Modelling Volatility Spillover in GCC Stock Markets Using Structural Time Series Analysis
35
Modelling Volatility Spillover in GCC Stock Markets
Using Structural Time Series Analysis
Talla Al-Deehani*
Kuwait University, Kuwait
Abstract This paper investigates volatility spillover among the stock markets of the six member
countries of the Gulf Cooperation Council (GCC) by applying the concept of stochastic volatility
and structural time series modelling. The results provide strong evidence for bidirectional and
unidirectional contemporaneous volatility spillover but reveal weak evidence for lagged volatility
spillover. Volatility in the Qatar stock market does not seem to affect or be affected by volatility of
any of the other five markets. Moreover, volatility in one market cannot be explained totally by
volatility in the other five markets.
Introduction
Globalization and the Multi-directional flow of capital between financial markets have led to
increasing market interdependence. Many empirical studies provide evidence for co-movements
and interdependence of stock markets in different countries. Two main approaches can be
recognized from the literature. The first approach is to examine various aspects of market
interdependence using cointegration and causality [see, for example, Taylor and Tonks (1989),
Mathur and Subrahmanyam (1990), Eun and Shim (1989), Malliaris and Urrutia (1992) and
Ghallager (1995)]. The second approach is to examine interdependence in terms of volatility
spillover1 [see, for example, Hamao et al. (1990), Koutmos and Booth (1995), Susmel and Engle
(1994), Theodossiou and Lee (1993), Koutmos (1996) and Kanas (1998)].
Research on the transmission mechanism of volatility between stock markets has been
advancing rather rapidly since the seminal work of Engle (1982) who introduced the ARCH
model. For example, Hamao et al (1990) studied first and second moment interdependencies 2 in
New York, Tokyo, and London during the 1987 crash using univariate Generalized Autoregressive
Conditional Hetroskdasticity (GARCH) models. They found that volatilities coming from New
York and London influence volatility in Tokyo and London. Koutmos (1996) studied the dynamic
interdependence of major European stock markets and documented significant volatility
interaction. Lin, Engle, and Ito (1991) examined the interaction of the US and Japanese stock
markets in terms of mean and volatility and found that the two markets influence each other.
Theodossiou and Lee (1993) examined first and second moment interactions in five major stock
*
1
2
Dr.Talla M Al-Deehani, Dept of Finance & Financial Institutions, College of Business Administration,
Kuwait University, P.O Box 5486, Safat 13055, Kuwait,
Email: [email protected], Fax (965) 4838980.
That is the effect of historical volatility in one market on the returns and volatility of another.
That is interdependence in terms of mean and volatility respectively.
36 Talla Al-Deehani / Journal of Accounting and Finance 4 (2005) 35~44
exchanges. Kanas (1998) found bidirectional spillover between the London and Paris markets and
between the Paris and Frankfurt markets, as well as unidirectional spillover from London to
Frankfurt.
Empirical research has also documented volatility transmission from developed markets to
emerging markets [see, for example, Bekaert and Harvey (1997, 2000) and Worthington and Higgs
(2004)]. Many emerging markets of less developed countries are relatively new compared to
markets of developed countries. However, some of these markets have attracted the attention of
local and regional investors. Examples of such markets are the stock markets of the Gulf
Cooperation Council (GCC): Bahrain, Kuwait, Saudi Arabia, UAE, Oman and Qatar. Economic
and financial integration has been a main target of the Council and a key discussion issue in almost
all of its summits ever since it was established in 1981. Nevertheless, the volatility spillover in the
stock markets of this region has not been examined. Although most of the GCC markets are not
open to foreign investors they remain important to GCC nationals3. For the reasons mentioned
earlier and because of the new policies and regulations adopted by the GCC to integrate the
markets, bidirectional volatility spillover is expected among these markets.
In this paper, the notion of stochastic volatility and structural time series modelling are used to
examine volatility spillover among the six emerging stock markets of the GCC. An extensive
comparison between stochastic volatility models and GARCH models was conducted by Kim,
