Integration at a cost: evidence from volatility impulse response functions

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Integration at a cost: evidence from volatility impulseresponse functionsEkaterini Panopoulou a & Theologos Pantelidis b ca Department of Statistics and Insurance Science , University of Piraeus , Piraeus, Greeceb Department of Economics, Finance and Accounting , National University of Ireland ,Maynooth, Irelandc Department of Banking and Financial Management , University of Piraeus , Piraeus, GreecePublished online: 05 May 2009.

To cite this article: Ekaterini Panopoulou & Theologos Pantelidis (2009) Integration at a cost: evidence from volatilityimpulse response functions, Applied Financial Economics, 19:11, 917-933, DOI: 10.1080/09603100802112300

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Applied Financial Economics, 2009, 19, 917–933

Integration at a cost: evidence from

volatility impulse response functions

Ekaterini Panopouloua and Theologos Pantelidisb,c,*

aDepartment of Statistics and Insurance Science, University of Piraeus,

Piraeus, GreecebDepartment of Economics, Finance and Accounting, National University of

Ireland, Maynooth, IrelandcDepartment of Banking and Financial Management, University of Piraeus,

Piraeus, Greece

We investigate the international information transmission between the US

and the rest of the G-7 countries using daily stock market return data

covering the last 20 years. A split-sample analysis reveals that the linkages

between the markets have changed substantially in the recent era (i.e. post-

1995 period), suggesting increased interdependence in the volatility of the

markets under scrutiny. Our findings based on a volatility impulse

response analysis suggest that this interdependence combined with

increased persistence in the volatility of all markets make volatility

shocks perpetuate for a significantly longer period nowadays compared to

the pre-1995 era.

I. Introduction

In the wake of the stock market crash of October

1987, the study of the transmission of financial

shocks across markets or countries has emerged as

one of the most intensive research topics in the

international finance literature. Earlier studies

focused on the return series and on how returns are

correlated across markets, i.e. they considered only

interdependence through the mean of the process.

However, the transmission of information to a

market is related primarily to the volatility of an

asset’s price changes in an arbitrage-free economy,

i.e. the second moment is more important than the

first one in the flow of information (Ross, 1989).

In this respect, a second strand of the literature,

which is growing rapidly, explicitly focuses on the

volatility of equity returns, suggesting the existence

of higher-order dependence stemming from the

second moments.

Most of the studies in the so-called volatility

spillover literature perform the analysis by means of

a variety of (multivariate) Generalized Autoregressive

Conditional Heteroscedasticity (GARCH) class of

models. Specifically, some researchers estimate stan-

dard GARCH or GARCH-in-mean models, while

others choose Exponential GARCH (EGARCH)

models which can capture possible asymmetries in

the volatility transmission mechanism. All these

models are appropriate to model high-frequency

financial time series that exhibit time dependence in

the conditional variance–covariance dynamics. To

the extent that a dynamic change in stock market

integration is depicted on the daily conditional

volatility of conditional index returns and their

conditional covariations, we can draw inference on

the degree of stock market integration.In this study, we focus explicitly on uncovering

the volatility dynamics/information transmission

between the US stock market and the remaining six

*Corresponding author. E-mail: [email protected]

Applied Financial Economics ISSN 0960–3107 print/ISSN 1466–4305 online � 2009 Taylor & Francis 917http://www.informaworld.com

DOI: 10.1080/09603100802112300

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of the G-7 countries using Volatility ImpulseResponse Functions (VIRFs) for GARCH modelsintroduced by Hafner and Herwartz (2006). Ourcontribution is twofold. First, we estimate a bivariateGARCH model, for which a BEKK (Baba, Engle,Kraft, Kroner) representation is adopted for each ofthe six countries against the US using daily returnsfor the last 20 years. This formulation enables us toreveal the existence of any ‘meteor showers’, i.e.transmission of volatility from one market toanother, as well as any ‘heat waves’, i.e. increasedpersistence in market volatility (Engle et al., 1990).Splitting our sample into two nonoverlapping sub-samples of equal length, we investigate whether theefforts for more economic, monetary and financialintegration have fundamentally altered the ‘direction’and intensity of volatility spillovers to the individualstock markets under examination. Second, by using arecently developed technique, we estimate the corre-sponding VIRFs implied by the specification of eachmodel. We then assess the impact of two historicallyobserved shocks, i.e. the 1987 stock market crash andthe 1997 Asian financial crisis on the volatility andco-volatility of the markets. To this end, we do notattempt to address the issue of contagion since ouranalysis does not focus on changes in the volatilitydynamics in the aftermath of a crisis. On thecontrary, we aim at analysing two on average calmperiods. The employment of the specific financialcrises facilitates the construction of realistic shockscenarios.

To the best of our knowledge, no other study(except for Hafner and Herwartz, 2006) has employedthis innovative technique of VIRFs to study volatilitydynamics in any market. More importantly, there areseveral reasons why VIRFs represent a convenientapproach to analyse volatility spillovers. First, thistechnique allows the researcher to determine preciselyhow a shock to one market influences the dynamicadjustment of volatility to another market and thepersistence of these spillover effects. Second, VIRFsdepend on both the volatility state and the unexpectedreturns vector when the shock occurs. As a result, theasymmetric response of volatility on negative andpositive ‘news’ typically documented in the literaturecan easily be accommodated. Third, contrary totypical Impulse Response Functions (IRFs), thisspecific methodology avoids typical orthogonaliza-tion and ordering problems which would be hardlyfeasible in the case of highly interrelated financial timeseries observed at high frequencies.

The only study that is closely related to ours isLeachman and Francis (1996). The authors useda two-stage procedure, i.e. they first estimatedunivariate GARCH models for the G-7 stock

market returns and then the estimated conditional

variances were used to construct a VarianceAutoregression (VAR) system. This methodology

enabled them to employ the standard impulse

response analysis and conduct variance decomposi-tions in order to determine how a shock to one market

influences the dynamic adjustment of volatility in theremaining markets and the persistence of these

volatility spillovers. They also quantify the relative

significance of each market in generating and trans-mitting fluctuations to other markets. Interestingly,

the authors suggested that a multivariate GARCHapproach would give more efficient parameter esti-

mates than their two-stage approach but would not

enable the researcher to obtain IRFs, as the latter werenot available for GARCH processes at this time.

It is this gap in the literature that we intend to

bridge by estimating the VIRFs for the G-7 stockmarket returns accommodated by the aforemen-

tioned methodology. Consistent with the increased

integration of capital markets already documented inthe literature, our results suggest that equity markets

have become more interdependent in the post-1995period compared with the pre-1995 period. This

greater integration resulted in a significant increase

in the persistence of volatility shocks for all thecountries at hand. The existence of both elevated

‘heat waves’ and ‘meteor showers’ effects is depictedin the pattern and size of the VIRFs.

The remainder of this study is organized as follows.

Section II discusses the econometric methodologyand data and Section III presents the empirical

findings for both the pre-1995 period and the post-

1995 period. Section IV offers a summary and someconcluding remarks.

II. Econometric Methodology and Data

The BEKK model

The analysis is based on a bivariate VAR(1)-

GARCH(1,1) model. Let Yt¼ (y1t, y2t)0 be the returns

vector, with y2t denoting the US stock market and y1tone of the remaining G-7 countries. A number ofprevious studies provide evidence of interdependence

in the mean returns of international stock markets

(see, among others, Becker et al., 1990; Koch andKoch, 1991; Gerrits and Yuce, 1999). We accom-

modate the possibility of causality-in-mean betweenthe components of Yt by modelling its conditional

mean as follows:

Yt ¼ CþM � Yt�1 þ Et ð1Þ

918 E. Panopoulou and T. Pantelidis

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where C is a 2� 1 vector of constants, M is a 2� 2

coefficient matrix and Et¼ (e1t, e2t)0 is the vector

of the zero-mean error terms. We allow Et to have

a time-varying conditional variance, that is

Var(Et |F t�1)¼Ht where F t�1 denotes the �-fieldgenerated by all information available at time t� 1.

