility
Models : A Sruvey", Journal of Economic Surveys, Vol.18, 5, 613-649.
Hamao,Y., Masulis ,R. and Ng,V.(1990), "Correlations in Price Changes and Volatility
across International Stock Markets", The Review of Financial Studies, 3,
281-307
Karolyi, A. (1995), "A multivariate GARCH model of international transmission ofstock returns and volatility", Journal of Business and Economic Statistics,
13,11-25.
Karolyi, G.A. and R.M. Stulz (1996), "Why do markets move together? An investigationof US-Japan stock return comovements", Journal of Finance, 51, 51-986.
Kobayashi, M. and X. Shi (2005), " Testing for EGARCH against stochastic volatility
models", Journal of time series analysis, 26, 1, 135-150.
Koutmos, G., and G. G. Booth (1995), "Asymmetric volatility transmission ininternational stock markets", Journal of International Money and Finance, 14,
747-762.
Koutmos, G.. (1998), "Asymmetries in the conditional mean and the conditionalvariance: evidence from nine stock markets", Journal of Economics and Business,
50, 277-290.
Miyakoshi, T. (2003), "Spillovers of stock return volatility to Asian equity markets fromJapan and the US", International Financial Markets, Instituitions and Money, 13,383-399.
Nam, K., C. S. Pyun and S. W. Kim (2003), "Is asymmetric mean-reverting pattern instock returns systematic? Evidence from Pacific-basin markets in the
short-horizon", International Financial Markets, Instituitions and Money,

11

13,481-502.
Nelson, D. B. (1991), "Conditional Heteroskedasticity in Asset Returns:A New
Approach", Econometrica, 59, 347-370.
Ng, A. (2000), "Volatility spillover effects from Japan and the US to the Pacific-Basin",
Journal of International Monetary and Finance, 19, 207-233.
Pagan, J. A. and Soydemir, G. A. (2001), "Response asymmetries in the Latin American
equity markets", International Review of Financial Analysis, 10, 175–185.
Shimada, J. and Y., Tsukuda (2005), "Estimation of Stochastic Volatility Models: An
approximation to the nonlinear state space representation ", Communications in
Statistics, Theory and Methods, 34, .
Taylor, S., (1994), "Modeling Stochastic Volatility", Mathematical Finance, 4, 183-204.
Watanabe, T. (1999), "A non-linear filtering approach to stochastic volatility models
with an application to daily stock returns", Journal of Applied Econometrics, 14,
101-121.

12

Table 1. Summary statistics
NOBS

MEAN

STDEV

SKEW

EXKURT

ρ(1)

ρ2(1)

(1)

(2)

(3)

(4)

(5)

(6)

(7)

Japan

2861

−0.007

1.231

0.008

2.368*

0.074*

0.099*

U.S.

2861

0.028

1.069

−0.178*3.770*−0.0020.216*

Note: “NOBS,” “STDEV,” “SKEW,” “EXKURT,” “ρ(1),” and “ρ2(1)” denote the number ofthe observations, standard deviation, skewness, excess kurtosis, the first-order autocorrelation of
the return process, and the first-order autocorrelation of the squared return process, respectively.
The asterisk (*) represents statistical significance at the 5% level.

13

Table 2. Estimates of the EGARCH model with asymmetric transmission
φ0

φ1

φ2

φ3

δ1

δ2

zJP,t-1-

zUS,t-1+

zUS,t-1-

a0

a1

a2

b1

b2

Const

RJP,t-1+

RJP,t-1-

RUS,t-1+

RUS,t-1--0.0510.104*

0.017

0.349*

0.398* -0.162* 0.964* 0.124* -0.242*(0.032)(0.031)(0.035) (0.033) (0.035) (0.018) (0.006) (0.017) (0.018) (0.021) (0.019)

Const lnσ2JP,t-1 zJP,t-1+

0.000 -0.069*

Note: Robust standard errors are in parentheses. The asterisk (*) represents statisticalsignificance at the 5% level.

14

Table 3. Test of Hypotheses: Asymmetric vs. Symmetric transmission

Hypotheses

EGARCHSV

H1: b1 = b2 and δ1 = δ2

11.530*7.155*(0.003)(0.028)

H2: b1 = b2

0.785

1.365

H3: δ1 = δ2

(0.376)11.018*(0.001)(0.243)5.988*(0.014)0.705

H4: λ1 = λ2(0.240)Note: The test statistics for H1 is asymptotically distributed as χ2(2), for H2 and H3 areasymptotically distributed as χ2(1), and for H4 is asymptotically as N(0, 1) under the null
hypothesis. P-values are within parentheses. In particular, the p-value for H4 is for a
one-sided test. The asterisk (*) represents statistical significance at the 5% level.

15

Table 4. Test for the EGARCH against the SV model,
and the log-likelihoodsLM

Log Likelihood

Log Likelihood

statistic(EGARCH)

(SV)

Japan

14.43*−4454.69−4409.68

U.S.

10.98*−3799.25−3769.89

Note: The LM test statistic proposed by Kobayashi and Shi (2005) is
asymptotically distributed as N (0, 1) under the null hypothesis of the
EGARCH model (i.e., ση = 0). The critical value at the 5% level is 1.65.
The asterisk (*) represents statistical significance at the 5%
level.

16

Table 5. Estimates of the SV model with asymmetric transmission
a0

a1

a2

b1

b2

Const.

RJP,t-1+

RJP,t-1-

RU.S..,t-1+

RU.S..,t-1-−0.0540.112*

0.005

0.328*

0.395*(0.032)(0.031)(0.034)(0.035)(0.036)

φ0

φ1

φ2

φ3

ση

Const.

lnσJP,t-12

ZJP,t-1+

ZJP,t-1-−0.0130.969*−0.094*−0.036(0.022)(0.007)(0.034)

δ1

δ2

ZU.S..,t-1+

ZU.S..,t-1-

ηU.S..,t-1+ ηU.S..,t-1-

0.008−0.075*0.575∆

0.097(0.035) (0.019) (0.033)(0.028)(0.396)(0.374)

0.157

λ1

λ2

Notes: Robust standard errors are in parentheses. The asterisk (*) represents
statistical significance at the 5% level and ∆ represents significance at the 10 %level.

17

Figure 1. Japanese Stock Prices
TOP IX
2000

1000

0
1993/1/4%
20

1998/1/4

2003/1/4

Ret ur ns

10
0
-10
-20
1993/1/4

1998/1/4

18

2003/1/4

Figure 2. Null Hypotheses for H2, H3, and H4(a) H2
RJP,tb1

R-US,t-1
b2

R+US,t-10(b) H3logσ2JP,t-δ2
R-US,t-1δ10

R+US,t-1(c) H4logσ2JP,tλ1

η-US,t-1 λ2

η+US,t-1

019