Shephard and Chib (1997). Using daily observations of exchange rates, they based their
comparison on likelihood ratios and Bayes factors. They found that the Gaussian GARCH models
do not fit the data very well because the data exhibits positive skewness and excess kurtosis. This
suggests that the models cannot accommodate extreme positive observations in data. They also
found that likelihood ratios and Bayes factors tests give strong evidence against the use of
Gaussian GARCH models as compared with stochastic volatility models.
Methodology
This paper applies a stochastic volatility model that has two main attractions. The first is that it
is the natural discrete time analogue of the continuous time model used in option pricing research
[see, for example, Hull and White (1987)]. The second is that its statistical properties are easy to
determine compared with the conditional variance models of the GARCH class. The disadvantage
of the conditional variance models of the GARCH class is that likelihood based estimation can
only be carried out by a computer intensive technique whereas a quasi-maximum likelihood
method is relatively easy to apply and it is often reasonably efficient.
Let
yt be the rate of return measured as the first log difference of the price that is generated
by the process
yt   t exp( ht / 2) ,  t ~ IID (0,1) ,
t  1,..., T
(1)
such that
3
It is interesting to note that the six markets represent a substantial proportion of all Arab capital markets.
The market capitalization of the GCC stock markets represents about 60% of that of all Arab capital
markets.
where
Modelling Volatility Spillover in GCC Stock Markets Using Structural Time Series Analysis
37
ht 1  ht  t , t ~ NID(0, 2 ) ,   1
(2)
2
is a scale factor,
uncorrelated with
t
 is a parameter, and t is a disturbance term which is
[see Shephard (1996) and Ghysels, Harvey and Renault (1996) for a review
of relevant literature]. The stochastic volatility transformation used in this paper follows the model
adopted by Fuller (1996) and analysed by Breidt and Carriquiry (1996) which makes the following
transformation:
log yt2  log( yt2  cs y2 )  cs y2 /( rt2  cs y2 ) ,
where
t  1,..., T ,
(3)
sr2 is the sample variance of yt and c is a small number. When  is close to 1, then
the fit is similar to that of GARCH(1,1) model and when it is 1, the fit is similar to that of
IGARCH(1,1) model.
After extracting stochastic volatility from returns in the markets, a seemingly unrelated time
series equations (SUTSE) is used to represent multivariate stochastic volatility. The model is
specified as
(4)
ht  μt  ε t ,
 t ~NID(0,   )
μ t  μ t 1  ηt ,
where
t ~NID(0,   )
(5)
  and   are N  N variance matrices and, ε t and η t are multivariate normal
disturbances characterised by being mutually uncorrelated in all time periods. In a homogenous
model,   q   , where q is a scalar. The model represented by (4) and (5) is a local level
model, which captures the underlying level plus a random white noise disturbance term. It
represents a random disturbance term around an underlying level that moves up and down but
without any particular direction, which adequately describes the behaviour of financial volatility.
This model can be estimated by maximum likelihood and the Kalman filter, once the models are
written in state space form (for details, see Koopman et al, 1999; Harvey, 1998).
Volatility spillover is tested by specifying a structural time series model, specifically a local
level with cycle plus explanatory variables. For n markets, the model can be written as
n1
n1
j 1
j 1
hi ,t  i ,t  i ,t   j h j ,t    j h j ,t 1   i ,t ,
i j
(6)
Equation (6) explains volatility in market i in terms of the contemporaneous and lagged
volatility in other markets, as well as a stochastic trend and the cycle that may be interpretted to
represent the effect of other factors that do not appear explicitly as explanatory variables on the
right hand side of the equation. The stochastic trend is represented by the local level model
 i ,t   i ,t 1   i ,t
(7)
whereas the cycle is specified as
t  a cos t  b sin t
(8)
38 Talla Al-Deehani / Journal of Accounting and Finance 4 (2005) 35~44
where t is time and the amplitude of the cycle is
(a 2  b 2 )1 / 2 .4 In order to make the cycle
stochastic, the parameters a and b are allowed to evolve over time, while preserving continuity is
achieved by writing down a recursion for constructing  before introducing the stochastic
elements. Thus
t   (t 1 cos   t*1 sin  )   t
t*   (t 1  t*1 cos  )  t*
if
(9)
(10)
Equation (6) shows that there is contemporaneous volatility spillover from market j to market i