We further assume that the conditional variance, Ht,

of Et follows a bivariate GARCH(1,1) model and

we, specifically, consider the following BEKK repre-

sentation, introduced by Engle and Kroner (1995):

Et ¼ H1=2t � Zt

Ht ¼ � ��0 þ A � Et�1 � E0t�1 � A

0 þ B �Ht�1 � B0

ð2Þ

where �¼ [!ij], i, j¼ 1, 2 is a 2� 2 lower triangular

matrix of constants, A¼ [aij] and B¼ [bij], i, j¼ 1, 2

are 2� 2 coefficient matrices and

Zt ¼ ðz1t, z2tÞ0� i:i:d:

0

0

� �,

1 0

0 1

� ��

Matrix A measures the extent to which conditional

variances are correlated with past squared unexpected

returns (i.e. deviations from the mean) and conse-

quently captures the effects of shocks on volatility.

On the other hand, matrix B depicts the extent to

which current levels of conditional variances and

covariances are related to past conditional variances

and covariances. Apart from displaying sufficient

generality, this model ensures that the conditional

variance–covariance matrices, Ht¼ [hij,t], i, j¼ 1, 2,

are positive definite under rather weak assumptions.

Specifically, Engle and Kroner (1995) showed that Ht

is positive definite if at least one of � or B is of full

rank. Our interest lies on the elements of the matrices

A and B. More in detail, significant estimates of the

off-diagonal elements of these matrices provide

evidence of increased interdependence (‘meteor

showers’) between the markets, while any ‘heat

waves’ (persistence) effects are to be captured by the

respective diagonal elements. To be more accurate

the persistence of the whole system is captured by the

eigenvalues of the system. A crude measure for

the persistence of the volatility of each country

could be obtained when considering the sum of the

diagonal elements of matrices A and B.Compared to alternative GARCH representations,

the BEKK model is more convenient for estimation,

because it involves fewer parameters. Engle and

Kroner (1995) proved that the BEKK model in

Equation 2 is second-order stationary if and only if

all the eigenvalues of ðA� Aþ B� BÞ are less than

unity in modulus. In this case, the unconditional

variance of Et, Var(Et), can easily be calculated by:

vec½VarðEtÞ� ¼ ½I4 � ðA� AÞ0 � ðB� BÞ0��1� vecð�0�Þwhere vec is the operator that stacks the columns ofa square matrix to a vector.

In particular, the conditional variance for eachequation can be expanded for the bivariate

GARCH(1, 1) as follows:

h11, t ¼ !211 þ a211e

21t�1 þ 2a11a12e1t�1e2t�1 þ a212e

22t�1

þ b211h11, t�1 þ 2b11b12h12, t�1 þ b212h22, t�1 ð3Þ

h22,t¼!221þ!

222þa

221e

21t�1þ2a21a22e1t�1e2t�1þa

222e

22t�1

þb221h11,t�1þ2b21b22h12,t�1þb222h22,t�1 ð4Þ

h12,t¼!11!21þa11a21e21t�1þða11a22þa12a21Þe1t�1e2t�1

þa12a22e22t�1þb11b21h11,t�1

þðb11b22þb12b21Þh12,t�1þb12b22h22,t�1 ð5Þ

Suppose that we estimate a bivariate system forCanada and the US based on Equations 1 and 2. In

such a case, h11,t and h22,t denote the conditionalvariance for Canada and the US, respectively, whileh12,t denotes the conditional covariance between theseries. Significance of any or both the elements b12,

a12 suggests that volatility in the Canadian market isaffected by developments in the volatility of the USmarket through either the past volatility of the US

market, h22,t�1, or the past squared innovations e22t�1(or even the cross products, e1t�1e2t�1, of pastinnovations). Furthermore, indirect feedback may

exist through the past value of the conditionalcovariance h12,t�1. When considering the evolutionof the US market volatility and its dependence on the

Canadian one, the reasoning is similar and followsdirectly from Equation 4. The contemporaneousco-movement in the volatility of the series is given

by Equation 5 and is a function of past-squaredinnovations, cross products of innovations, past-conditional volatilities and naturally past-conditional

covariance. This rich parameterization suggests thateven in the case that conditional volatilities betweenthe series are not linked directly, i.e. b12¼ b21¼ 0,

the interaction between the conditional variances isensured by past return innovations.

To cope with the excess kurtosis we find in theestimated standardized residuals under the assump-tion of Gaussian innovations, we follow Bollerslev

(1987) and evaluate (and maximize) the samplelog-likelihood function under the assumption thatinnovations are drawn from the t-distribution with

� degrees of freedom. When modelling high-frequency financial data, the employment of thet-distribution generates a more efficient estimation

Integration at a cost: evidence from VIRFs 919

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for conditional errors than the normal distribution

(Susmel and Engle, 1994). In such a case, given a

sample of T observations, a vector of unknown

parameters � and a 2� 1 vector of returns Yt, the

bivariate BEKK model is estimated by maximizing

the following likelihood function:

Lð�Þ ¼XTt¼1

lnðlt�Þ ð6Þ

with

lt ¼�ððTþ �Þ=2Þ

�ð�=2Þ½�ð�� 2Þ�T=2jHtj

�1=2

� 1þ1

�� 2E0tH

�1t Et

� ��ðTþ�Þ=2ð7Þ

where � denotes the degrees of freedom of the

t-distribution and �(�) is the gamma function. This

log-likelihood function is maximized using the

Berndt, Hall, Hall and Hausman (BHHH) (1974)

algorithm. Initial values for the estimation of the

BEKK model are taken from the respective

univariate GARCH(1, 1) estimates for every series

at hand. Diagonal elements of the matrices A and B

are taken to be the square root of the corresponding

univariate estimates, while the off-diagonal elements

of A and B are initialized to zero.Next, we describe the calculation of the VIRF

introduced by Hafner and Herwatz (2006) and

analyse their behaviour for alternative parameteriza-

tions of the BEKK model that are of particular

interest.

Volatility impulse response functions

Following Hafner and Herwatz (2006), we calculate

VIRFs based on an alternative multivariate GARCH

representation, namely the vec-representation (intro-

duced by Engle and Kroner, 1995), given by

vechðHtÞ ¼ Qþ R � vechðEt�1 � E0t�1Þ

þ P � vechðHt�1Þ ð8Þ

where Q is a 3� 1 matrix of constants, while R and P

are 3� 3 coefficient matrices, vech is the operator

that stacks the lower triangular part of a square

matrix to a vector. Given that any BEKK model has,

in general, a unique equivalent vec-representation

(Engle and Kroner, 1995), it is straightforward to

derive the necessary assumptions for the equivalence

of the two representations. Two GARCH representa-

tions are equivalent if every sequence of errors {Et}

generates the same sequence of conditional volatilities

{Ht} for both representations. Specifically, the Q, R

and P matrices of the vec-model are linked to the

parameters of the BEKK model Equation 2 asfollows:

Q ¼

!211

!11!21

!221 þ !

222

264

375,

R ¼

a211 2a11a12 a212a11a21 a11a22 þ a12a21 a22a12

a221 2a21a22 a222

264

375 and

P ¼

b211 2b11b12 b212

b11b21 b11b22 þ b12b21 b22b12

b221 2b21b22 b222

264

375

Modelling volatility dynamics through the BEKKmodel and calculating VIRFs through its equivalentvec-representation reduces the number of parametersto be estimated (by 10) by imposing some specificrestrictions on the vec-model. However, this reduc-tion in the number of parameters comes with virtuallyno cost in terms of the generality of our model. Ouranalysis of VIRFs that follows is based on modelEquation 8.

