consisted of a daily stock index and
its trading volume on the Korea Exchange (KRX) from 4
January 2000 to 30 December 2010. Daily index returns
and trading volume were calculated in terms of percent-
age logarithmic change, based on the following formulae:
1
ln 100
ttt
rPP

(1)
1
ln 100
ttt
VTT
 (2)
where Pt is the daily close of the index and Tt is the trad-
ing volume.
Figure 1 shows the change in value of the KOSPI and
its trading volume. Prices gradually increased until 2008,
then dropped due to the 2008 global financial crisis, and
then recovered. High trading volume was observed in
2002-2003 and then remained constant.
Table 1 lists the descriptive statistic for KOSPI returns
and its trading volume. Mean return and trading volume
were positive for the market. The kurtosis was positive
for daily stock returns and trading volume, and greater
than 3. Returns skewness was negative and trading vol-
ume skewness was positive. Applying the Jarque-Bera
(J-B) test for normality rejected the null hypothesis of
normality for returns and trading volume. The Q-statistic
can be used to test whether a group of autocorrelations is
significantly different from zero. The autocorrelation coef-
ficient shows that returns did not exhibit a serial correla-
tion whereas trading volume did.
Additionally, we tested the stationarity of returns and
trading volume, for which the most common test is the
2,400,000,000 2,800
0
400,000,000
800,000,000
1,200,000,000
1,600,000,000
2,000,000,000
400
800
1,200
1,600
2,000
2,400
00 0102 03040506 07 080910
TRADE KOSPI
Figure 1. KOSPI index and trading volume.
Copyright © 2012 SciRes. ME
K.-H. CHOI ET AL.
586
unit test. To test for a unit root, we employed both the
augmented Dickey-Fuller (ADF) test and the Phillips-
Perron (PP) test. Table 2 provides the results. The null
hypothesis that returns and trading volume are nonstation-
ary was rejected at the 1% significance level, indicating
that both trading volume and returns are stationary.
4. Methodology
In general, the ARCH model of Engle [15] and the GARCH
model of Bollerslev [16] are the most popular tools for
capturing the volatility dynamics of financial time series.
The GARCH model is particularly useful because it makes
current conditional variance dependent on lags in its prev-
ious conditional variance. One of its primary limitations
is that it enforces a symmetric response of volatility to
both positive and negative market shocks, because cond-
itional variance is regarded as a function of the magnitude
of lagged residuals, not whether they are positive or nega-
tive. However, it has been argued that a negative market
shock may lead to more volatility than a positive shock
of the same magnitude. To account for this, Nelson [1]
developed the EGARCH model and Glosten, Jagannathan
and Runkle [17] introduced the GJR-GARCH model. This
study used both of these models to assess asymmetric
volatility and the effect of new information arrival to the
market.
Table 1. Summary of descriptive statistics.
Returns Trading Volume
Mean 0.0234 0.0163
Median 0.1266 –1.2264
Maximum 11.2843 143.8069
Minimum –12.8047 –92.5004
Std. Dev. 1.8028 18.777
Skewness –0.5513 0.4688
Kurtosis 7.8372 6.0971
J-B 2789*** 1186***
Q(12) 16.526
(0.168)
338.36***
(0.000)
Note: Jarque-Bera (J-B) is the test statistic for the null hypothesis of nomal-
ity in sample returns distributions. Ljung-Box Q(12) statistics test serial
correlations up to a 12th lag length. Significance levels: ***1%, **5%, *10%.
Table 2. Unit root tests for returns and trading volume.
Returns
Trading
Volume
Intercept –51.06*** –25.12***
ADF Test
Trend and Intercept –51.08*** –25.12***
Intercept –51.12*** –180.98***
PP Test
Trend and Intercept –51.15*** –183.08***
Note: The critical value for the ADF and PP tests are –3.9611 and –3.4323
at the 1% significance level, respectively. Significance levels: ***1%, **5%,
*10%; ADF, augmented Dickey-Fuller test; PP, Phillips-Perron test.
The GJR-GARCH (1,1) and EGARCH (1,1) models with
trading volume are defined as follows, respectively:
tt
r (3)
tt
hz
 