and lagged spillover if  j  0 . Again, this model is estimated by maximum likelihood
j 0
and the Kalman filter.
Data, results and analysis
The data sample is drawn from the daily index of the six markets: Bahrain, Kuwait, Saudi
Arabia, UAE, Oman, and Qatar. It consists of 688 daily observations covering the period 1 January
2000 to 15 April 2003. Due to differences in weekly holidays between the countries, some
observations were deleted. The data sample was obtained from the Gulf Investment Company, a
shareholding company that is owned by the GCC member countries.
The six GCC markets account for about 79% of the total capitalisation and 85% of the value
traded of all Arab markets. This indicates the importance of the region hence the significance of
GCC markets' selection. It is also worth noting that the combined capitalization of Saudi Arabia
and Kuwait account for about 67% of the total capitalization of the six GCC countries. If size has
anything to do with the spillover effect, the Saudi and Kuwait market should be the most
influential, given their relative size.
Table 1 reports the basic statistics of daily stock returns, which shows typical non-normality of
the returns and that they are more volatile in Oman than in the other five markets. Table 2 reports a
correlation matrix, which indicates that the highest correlation is found between the Kuwait and
Saudi markets, whereas the lowest is that between the Saudi and the UAE as well as Oman
markets.
4
The incorporation of the cycle may be justified on the basis of the notion of volatility clustering. Otherwise,
it is always advisable to start with the most general (unrestricted) specification (including cycles). If cycles
are not important they will turn out to be statistically insignificant.
Modelling Volatility Spillover in GCC Stock Markets Using Structural Time Series Analysis
39
Table 1: Basic Statistics of Daily Returns
Maximum
Minimum
Mean
Standard
Deviation
Skewness
Kutosis
Bahrain
.0278
-.0408
-.00045
.0070
Kuwait
.0542
-.0908
.000968
.00949
Saudi Arabia
.0362
-.0677
.00047
.0090
UAE
.033189
-.02577
.000327
.0056
Oman
.0928
-.0498
-.00010
.01258
Qatar
.0542
-.04266
.00119
.00926
-.2078
4.726
-1.3886
18.056
-1.1769
9.8630
.75643
6.9737
1.0700
8.7245
.3484
3.9810
Oman
0.03
0.04
0.02
0.07
1.00
Qatar
0.07
0.04
0.08
0.15
0.06
1.00
Table 2: Correlation Matrix
Bahrain
Kuwait
S.Arabia
UAE
Oman
Qatar
Bahrain
1.00
Kuwait
0.19
1.00
Saudi Arabia
0.09
0.30
1.00
UAE
0.09
-0.07
-0.02
1.00
Table 3 reports estimation results of the SUTSE model represented by equations (4) and (5).
The table includes  t , the estimated stochastic trend, with its t statistics placed in parentheses.
Rd2 is the modified coefficient of determination [for specification, see Koopman et al (2000) and
~ is the standard error of the estimated equation (calculated as the square root of
Harvey (1989)]. 
the prediction error variance). The Q statistic is the diagnostic for serial correlation, which is
distributed as  (n  1  k ) where n is the number of autocorrelation coefficients and k is the
number of estimated parameters. N is a test statistic for normality, which measures the departure of
2
the third and fourth moments from their expected values under normality (distributed as  ( 2) )5.
H is a test statistic for heteroscedasticity, calculated as the ratio of the squares of the last h
residuals to the squares of the first h residuals, where h is the closest integer to one third of the
sample size. It is distributed as F(h,h).
2
5
The normality test used here is the Bowman and Shenton (1975) test, not the more frequently used JarqueBera test.
40 Talla Al-Deehani / Journal of Accounting and Finance 4 (2005) 35~44
Table 3: Estimated SUTSE Model
Bahrain
Kuwait
UAE
Oman
Qatar
-8.62*
(-9.86)
Saudi
Arabia
-10.56*
(-11.60)
t
-11.268*
(-11.60)
-9.97*
(-10.75)
-8.57*
(-9.14)
9.42*
(-10.82)
Rd2
0.37
0.42
0.34
0.37
0.30
0.40
~
DW
2
Q (  (24) )
2.137
2.124
64.03
1.925
2.282
75.55
1.990
2.022
84.39
2.035
2.109
57.39
2.046
1.905
51.86
1.920
2.239
62.49
2
9.121
N (  ( 2) )
H (F(228, 228))
1.051
*
Significant at the 5% level.
5.067
2.839
4.556
7.069
10.13
1.135
1.273
1.053
0.837
0.960
The stochastic trend,
 t , appears significant for all six markets. The estimated equations seem
to be well-determined in terms of the goodness of fit. While the models pass the heteroskedasticity
diagnostic, they do not pass the diagnostics for serial correlation indicating some missing
variables. The estimated covariance matrices are
3.24 0.12 0.08 0.17 0.15
 0.36 2.64 0.16 0.15 0.06