Assume that at time t¼ 0 the conditional varianceis at an initial state H0 and an initial shockZ0¼ (z1,0, z2,0)

0 occurs. The VIRF, Vt(Z0), is thendefined as follows:

VtðZ0Þ ¼ E ½vechðHtÞ j F t�1,Z0� � E ½vechðHtÞ j F t�1�

The first and third elements of Vt(Z0) (denoted as �1,tand �3,t, respectively) represent the reaction of theconditional variance of the first and second variablerespectively to the shock, Z0, that occurred t periodsago. Similarly, the second element of Vt(Z0) (denotedas �2,t) represents the reaction of the conditionalcovariance to the shock, Z0, that occurred t periodsago. The VIRF can easily be computed recursivelybased on the following relations:

V1ðZ0Þ ¼ R �nvech H1=2

0 Z0Z00H

1=20

� �� vechðH0Þ

o

V1ðZ0Þ ¼ ðRþ PÞ � Vt�1ðZ0Þ, t > 1 ð9Þ

We should note that the persistence of the volatilityshocks depends on the eigenvalues of the matrixRþP. More specifically, the closer the eigenvaluesof RþP are to unity, the higher would be thepersistence of shocks. In the case of eigenvaluesgreater than unity, the VIRF would be explosive(i.e. VtðZ0Þ �!

t!11). Contrary to the traditional

IRF in the conditional mean, which is an oddfunction of the initial shock, the VIRF is an evenfunction of the initial shock, that is Vt(Z0)¼Vt(�Z0).Finally, the IRF is a linear function,


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i.e. IRF(k *Z0)¼ k * IRF(Z0), while the VIRF is nothomogeneous of any degree.

It is important to note that VIRFs depend on theinitial volatility, H0. This initial volatility can beeither the volatility state the time the shock occurred,or any other date chosen arbitrarily from our sampledepending on the analysis at hand. For example, ifwe are interested in examining the reaction of stockmarkets immediately after a shock occurs, we wouldemploy as initial state of volatility the state ofvolatility the time the shock occurred. In a moregeneral framework, such as ours, where our interestlies in comparing volatility dynamics between twosample periods, the initial volatility state has to befixed at a common value so as not to mask any realdifferences in volatility dynamics. To avoid confu-sion, we will denote such an initial state of volatilityas the baseline state H�0.

VIRFs also depend on the unexpected returnsvector when the shock occurs. As a result, theasymmetric response of volatility on negative andpositive ‘news’ typically documented in the literature(see e.g. Koutmos and Booth, 1995; Kanas, 1998;Marcelo et al., 2008) can easily be accommodated.Negative ‘news’, i.e. unexpected returns, in onemarket can result in a different volatility profilethan positive ‘news’, other things being equal.

To facilitate the discussion of our results in thefollowing section, we first comment on the behaviourof the VIRF in three cases of interest, namely thecases of no volatility spillovers, the case of unidirec-tional spillovers and the more general one ofbidirectional spillovers. As a measure of the decayof persistence of the volatility shocks we employ thehalf-life of a volatility shock defined as the timerequired for the impact of the shock to reduce to halfof its maximum value. Let the 3� 1 matrix � be�¼ ½ i;1� :¼ vechðH�1=20 Z0Z

00H�1=20 Þ�vechðH�0Þ where

i¼ 1, 2, 3. It is obvious that the elements of � arefunctions of the elements of the baseline state H�0 andthe elements of the shock Z0.

Case 1: Diagonal BEKK model (i.e. a12¼ a21¼b12¼ b21¼ 0). In this case, both R and P (and thusRþP) are diagonal matrices. It is easy to show that:

�1,1 ¼ a211 1,1 and �1, t ¼ a211þ b211� t�1

�1,1 for t> 1

�2,1 ¼ a11a22 2,1 and

�2, t ¼ ða11a22þ b11b22Þt�1�2, 1 for t> 1

�3,1 ¼ a222 3,1 and �3, t ¼ a222þ b222� t�1

�3,1 for t> 1

Therefore, in this particular case there are novolatility spillovers, since both �1,t and �3,t depend

only on their own history. It is important to note thatin this case of a diagonal BEKK model, the half-lifeof a volatility shock is independent of both the initialshock, Z0 and the baseline state H�0.

Case 2: a12¼ b12¼ 0, while a21 6¼ 0 and/or b21 6¼ 0.In this case, both R and P (and thus RþP) are lowertriangular matrices. Therefore,

�1,1 ¼ a211 1,1 and �1, t ¼ a211þ b211� t�1

�1,1 for t> 1

�2,1 ¼ a11a21 1,1þ a11a22 2,1 and

�2, t ¼ fð�1,1,�2,1Þ for t> 1

�3,1 ¼ a221 1,1þ 2a21a22 2,1þ a222 3,1 and

�3, t ¼ gð�1,1,�2,1,�3,1Þ for t> 1

where f is a function of �1,1, �2,1, aij and bij, i,j¼ 1, 2 andg is a function of �1,1, �2,1, �3,1, aij and bij, i.j¼ 1, 2.1 It isclear that in this particular case there are unidirec-tional volatility spillovers from the first to the secondvariable of the system. Consequently, the effect of theshock on the conditional variance of the first variableof the system does not depend on the behaviour of thesecond variable of the system. We should note thateven if a21¼ 0 or b21¼ 0, there are still volatilityspillovers from the first to the second variable ofthe system. Finally, in this particular case, the half-lifeof a volatility shock in h11,t is independent of theinitial shock, Z0, and the baseline state H�0, whilethe half-life of a volatility shock in h22,t and h12,tdepends on both the initial shock, Z0, and the baselinestate H�0.

Case 3: a12 6¼ 0 and/or b12 6¼ 0, while a21 6¼ 0 and/orb21 6¼ 0. In this general case, it is easy to verify thatbidirectional volatility spillovers exist between thevariables of the system. As expected, the half-life of avolatility shock in h11,t, h22,t and h12,t depends on boththe initial shock, Z0 and the baseline state H�0.

Data

Our dataset includes daily closing stock marketindices (expressed in US dollars) of the G-7 countriesof Canada, France, Germany, Italy, Japan, UK andthe USA from Ecowin between 31 December 1985and 8 October 2004, excluding the weekends. Thedenomination of the series in US dollars suggests thatthe analysis is conducted from the point of view of aUS investor facing the remaining G-7 equity marketsas foreign ones. Moreover, we prefer daily returndata to lower frequency data, such as weekly andmonthly returns, because longer horizon returns canobscure transient responses to innovations which may

1For example, fð�1, 1, �2, 1Þ ¼ða11a21þb11þb21Þ a2

11þb2

11ð Þt�1�ða11a22þb11b22Þ

t�1 �

a211�a11a22þb11ðb11�b22Þ

.


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last for a few days only. Eun and Shim (1989) and

Karolyi and Stulz (1996) suggest that high-frequency

data (even intra-day) are more practical for studying

international correlations or spillovers than low-

frequency ones. For each index, we compute the

return between two consecutive trading days, t� 1

and t as ln(pt)� ln(pt�1) where pt denotes the closing

index on day t.Our whole sample spans an era of economic and

monetary policy coordination initiated by the Plaza

Agreement of September 1985 and the subsequent

Louvre Accord of February 1987. Consequently, the

period under examination is one marked with

attempts centered on coordinating economic growth,

bringing about exchange rate stability and maintain-

ing lower interest rates. Leachman and Francis (1996)

found that the G-7 equity markets have become more

interdependent in the post-1985 period. It is this

period of increased integration over which we conduct

our analysis for two nonoverlapping subsamples of

approximately equal length. The first subsample ends

at 31 December 1994. Our rationale behind the choice

of this date lies basically on developments within the

European Union, of which the majority of G-7

countries are members and whose size and importance

make it an increasing presence on global financial

markets. Specifically, in the aftermath of the severe

European Monetary System (EMS) crisis during

1992–1993, European stock markets were heading

towards segmentation stemming mainly from uncer-

tainty over the single currency project, a process that

had stabilized by roughly 1995. Since then andwith the

Treaty of Amsterdam, real integration took place

through convergence in macroeconomic fundamen-

tals. Our first sub-sample period indicates the phase

before major changes took effect in the process of

equity markets, while the second sub-sample is

comprised of both the pre-euro integration phase

and the post-euro one. Existing evidence suggests that

the European Monetary Union has induced stock

market integration not only between European

countries but also vis-a-vis Japan and the US

(Baele, 2005; Kim et al., 2005).