~. ..with0,var1
ttt
ziid Ezz
22
1111tttttt
hhdV
t
(4)
(5)
(6)
 

 
11
1
11
2
log log
π
tt
ttt
tt
hhV
hh



 


2
(7)
where rt is the realized return of KOSPI, μ denotes the
mean of the returns, and Vt is trading volume, which is
used as a proxy for information arrival to the market.
Equation (6) specifies conditional variance as a function
of mean volatility ω, where 1t
is the lag in the squared
residual of the mean (the ARCH term) and provides info-
rmation about volatility clustering, ht – 1 is the previously
forecasted variance (the GARCH term), 11tt
2
d

is a term
that captures asymmetry, and dt – 1 is a dummy variable
that is equal to one if εt – 1 < 0 (bad news) and is equal to
zero if εt – 1 0 (good news). When εt – 1 < 0 and dt – 1 = 1,
the effect of an εt – 1 shock on ht is 1t

2

2
1t
. If δ > 0,
negative shocks will have a larger effect on volatility
than positive shocks. In Equation (7), conditional varia-
nce is log-linear, which has several advantages over the
pure GARCH specification. First, regardless of the mag-
nitude of loght, the implied value of ht can never be
negative, but the coefficients can be negative. Second,
instead of using
, EGARCH model uses a standard-
ized value of 11tt
h
, which allows asymmetry to be
considered. Hence, the effect of shock on log conditional
variance is
if 11tt
h
is positive and
if 11tt
h
When trading volume is included in the variance equ-
ation, θ = 0 in both GJR-GARCH (1,1) and EGARCH
(1,1) models when the effect of trading volume on cond-
itional variance is ignored. In the two asymmetric models,
the persistence of conditional variance is measured by
is negative.
, where a larger value indicates greater persis-
tence of market shock. If trading volume is considered a
proxy for information arrival, then it is expected that θ > 0.
If
is smaller when trading volume is included
than when it is excluded, then α or β may be insignificant.
We also tested the relationship between return volatility
and lagged trading volume as follows:
22
11111tttttt
hhdV
 

 (8)
11
11
11
2
log log
π
tt
ttt
tt
hhV
hh
 





 (9)
where Vt – 1 is lagged trading volume. All parameters of
variance in Equations (6)-(9) can be estimated using the
Copyright © 2012 SciRes. ME
K.-H. CHOI ET AL. 587
Brendt, Hall, Hall, and Hausman (BHHH) algorithm,
assuming Student’s t-distribution innovation.
The distribution of the actual returns is shown as the
histogram in Figure 2. The histogram of returns has a more
pronounced peak than a normal distribution, that is, it is
more similar to a t-distribution and, thus, the t-distribution
may be more appropriate to the error term assumption.
Assuming the innovations follow Student’s t-distribution,
the log-likelihood function is defined as follows:

 
2
π2
2
2
t




1
11
log logloglog
22
1log1log 1
2
T
t
tt
LT
hh


 
 
 
 

(10)
where the degree of freedom υ > 2 controls the tail be-
havior. The t-distribution approaches normal distribution
as
.
5. Empirical Results
Table 3 shows the estimation results of GJR-GARCH
and EGARCH model excluding trading volume variable.
The coefficients α and β represent ARCH and GARCH
terms, respectively, and are shown to be statistically sig-
nificant at the 1% level. The dynamics of returns exhibit
high persistence in conditional variance. Note that the
asymmetry term, δ, has the correct sign and is significant
at the 1% level. These results imply that good news has a
smaller effect on conditional volatility than bad news,
that is, the market exhibits asymmetry.
Table 4 presents the results when contemporaneous
trading volume is included. The GARCH term
is
statistically significant at the 1% level in both models,
whereas the ARCH term