 0.23 0.45 2.78 0.14 0.08
 ε 
 0.53 0.41 0.39 2.92 0.11
0.47 0.18 0.24 0.33 2.94

0.29 0.29 0.07 0.17 0.61
0.39
0.04

0.03
  
0.06
0.05

0.03
0.10 
0.11 
0.02 

0.06 
0.07 

2.62 
(9)
0.12 0.09 0.15 0.14 0.09 
0.31 0.18 0.16 0.07 0.09 
0.06 0.35 0.15 0.08 0.03 

0.05 0.05 0.36 0.11 0.06 
0.02 0.03 0.04 0.37 0.09 

0.03 0.01 002 0.03 0.31
(10)
The 36 elements in the covariance matrices are 6 variances, 15 covariances and 15 correlation
coefficients. The highest correlation coefficients of the disturbances of the random components
and the disturbances of the levels of the trends are between Bahrain and Kuwait, Bahrain and
UAE, Bahrain and Oman, Kuwait and Saudi, Kuwait and UAE, Saudi and UAE, and UAE and
Oman. Volatility spillover is expected to be among these markets. Qatar market has the lowest
correlation coefficient and therefore is not expected to experience volatility spillover.
The estimation results of equation (6) are reported in Table 4. It appears from the results that
the model is well specified, as the estimated equations pass the diagnostics for serial correlation
Modelling Volatility Spillover in GCC Stock Markets Using Structural Time Series Analysis
41
and heteroskedasticity but not normality. However, high values of the normality test statistic
should not necessarily mean model misspecification as they are often caused by outliers 6 .
Therefore, we can derive sound inference from the results. From table 4, we observe:
(1) The stochastic trends of the volatilities are significant in all six markets, implying that
volatility is affected by factors other than volatility in the other two markets. Potential
factors include local financial and economic factors or volatility of international markets
(2) The insignificance of the cyclical components implies that the cyclical variation in the
dependent variable is fully explained by the cyclical variation in the explanatory variables.
Yet, the cyclical components are included to overcome serial correlation.7
(3) There is strong evidence for contemporaneous volatility spillover. Bahrain, Kuwait, Saudi
Arabia and UAE all have bi-directional contemporaneous effect on each other. Oman has a
bi-directional contemporaneous effect with Bahrain, Kuwait and UAE, but not with Saudi
Arabia or Qatar. Although it has a contemporaneous effect on Kuwait, Qatar is not affected
by any of the other five markets.
(4) There is weak evidence for lagged volatility spillover, as the coefficients on lagged
volatility terms are significant only in two cases. They indicate that past volatility in Saudi
Arabia and Oman markets affect volatility in Bahrain market. This result can be attributed
to the speed of response and adjustment in financial markets.
6
In this case, normality may affect the predictive power of the model, which is not what are concerned with
here. The objective of this paper is hypothesis testing rather than forecasting. If the objective was
forecasting, then the problem can be dealt with easily by examining the pattern of the empirical residuals
and determining the source of the outliers. Ones these have been identified, dummy variables can be
introduced to accommodate the effect of the outliers and boost the predictive power of the model.
7
Serial correlation is a symptom of model misspecification. Exploratory empirical work showed that the
exclusion of the cyclical components invites serial correlation.
42 Talla Al-Deehani / Journal of Accounting and Finance 4 (2005) 35~44