III. Empirical Results

Descriptive statistics

Table 1 reports the descriptive statistics of

stock returns for the samples under consideration.

Panel A reports the statistics for the full sample, while

Panels B and C refer to the two subperiods

considered, namely the pre-1995 and the post-1995period.

The UK stock market consistently yields the highestdaily returns for the periods under consideration,although during the post-1995 subperiod, it is closelyfollowed by the US and Canadian markets. The worstperformance in terms of daily returns is that of Japanover the full sample and the second subperiod.Notably, in the post-1995 period, Japan is the onlycountry with negative mean returns. Volatility (asmeasured by the SD of the return series) is highest inJapan followed by Germany for all the periods underconsideration, while the least volatile market isCanada. A comparison between the two subsamplessuggests that the more recent era was the moreturbulent with increased volatility in all marketsexcept Italy and the UK. The results of properstatistical tests, not reported for brevity, indicate thatin the cases of Canada, France, Germany, Japan andthe US the volatility is higher during the post-1995period compared to the pre-1995 period. On thecontrary, we find that in the case of Italy volatility ishigher in the first period than in the second one.Finally, in the case of the UK, most of the tests fail toreject the null hypothesis of equal volatilities betweenthe two periods.

Moreover, all return distributions seem to exhibitasymmetries and fat tails with relation to normaldistribution. All the markets have negative skewness,with the exception of Japan for the full and post-1995periods. Skewness is higher, in absolute terms, duringthe pre-1995 era reflecting the effects of the 1987crash. As expected, the highest skewness is related tothe US, the country where the crash originated. Fattails, as depicted in the kurtosis of the distribution,are also more prominent in the US followed byCanada and the UK. The above suggest that thedistribution of the return series suffers from seriousdepartures from the Gaussian distribution, which wetake into account when modelling volatility returns.On the whole, this preliminary analysis shows thatthe nature of the data varies significantly between thetwo subsamples, justifying our modelling strategy.

Next, we analyse our findings with respect to thevolatility dynamics between the US and the rest of theG-7 countries.

Bivariate volatility dynamics

We estimate a bivariate VAR(1)-GARCH(1, 1)-BEKK model for each country against the USbased on the specification given by Equations 1 and2. Our choice of the US as the country against whichall volatility dynamics are modelled stems from theprice leadership of the US equity market. Since the US


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economy dominates the world economy and trade,it is natural to expect the existence of economic andfinancial relationships with the rest of the world. Asa result, information about the US economic funda-mentals and equity market developments are trans-mitted all over the world and have a significant impacton worldwide stock markets (Hamao et al., 1990;Theodossiou and Lee, 1993; Lee, 2004). Furthermore,the US capital market is by far the largest capitalmarket in the world, accounting for approximatelyhalf the world market capitalization. Japan andthe UK account for 13% and 9.3% of the worldmarket, while the respective figures for theremaining G-7 countries range from 2 to 4% (Flavinet al., 2002).

As is apparent from the specification of our model,we model both mean and volatility dynamics for thesix pairs of countries. However, since our focus is onthe volatility dynamics, we do not comment on thedependence of the series through the mean and asa result our discussion is confined to second orderdependence. The estimated parameters of the condi-tional variances and covariances with associated SEs,the estimated degrees of freedom of the t-distributionand the likelihood function values along with theeigenvalues of the whole system are given in Table 2.Panel A refers to the pre-1995 period, while the

results for the post-1995 period are reported inPanel B.

The estimates of the two unrestricted models,reported in Table 2, suggest that some of theparameters of our models are statistically insignif-icant. Given that insignificant parameters mayobscure the results of the impulse response analysis,it is important to clear them from our system. In thisrespect, each model was sequentially re-estimatedwhile testing down along the lines of the General-to-Specific methodology (see, inter alia, Mizon, 1995),i.e. we re-estimate our models by dropping theleast significant coefficient at a time. We end upwith the two restricted models reported in Table 3(Panels A and B for the pre-1995 and post-1995periods, respectively).

Before discussing the estimated restricted models,we establish the validity of the zero restrictionsimposed on the unrestricted models by employingthe typical Likelihood Ratio (LR) test. However, weshould note that since the distribution of LR underthe null depends on nuisance parameters, we cannotclaim that it follows asymptotically a �2(k) distribu-tion where k is equal to the number of restrictionsimposed in the restricted model. Simulation resultsreported in previous studies (Caporale et al., 2006)reveal that the performance of LR (based on the �2(k)

Table 1. Summary descriptive statistics

Canada France Germany Italy Japan UK US

Panel A: Full sample (31/12/84–8/10/04)Mean 0.00025 0.00035 0.00028 0.00029 9.59� 10�5 0.00044 0.00034Median 0.00049 0.00046 0.00032 0.00037 0.00000 0.00055 0.00025Maximum 0.08874 0.08289 0.08769 0.07099 0.12883 0.07231 0.09095Minimum �0.12111 �0.08430 �0.11494 �0.10678 �0.13823 �0.14047 �0.22899SD 0.00960 0.01355 0.01453 0.01304 0.01602 0.01150 0.01093Skewness �1.17403 �0.22157 �0.29519 �0.36396 0.11682 �0.59935 �2.07463Kurtosis 17.7069 5.88741 7.16838 6.90276 7.63023 10.6913 47.1517

Panel B: First subsample (31/12/84–31/12/94)Mean 0.00016 0.00044 0.00031 0.00027 0.00048 0.00054 0.00033Median 0.00037 0.00049 0.00000 0.00034 0.00053 0.00054 0.00029Maximum 0.08874 0.08289 0.08769 0.07099 0.12883 0.07231 0.09095Minimum �0.12111 �0.08430 �0.11494 �0.10678 �0.13823 �0.14047 �0.22899SD 0.00800 0.01317 0.01351 0.01397 0.01560 0.01179 0.01045Skewness �2.07996 �0.36377 �0.50435 �0.39156 �0.01657 �1.01165 �4.80774Kurtosis 43.4971 7.11751 10.3723 7.59009 10.1313 15.5090 108.379

Panel C: Second subsample (1/1/95–8/10/04)Mean 0.00034 0.00028 0.00027 0.00029 �0.00025 0.00035 0.00025Median 0.00064 0.00041 0.00053 0.00045 �0.00043 0.00056 0.00017Maximum 0.04690 0.06198 0.06837 0.05592 0.12354 0.05797 0.05574Minimum �0.09033 �0.07362 �0.08559 �0.07543 �0.06592 �0.05886 �0.07114SD 0.01088 0.01389 0.01542 0.01213 0.01639 0.01124 0.01136Skewness �0.80306 �0.10832 �0.16263 �0.31626 0.22749 �0.16387 �0.10826Kurtosis 8.96719 4.94645 5.24439 5.42687 5.72985 5.29419 6.25458


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Table

2.Unrestricted

estimatedGARCH(1,1)-BEKK

models

!11

�11

�12

b11

b12

!21

!22

�21

�22

b21

b22

Eigenvalues

d.f.(SE)