is significant in EGARCH
Note: Comparison of actual returns distribution to a standardized normal and
Student’s t-distribution. The t-distribution assumes a greater likelihood of
large returns than does the normal distribution.
Figure 2. Returns of the KOSPI.
but not in GJR-GARCH models. The coefficient of trad-
ing volume
is positive and statistically significant at
the 1% level in both models. These results suggest that
contemporaneous volume significantly explains volatility,
supporting the MDH. Including trading volume slightly
increases δ, implying that volume leads to more asym-
metric volatility on the market.
Table 5 shows the estimation results of the two mod-
els when lagged trading volume is included in the condi-
tional variance equation. The estimated coefficients of α,
β, and δ are highly significant but the lagged trading vol-
ume coefficients are not significant. So we conclude that
lagged trading volume does not significantly reduce per-
sistence and does not explain volatility and, thus, does
not support the SIAH.
We evaluated the accuracy of each model specification
using Ljung-Box
12Qs and ARCH (5) tests, as shown
in Tables 4 and 5. Neither test was significant at the 1%
level, indicating that both models are sufficient for meas-
Table 3. Estimation results of GJR-GARCH and EGARCH
models without trading volume.
GJR-GARCH (1,1) EGARCH (1,1)
0.036***
(0.008)
–0.107***
(0.014)
0.021*
(0.012)
0.159***
(0.020)
0.911***
(0.001)
0.979***
(0.004)
0.103***
(0.017)
–0.089***
(0.013)
(12)
s
Q 9.878
[0.541]
14.176**
[0.290]
ARCH(5) 1.041
[0.318]
1.501**
[0.186]
Note: Standard errors are in parentheses and p-values are in brackets. The
Ljung-Box statistic tests serial correlations up to a 12th lag length
in the squared standardized returns. The ARCH(5) statistic tests the ARCH
effects at 5th order lagged, squared residuals. Significance levels: ***1%,
**5%, *10%.
(12)
s
Q
Table 4. Estimation results of GJR-GARCH and EGARCH
models with contemporaneous trading volume.
GJR-GARCH (1,1) EGARCH (1,1)
0.037***
(0.009)
–0.099***
(0.014)
0.0183
(0.007)
0.148***
(0.019)
0.909***
(0.011)
0.977***
(0.004)
0.111***
(0.017)
–0.103***
(0.013)
0.010***
(0.003)
0.007***
(0.002)
12
s
Q 7.675
[0.810]
6.954
[0.861]
ARCH (5) 0.724
[0.605]
0.693
[0.629]
Note: See Table 3.
Copyright © 2012 SciRes. ME
K.-H. CHOI ET AL.
588
Table 5. Estimation results of GJR-GARCH and EGARCH
models with lagged trading volume.
GJR-GARCH (1,1) EGARCH (1,1)
0.037***
(0.008)
–0.107***
(0.014)
0.023***
(0.011)
0.158***
(0.019)
0.912***
(0.011)
0.980***
(0.004)
0.097***
(0.017)
–0.087***
(0.013)
–0.005
(0.003)
–0.001
(0.002)

12
s
Q 10.255
(0.594)
14.190***
[0.289]
ARCH (5) 1.032
(0.397)
1.529
[0.177]
Note: See Table 3.
uring the effects of information arrival to the market, when
trading volume is included.
6. Conclusions
We examined the persistence of return volatility on the
Korean Stock Market (KSM), both including and excluding
trading volume as a proxy for information flow, and con-
sidering lagged volume.
The main conclusions of this study are as follows. First,
the KSM index exhibits strong volatility persistence and
asymmetry. Second, the inclusion of contemporaneous trad-
ing volume in the GJR-GARCH and EGARCH models
results in a positive relationship between trading volume
and volatility. Third, when contemporaneous and lagged
trading volumes are included in the conditional variance
equation, the former is positively correlated with volatil-
ity but the latter is not. Thus, trading volume affects the
flow of information, supporting the validity of MDH.
Finally, the asymmetric effect of bad news on volatility is
higher when contemporaneous trading volume is included,
although market shocks, whether positive or negative, have
similar effects on conditional volatility. Thus, we conclude
that trading volume is a useful tool for predicting the
volatility dynamics of the KSM.
7. Acknowledgements
This work was supported by the National Research Foun-
dation of Korea Grant, funded by the Korean Govern-
ment (NRF-2011-330-B00044).
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