Table 4: Estimation Results of Equation (6)
Bahrain
Kuwait
UAE
Oman
Qatar
-5.54*
(-4.98)
Saudi
Arabia
-7.62*
(-6.53)
t
-7.84*
(-6.44)
-7.12*
(-5.83)
-4.36*
(-3.58)
-8.47*
(-8.18)
0
0.113
(0.14)
0.642
(1.48)
-0.229
(-0.28)
0.170
(0.35)
1.070
(1.16)
0.403
(0.71)
 0*
0.024
(0.03)
0.10*
(2.34)
0.04
(0.97)
0.11*
(2.73)
0.14*
(3.52)
0.07
(1.68)
-0.04
(-0.93)
0.08*
(2.03)
-.05
(-1.15)
-0.09*
(-2.24)
-0.005
(-0.12)
0.470
0.065
(0.14)
0.08*
(2.43)
0.14*
(3.87)
0.11*
(2.96)
0.01*
(0.40)
0.08*
(2.04)
-.03
(-.84)
0.03
(0.71)
-0.01
(-0.35)
0.07
(1.95)
-0.03
(-0.81)
0.50
0.000
(0.00)
0.04
(0.97)
0.15*
(3.89)
0.09*
(2.41)
0.06
(1.50)
-0.01
(-0.32)
-0.01
(-0.40)
0.02
(0.47)
0.02
(0.44)
-0.06
(-1.63)
0.02
(0.50)
0.42
0.181
(0.36)
0.11*
(3.02)
0.13*
(3.11)
0.10*
(2.48)
0.09*
(2.31)
0.04
(0.89)
-0.02
(-0.51)
0.04
(0.92)
-0.03
(-0.75)
-0.02
(-0.60)
-0.06
(-1.47)
0.44
-0.245
(-0.20)
0.13*
(3.46)
0.01
(0.29)
0.06
(1.46)
0.07*
(1.98)
0.07
(1.86)
0.05
(1.47)
-0.02
(0.50)
0.06
(1.54)
0.04
(1.12)
0.06
(1.60)
0.40
0.000
(0.00)
0.06
(1.77)
0.07
(1.87)
-0.01
(-0.15)
0.04
(1.19)
0.07
(1.82)
-.03
(-0.81)
-0.02
(-0.63)
-0.05
(-1.40)
0.05
(1.27)
0.03
(0.75)
0.47
~
DW
2
Q (  (21) )
1.967
2.000
20.91
1.790
2.045
30.78
1.864
1.992
32.16
1.914
1.943
17.07
1.889
2.016
16.63
1.810
2.015
32.48
N(
17.61
11.07
13.12
6.464
10.52
16.49
 1,t
 2 ,t
 3,t
 4 ,t
 5 ,t
1,t
 2 ,t
 3,t
 4 ,t
 5 ,t
Rd2
*
2
(2) )
Significant at the 5% level.
Modelling Volatility Spillover in GCC Stock Markets Using Structural Time Series Analysis
43
Conclusions
A structural time series model was used to test for volatility spillover among six GCC markets:
Bahrain, Kuwait, Saudi Arabia, Oman and Qatar. Volatility in one market is modelled as a
function of a time-varying trend, a cycle, as well as contemporaneous and lagged volatility in the
other five markets. The results indicate the existence of volatility spillover among these markets
with the following main remarks:
1. There is strong evidence of bi-directional contemporaneous volatility spillover between most
of the markets. This may be due to the increased economic and financial ties and the fast
moving attempts of deregulation and integration initiated by the GCC.
2. There is weak evidence of lagged volatility spillover among the markets.
3. There is no evidence of cyclical effect on volatility.
4. The significance of the stochastic trend of the volatility in each of the six markets indicates
that volatility in one market cannot be fully explained by volatility in the other five markets.
These findings suggest that GCC markets are integrated in the sense that each market responds
to news currently existing in the other markets. From an investment management point of view,
this finding is important because investment managers with access to news on other regional
markets may react to this news faster than those who do not. The findings also suggest that
investment managers should not rely on regional historical news as they are of no significant use
to their investment decision. The significance of the stochastic trend of the volatility implies that
there are other factors that affect volatility. This finding suggests the need for further research to
determine the factors that might affect the volatility of GCC markets. This might be achieved by
considering the lagged volatility of the same market as well as the lagged volatility of larger
international markets and other financial and economic factors.
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