Panel

A:1st

subsample

(31/12/84–31/12/94)

Canada

0.0013*

(0.0001)

0.2596*

(0.0291)�0.0173

(0.0183)

0.9387*

(0.0116)

0.0149*

(0.0060)

0.9885

0.9710

4.8333*

(0.3160)

0.0004*

(0.0001)

0.0006*

(0.0002)

0.0656*

(0.0331)

0.1355*

(0.0193)�0.029*

(0.0128)

0.9938*

(0.0062)

0.9692

0.9625

LL

17066.3

France

0.0036*

(0.0004)

0.2614*

(0.0280)

0.0545*

(0.0221)

0.9213*

(0.0160)�0.0012

(0.0078)

0.9890

0.9458

5.6514*

(0.4033)

0.0004

(0.0002)

0.0007*

(0.0001)�0.0110

(0.0146)

0.1533*

(0.0130)�0.0019

(0.0073)

0.9830*

(0.0026)

0.9425

0.9214

LL

15138.7

Germany

0.0028*

(0.0003)

0.2738*

(0.0257)

0.0423*

(0.0207)

0.9339*

(0.0109)

0.0044

(0.0067)

0.9881

0.9593

5.2204*

(0.3353)

�0.0001

(0.0001)

0.0008*

(0.0001)�0.0064

(0.0137)

0.1415*

(0.0123)

0.0041

(0.0055)

0.9828*

(0.0027)

0.9566

0.9423

LL

15197.8

Italy

0.0021*

(0.0003)

0.2436*

(0.0223)

0.0132

(0.0163)

0.9584*

(0.0076)�0.0044

(0.0046)

0.9896

0.9786

5.6541*

(0.4018)

0.0002

(0.0001)

0.0007*

(0.0001)

0.0082

(0.0107)

0.1477*

(0.0121)�0.0027

(0.0036)

0.9836*

(0.0022)

0.9784

0.9780

LL

14978.5

Japan

0.0025*

(0.0002)

0.3437*

(0.0235)

0.0593*

(0.0279)

0.9281*

(0.0089)�0.0104

(0.0074)

0.9898

0.9808

5.2258*

(0.3588)

0.0002

(0.0002)

0.0007*

(0.0001)

0.0243*

(0.0100)

0.1537*

(0.0122)�0.008*

(0.0038)

0.9827*

(0.0024)

0.9648

0.9634

LL

14890.7

UK

0.0031*

(0.0004)

0.2693*

(0.0304)

0.0061

(0.0250)

0.9239*

(0.0164)

0.0057

(0.0073)

0.9864

0.9497

6.0113*

(0.4041)

0.0004

(0.0002)

0.0008*

(0.0001)�0.0049

(0.0188)

0.1656*

(0.0135)�0.0020

(0.0090)

0.9796*

(0.0033)

0.9485

0.9281

LL

15438.0

Panel

B:2ndsubsample

(1/1/95–8/10/04)

Canada

0.0007*

(0.0001)

0.2125*

(0.0183)

0.0314

(0.0185)

0.9747*

(0.0043)�0.0074

(0.0050)

0.9963

0.9961

7.3849*

(0.5860)

0.0005*

(0.0002)

0.0006*

(0.0001)

0.0344

(0.0208)

0.2301*

(0.0213)�0.0074

(0.0054)

0.9705*

(0.0055)

0.9940

0.9939

LL

17029.1

France

0.0013*

(0.0002)

0.2167*

(0.0189)�0.0271

(0.0235)

0.9692*

(0.0057)

0.0110

(0.0071)

0.9977

0.9886

8.4343*

(0.8219)

�0.0003

(0.0002)

0.0008*

(0.0001)

0.0106

(0.0164)

0.2315*

(0.0186)

0.0018

(0.0051)

0.9682*

(0.0053)

0.9883

0.9798

LL

15977.8

Germany

0.0007*

(0.0002)

0.2205*

(0.0165)

0.0384

(0.0227)

0.9733*

(0.0043)�0.0055

(0.0069)

0.9997

0.9932

8.4185*

(0.8173)

�0.0003

(0.0002)

0.0009*

(0.0001)

0.0017

(0.0122)

0.2415*

(0.0162)

0.0021

(0.0034)

0.9656*

(0.0047)

0.9931

0.9869

LL

15921.2

Italy

0.0017*

(0.0002)

0.2409*

(0.0205)

0.0068

(0.0180)

0.9572*

(0.0074)

0.0027

(0.0053)

0.9964

0.9863

8.6927*

(0.8834)

0.0001

(0.0002)

0.0007*

(0.0001)

0.0236

(0.0180)

0.2293*

(0.0165)�0.0067

(0.0064)

0.9718*

(0.0042)

0.9855

0.9745

LL

16219.0

Japan

0.0020*

(0.0003)

0.2072*

(0.0170)

0.0069

(0.0249)

0.9696*

(0.0050)

0.0041

(0.0063)

0.9946

0.9902

8.3958*

(0.8265)

�0.0002

(0.0002)

0.0007*

(0.0001)�0.026*

(0.0132)

0.2308*

(0.0153)

0.0049

(0.0039)

0.9709*

(0.0038)

0.9893

0.9837

LL

15242.6

UK

0.0013*

(0.0001)

0.2186*

(0.0170)�0.095*

(0.0191)

0.9574*

(0.0065)

0.0320*

(0.0073)

0.9976

0.9776

9.0356*

(0.8716)

�0.000*

(0.0002)

0.0008*

(0.0002)

0.0565*

(0.0182)

0.2343*

(0.0209)

0.0003

(0.0075)

0.9623*

(0.0072)

0.9649

0.9506

LL

16512.5

Notes:SEsare

reported

inparentheses.d.f.refers

todegrees

offreedom

ofthet-distribution.LLrefers

tothevalueofthelog-likelihoodfunction.

*indicatessignificance

atthe5%

level.


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Table

3.RestrictedestimatedGARCH(1,1)-BEKK

models

!11

�11

�12

b11

b12

!21

!22

�21

�22

b21

b22

Eigenvalues

d.f.(SE)

Panel

A:1st

subsample

(31/12/84–31/12/94)

Canada

0.0010*

(0.0001)

0.2161*

(0.0170)

0.9567*

(0.0073)

0.0099*

(0.0026)

0.9923

0.975

5.0970*

(0.3232)

0.0007*

(0.0001)

0.1580*

(0.0125)

0.9835*

(0.0022)

0.975

0.9619

LL

17065.9

LR-stat.

0.8529

p-value

0.9906

France

0.0036*

(0.0004)

0.2692*

(0.0263)

0.0424*

(0.0197)

0.9218*

(0.0143)

0.9886

0.9459

5.6243*

(0.3983)

0.0002*

(0.0001)

0.0008*

(0.0001)

0.1465*

(0.0122)

0.9834*

(0.0023)

0.9459

0.9221

LL

15137.2

LR-stat.

3.1034

p-value

0.7958

Germany

0.0028*

(0.0003)

0.2667*

(0.0221)

0.0545*

(0.0152)

0.9373*

(0.0089)

0.9881

0.9603

5.2190*

(0.3334)

0.0009*

(0.0001)

0.1445*

(0.0109)

0.9835*

(0.0022)

0.9603

0.9496

LL

15196.3

LR-stat.

3.0371

p-value

0.8815

Italy

0.0021*

(0.0003)

0.2426*

(0.0216)

0.9596*

(0.0072)

0.9898

0.9796

5.6196*

(0.3938)

0.0008*

(0.0001)

0.1435*

(0.0121)

0.9845*

(0.0022)

0.9795

0.9795

LL

14977.0

LR-stat.

2.8405

p-value

0.9440

Japan

0.0025*

(0.0003)

0.3386*

(0.0231)

0.9317*

(0.0085)

0.9891

0.9827

5.1422*

(0.3418)

0.0008*

(0.0001)

0.1569*

(0.0128)

0.9821*

(0.0025)

0.9681

0.9681

LL

14885.1

LR-stat.

11.2143

p-value

0.1898

UK

0.0028*

(0.0004)

0.2601*

(0.0270)

0.9355*

(0.0130)

0.9851

0.9583

6.0111*

(0.3949)

0.0003*

(0.0001)

0.0009*

(0.0001)

0.1631*

(0.0130)

0.9791*

(0.0028)

0.9583

0.9428

LL

15437.0

LR-stat.

2.0793

p-value

0.9553

Panel

B:2ndsubsample

(1/1/95–8/10/04)

Canada

0.0007*

(0.0001)

0.1896*

(0.0132)

0.0495*

(0.0164)

0.9796*

(0.0028)�0.0116*

(0.0042)

0.9968

0.9956

7.3827*

(0.5843)

0.0006*

(0.0002)

0.0007*

(0.0001)

0.2555*

(0.0169)

0.9652*

(0.0044)

0.9939

0.9939

LL

17026.8

LR-stat.

4.4864

p-value

0.4817

France

0.0015*

(0.0002)

0.2108*

(0.0162)

0.9696*

(0.0047)

0.0064*

(0.0020)

0.9962

0.9900

8.4791*

(0.8214)

0.0008*

(0.0001)

0.2375*

(0.0148)

0.9694*

(0.0036)

0.9900

0.9846

LL

15975.4

LR-stat.

4.8151

p-value

0.4389

Germany

0.0009*

(0.0002)

0.2233*

(0.0145)

0.0187*

(0.0075)

0.9726*

(0.0033)

0.9964

0.9959

8.4130*

(0.8164)

0.0009*

(0.0001)

0.2358*

(0.0146)

0.9700*

(0.0036)

0.9959

0.9957

LL

15919.6

LR-stat.

3.1584

p-value

0.3969

Italy

0.0017*

(0.0002)

0.2335*

(0.0193)

0.9597*

(0.0068)

0.0044*

(0.0017)

0.9964

0.9859

8.6295*

(0.8451)

0.0008*

(0.0001)

0.2336*

(0.0154)

0.9705*

(0.0037)

0.9859

0.9755

LL

16217.8

LR-stat.

2.4012

p-value

0.8794

Japan

0.0021*

(0.0003)

0.2112*

(0.0171)

0.9682*

(0.0052)

0.0060*

(0.0025)

0.9936

0.9893

8.4674*

(0.8384)

0.0008*

(0.0001)�0.0115*

(0.0058)

0.2323*

(0.0151)

0.9712*

(0.0036)

0.9874

0.9874

LL

15240.8

LR-stat.

3.6086

p-value

0.7295

UK

0.0014*

(0.0002)

0.2192*

(0.0168)�0.0943*

(0.0190)

0.9575*

(0.0063)

0.0317*

(0.0070)

0.9976

0.9781

9.0840*

(0.8752)

�0.0006*

(0.0002)

0.0008*

(0.0002)

0.0561*

(0.0145)

0.2347*

(0.0160)

0.9626*

(0.0043)

0.9658

0.9513

LL

16511.2

LR-stat.

2.6975

p-value

0.2596

Notes:SEare

reported

inparentheses.d.f.refers

todegrees

offreedom

ofthet-distribution.LLrefers

tothevalueofthelog-likelihoodfunction.Thedegrees

offreedom

for

theLR

test

includerestrictionsin

both

theconditionalmeanandtheconditionalvariance

oftheprocess.Thenullhypothesis

tested

is:RestrictedModel

preferred

toUnrestricted

Model.

*indicatessignificance

atthe5%

level.


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distribution) improves considerably as the sample sizeincreases, requiring T 3000 for empirical rejectionfrequencies to approximate well the nominal signifi-cance level. In our case, we have about 2500observations in each subsample and thus we considerthe use of the �2(k) distribution for LR to bemeaningful. Our results (reported in Table 3) indicatethe validity of the zero restrictions in all cases,suggesting that the restricted models are preferable tothe unrestricted ones. Thus, we only comment on theestimates of the restricted models and mainly focuson comparing the results of the two sub-periods.

Starting with Canada, France and Germany, wefind that volatility (conditional variance) in thesecountries is directly affected by US volatility in bothperiods under examination, while no evidence of theopposite effect is present. For example, in the case ofCanada, volatility is transmitted through the US pastvolatility in the pre-1995 period (b12¼ 0.0099), whilein the post-1995 period volatility is transmitted notonly from the US past volatility (b12¼�0.0116), butalso through the cross product of past innovationsand past squared US innovations (a12¼ 0.0495).Karolyi (1995) reports similar evidence of volatilityspillovers from the US to Canada. On the whole, ourfindings for these three countries are consistent withthe notion that these markets do not have asignificant influence on the volatility dynamics ofthe US market.

The same holds for the Italian market, whichexhibits a considerable degree of volatility indepen-dence during the pre-1995 period, when the onlychannel of volatility transmission seems to be theindirect one through the conditional covariance ofItalian and US returns. However, our findings for thepost-1995 period suggest that the Italian market hasbecome more integrated and consequently, moreresponsive to spillovers from the US. Specifically,increases in the conditional volatility of the US havea significant positive effect on the Italian volatility(b12¼ 0.0044).

Contrary to the aforementioned countries, theJapanese and the UK stock markets paint acompletely different picture. The behaviour of theconditional variances of the series is starkly differentin the periods under examination. During the pre-1995 period, no cross-market dependencies areapparent, as indicated by the diagonality of thecorresponding BEKK models. However, our esti-mates for the second subperiod support the increasedintegration of both markets with the US stockmarket, allowing for bidirectional volatility transmis-sion. Specifically, positive feedback is transmittedfrom the US stock volatility to the Japanese volatility(b12¼ 0.0060), while negative ones are transmitted in

the opposite direction (a21¼�0.0115). Turning tothe UK, volatility transmission is likely to be moreintense from the US to the UK than in the oppositedirection, since the transmission channel in this caseis both through cross-innovations and past USvolatility (a12¼�0.0943, b12¼ 0.0317, a21¼ 0.0561).

In general, our results corroborate and extend theresults of Hamao et al. (1990), Lin et al. (1994),Cheung and Ng (1996), Leachman and Francis (1996)and other authors. However, all these studies wereperformed prior to 1996 and consequently theirresults are comparable to our ‘pre-1995 period’results. On the other hand, Berben and Jansen(2008), using a similar sample with our study (butweekly instead of daily observations), examineintegration between nine European markets and theUS market. Their results provide strong evidence ofincreased interdependence between the marketsduring the more recent years.

More importantly, our estimates of the eigenvaluesof the BEKK models (reported in Tables 2 and 3)suggest that volatility has become more persistent inthe more recent years, indicating that the duration ofvolatility spillovers is likely to increase. Specifically,the eigenvalues of the system for our earlier samplerange between 0.92 and 0.99, while for the recentsample they are well above 0.95. Although thisdifference in absolute value may seem small, it isquite important with respect to the persistence ofshocks. Billio and Pelizzon (2003), using a switchingregime beta model, also found an increase in theworld volatility persistence for the post-1997 period,even for tranquil periods.

This change in the volatility persistence along withthe change in volatility linkages is directly related tothe pattern of the VIRFs presented in the nextsection. While it is clear from the aforementionedanalysis that volatility transmission has increased andthe markets under examination have become moreinterdependent during the recent era, the plethoraof transmission channels renders us incapableof quantifying the responses of each of the G-7equity markets to a volatility shock, judging onlyby the coefficient estimates of our bivariateGARCH model.

Estimates of VIRFs

In this section, we undertake a more in-depth analysisof volatility spillovers among the markets. Wespecifically determine how a shock to one marketinfluences the dynamic adjustment of volatility in theother markets along with the persistence of this shockby means of the VIRF. Instead of considering a set ofrandom (and probably controversial) volatility


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shocks, we investigate two observed historical shocks.In this way, the analysis is realistic and providesuseful insights with respect to the size, pattern andpersistence of volatility spillovers in internationalstock markets in the event of a similar crisis. As ameasure of the intensity of the volatility spillover, wecalculate the half-life of a shock, i.e. the time period(in days) required for the impact of the shock toreduce to half its maximum value. Our analysis isconfined to the two sub-periods under scrutiny, inorder to reveal possible changes in the behaviour ofvolatility for the countries under examination. Theemployment of observed shocks during periods ofcrises does not imply that we examine contagioneffects. Our analysis is based on two ‘tranquil’ periodson average and does not attempt to discriminatebetween ‘crises’ and ‘tranquil’ periods.

First, we compute the historical shocks which are,by construction, the standardized residuals of ourseries that have the desirable property of news, thatis, they form an i.i.d. sequence. As opposed totraditional impulse response analysis through themean equations, our shocks are not shocks in thestock returns and consequently are unobservable.The first historical shock considered in our study isthe 1987 stock market crisis. On 19 October 1987,

the estimated residual vector, Et, and the estimatedvolatility state, vechðHtÞ, were (�0.1162,�0.2295)0

and (0.562� 10�4, 0.764� 10�4, 2.03� 10�4)0, respec-tively for the Canada–US model. In this case, theinitial shock is estimated to be Z0 ¼ ðH

1=2t Þ�1Et ¼

ð�9:74, � 14:04Þ0. The corresponding initial shocksfor the remaining five models are calculated in asimilar way and reported in Table 4 (Panel A).

As expected this shock is negative for all countriesunder scrutiny. Furthermore, irrespective of the pairof countries considered, the magnitude of the shock isgreater in the US, the country from which the stockmarket crash originated. Judging from the initialshock, the worst affected countries seem to beCanada, the UK and Japan, which at that timewere the more developed ones. On the other hand, theshock for France, Germany and Italy was milderreaching about one-fifth or less of its US counterpart.The second shock is drawn from our post-1995 periodand refers to the Asian financial crisis in 1997.Actually, it is difficult to decide on a specific date forthis crisis, since it actually spanned from July 1997 toDecember 1998 building upon a series of events thatled to a huge drop of stock prices. For example, theThai market declined sharply in June, the Indonesianmarket fell in August and the Hong Kong market

Table 4. Historical shocks and half-life of volatility impulse responses

Canada France Germany Italy Japan UK

Panel A: Crash 1987Historical shocksZ10 �9.74 �3.99 �2.46 �3.63 �7.28 �8.63Z20 �14.04 �16.85 �16.97 �17.39 �17.32 �15.74

Half-life (1st subsample)h11 34 13 25 35 41 13h12 46 15 22 35 23 18h22 91 62 60 70 65 48

Half-life (2nd subsample)h11 130 305 548 274 155 336h12 164 292 443 249 121 339h22 219 184 194 195 98 98

Panel B: Asian crisisHistorical shocksZ10 �8.83 0.68 �0.41 �0.82 �1.37 0.96Z20 �4.24 �7.47 �7.07 �6.82 �6.85 �7.05

Half-life (1st subsample)h11 25 24 30 35 41 13h12 36 18 23 35 23 18h22 91 62 60 70 65 48

Half-life (2nd subsample)h11 119 306 547 273 197 341h12 142 293 443 272 189 12h22 219 184 194 195 117 32

Notes: Initial amplification shock is deducted. Half-life is expressed in days.


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crashed in mid-October. Only then did the press in

the West pay attention to developments in the East

and the turmoil start spreading to the developed

countries. By October 27, the crisis had had a

worldwide impact. On that day the Dow Jones fell

by 7.18% causing stock exchange officials to suspend

trading. We calculate the initial shock for the Asian

crisis on this day (see Panel B of Table 4). Quite

strikingly, Canada is the market bearing the greatest

shock on this day, closely followed by the US. Japan,

which is the only Asian country in our sample, comes

third. It is worth mentioning that France and the UK

had positive shocks on this day, albeit of a small

magnitude (0.68 and 0.96, respectively).Having quantified the two historical shocks, we

proceed with the impulse response analysis.

As already mentioned, apart from the estimated

parameters of the BEKK models and the correspond-

ing initial shocks, the calculation of the VIRFs

requires the definition of a baseline state of volatility,

H�0. To make our findings invariant to the choice of

initial state, we select the last day of our sample, i.e.

8 October 2004 and employ this estimated conditional

variance–covariance matrix as baseline state in both

sub-periods.2 This allows for a direct comparison of

the VIRFs between the two sub-periods under

consideration.While the analysis in the preceding section revealed

the existence of volatility spillovers among the stock

markets under examination, it does not provide us

with information concerning the dynamic adjustment

of the system to volatility shocks. Better insights on

both this adjustment and the differences in the

pattern of volatility spillovers between the two sub-

samples can be gained when the path of the impulse

responses in the volatility of each country over time is

considered. Figure 1 plots the VIRFs for the stock

market crash of 1987 shock.3

With respect to the pre-1995 sample, the VIRF is

maximized the day after the shock occurs for all the

G-7 countries and then decreases towards zero. The

same is true for the more recent era for Canada,

Japan and the US. However, in the cases of France,

Germany, Italy and the UK, the effect of the shock

gradually increases, reaching its maximum value after

many days or even weeks before the VIRFs resume

their declining path towards zero. Similar conclusions

can be reached when considering the Asian financial

crisis (the results are not reported for brevity).

Irrespective of the shock, a common finding for allthe countries under consideration is the upward shiftof VIRFs induced by the increased persistence of thevolatility in the more recent years. The effect ofpersistence on volatility spillovers can be quantifiedthrough the half-life of the volatility shocks, whichare reported in Table 4. Half-lifes are calculated afterthe Initial Shock Amplification (the number of daysneeded so that the VIRF reaches its maximum value)has been deducted.

Our estimates suggest that with respect to the 1987stock market crash, it took France and the UK just13 days to absorb half the shock. Quite naturally thepersistence of the shock was greater in the US. In thiscase our half-life estimates ranges from 60 to 91 days.The respective figures for the remaining countriesstay conformably below 41 days. With respect to thehalf-life of the shock to the covolatility between theUS and the markets at hand, our estimates point to amaximum half-life of 46 days for the case of Canada,which is quite normal given the proximity of themarkets. Our results corroborate existing evidence onthe rate of decay of volatility shocks. Specifically,Leachman and Francis (1996) studying real monthlyreturns from the G-7 countries for the period of1973–1993, which has some overlap with our firstsample, found that volatility shocks that originate inthe US die out within a year.

Turning to the more recent era, the half-lifes ofvolatility shocks point to significantly more persistentshocks. Half-lifes for all the countries range from98 days (US) to even 548 days (Germany), suggestingthat a shock similar to the ‘1987 crash’ one wouldinduce volatility spillovers that would last for asignificantly longer period nowadays compared to thepre-1995 period. Volatility shocks with a half-life ofmore than 2 years are difficult to explain. Oneexplanation for this high persistence of equitymarkets in the more recent era could be a reductionin inflation volatility through coordinated monetarypolicy. Kearney (2000), employing monthly returns ofthe G-5 equity markets over the period 1975–1994,finds that inflation volatility is negatively related tostock market volatility. Given that inflation volatilityis positively related to its level, the low-inflationenvironment in all countries in the more recent eraprobably induces the higher persistence in stockmarket volatility. Furthermore, Baele (2005), usinga large set of economic and financial variables thatmay influence volatility shock spillover intensity in

2Alternatively, the estimated unconditional variance matrix of Et was employed as an initial state. Our results werequalitatively similar to the ones reported and are available upon request.3 The analysis for the US is based on the Canada–US model, although quantitatively similar results are drawn from the rest ofthe bivariate models.


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the EU, finds that inflation enters in his systemnegatively for the majority of the countries in hand.In this vein, a low-inflation environment points to anincrease in spillover intensity, suggesting that equitymarkets share more information in such an environ-ment. Another possible explanation could be theexistence of time-varying risk premia. Poterba andSummers (1986) argue that shocks which do notpersist for long time periods are not persistent enoughto generate time varying risk premia. Based on thisobservation and their finding that shocks take about6 months to decay, Leachman and Francis (1996)concluded that time-varying risk premia were not thesource of transmission of volatility in the period1973–1993. This finding is consistent with ours for thepre-1995 sample as already argued.

The respective calculated half-lives for the Asianfinancial crisis are given in Table 4 (Panel B). Ourfindings are qualitatively similar to the previouslyanalysed shock. However, interesting insights can bedrawn as far as the sensitivity of the half-lives to thebaseline state and the shock is concerned. As shownin Section II, when there are no direct interactionsbetween the volatilities of the markets, the half-life ofany shock does not depend on either the initial shockor the baseline state. This is true for the cases of Italy,Japan and the UK and for the first sub-sample.A similar picture emerges when only unidirectionalspillovers exist. Our estimates for the bivariatedynamics suggest that there are no spillovers fromany country to the US for the first period and for themore recent era with the exception of Japan and UK.

0

2

4

6

8

10

12

250 500 750 1000

1st subsample 2nd subsample

250 500 750 1000


250 500 750 1000


250 500 750 1000


250 500 750 1000


250 500 750 1000


250 500 750 1000


Canada

0

1

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7France

0

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10Germany

0.0

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1.2

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0

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US

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Fig. 1. Volatility impulse responses: the 1987 crash


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In these cases, the half-lives of US volatility

shocks are invariant to both the initial shock and

the baseline state.

Robustness tests

In this section, we present some sensitivity tests on the

volatility spillovers between the G-7 countries.4

We first consider the impact of foreign exchange

risk by employing stock market returns in local

currency, next we deal with the non-synchronicity of

the data by employing 2-day moving average returns

and finally we remove the noise of big events that

occurred during the last two decades by employing a

truncated sample. For brevity, we focus and comment

on the half-life of VIRFs for the two shocks and

periods under consideration (a full set of results is

available from the authors). Table 5 (Panels A–C)

reports the respective estimates.Employing local currency returns is akin to holding

a portfolio where foreign exchange risk has been

completely eliminated. Consequently, this could be

the case of an investor from any G-7 country.

Our results (Table 5, Panel A) suggest that in general

the impact of exchange rate risk exacerbates the

persistence of volatility and increases volatility

transmission between the G-7 countries. Half-lifesof the volatility shocks range from 18 (UK) to 182(Japan) days for the 1987 stock market crash and thepre-1995 period, while for the more recent era half-lifes range from 100 (Canada) to 579 (Italy). The onlycase where half-life is reduced in the post-1995 periodis Japan for which half-life reduces to 113 days from182 days. Similarly, the results for the Asian crisisshock suggest that (for all G-7 countries) thepersistence of volatility shocks increases in the post-1995 era compared to the pre-1995 one.

The next robustness test accounts for the non-synchronicity of the trading times between countries.In order to test whether our results are affected by thedifferent trading hours of the G-7 stock markets, weemploy 2-day moving average returns along the linesof Forbes and Rigobon (2002). Alternatively, wecould adjust the time lags of the returns for thenonsynchronicity in trading hours (Cifarelli andGiannopoulos, 2002), but since US and Europeanmarkets have overlapping trading hours we prefer thefirst approach. Our results for this case, reported inTable 5 (Panel B), corroborate our findings so far.Overall, the moving average filter smoothes the seriesof returns and as a result the persistence and durationof the shocks appear reduced. However, a

Table 5. Half-life of volatility impulse responses – robustness tests

Canada France Germany Italy Japan UK US

Panel A: Currency effects (local currency effects)Crash 19871st subsample 38 25 49 161 182 18 542nd subsample 100 344 442 579 113 270 180

Asian crisis1st subsample 38 25 50 161 208 18 542nd subsample 66 344 440 574 313 294 182

Panel B: Nonsynchronous trading effects (2-day moving average returns)Crash 19871st subsample 9 8 10 18 37 6 462nd subsample 35 170 278 282 106 213 202


Panel C: Tranquil periods effects (restricted sample)Crash 19871st subsample 18 11 16 25 33 11 212nd subsample 49 134 200 93 103 94 114


Notes: Initial amplification shock is deducted. Half-life is expressed in days. In Panel C, the historical shockfor the Asian crisis is calculated based on estimates for the 02/01/1995–08/10/2004 period.

4We would like to thank the referees of this journal for pointing out these issues.


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qualitatively similar pattern is evident with respect tothe behaviour of VIRFs in the two periods underconsideration. That is, volatility shocks last forsubstantially longer time in the post-1995 periodcompared to the pre-1995 period.

Finally, we check whether our results are drivenfrom periods in turbulence in the stock marketscaused by major events such as the EMS crises in1992–1993 and the Asian Financial crises in 1997–1998. To account for these issues we perform ouranalysis in two truncated subsamples excluding theaforementioned crises; the first subsample is 31December 1985 to 31 December 1991 and thesecond sample is 2 January 1999 to 8 October 2004.This set of results is reported in Panel C of Table 5.Overall, excluding these periods does not alter ourfindings, although half-lives are lower. For example,the half-life of the 1987 crash volatility shock is 11days for France and UK in the early period and itincreases to 134 days and 94 days, respectively, whenthe second subsample is considered.

In summary, our empirical findings suggest that theincreased persistence of volatility combined with anincrease in the volatility transmission channelsbetween the G-7 countries result in volatility shocksthat perpetuate for a significant longer periodnowadays compared to the pre-1995 era.

IV. Conclusions

There is extensive empirical work in the literaturewith respect to interdependencies between financialmarkets and more specifically, national stock mar-kets. This article focuses on second-order interdepen-dencies, i.e. linkages through the conditionalvariances of the series. The analysis was performedusing daily closing stock index data from the G-7stock markets for the last 20 years. By adopting abivariate BEKK representation and splitting oursample into two 10-year sub-samples, we firstexamined whether stock market linkages betweenthe US and the remaining of the G-7 countries havechanged during the more recent years. As a secondstep, we employed a new technique developed byHafner and Herwartz (2006) and estimated theVIRFs related to each pair of countries. Thistechnique enabled us to quantify the size and thepersistence of two historical shocks that have causedstock market turbulence. Furthermore, the signifi-cantly different structure of stock markets in thepre- and post-1995 periods allowed comparisonsthat shed some light into the current behaviour ofstock markets.

Our empirical findings can be summarized asfollows. We confirmed the established view that theUS stock market is the major volatility exporter.Specifically, there is evidence of significant volatilityspillovers from the US to Canada, France andGermany during the pre-1995 period. For the sameperiod, the rest of the G-7 countries, i.e. Italy, Japanand the UK appear secluded and invulnerable toshocks originating in the US. On the other hand, ourfindings for the post-1995 period point to increasedintegration between the markets. Specifically, thesmaller G-7 countries, i.e. Canada, France, Germanyand Italy mainly import volatility from the US.A more important finding, however, is the evidence infavour of bidirectional volatility spillovers betweenthe US and Japan, as well as the US and the UK. Ourresults suggest that shocks originating in the UKaffect positively the volatility of the US stock marketwhile the Japanese ones influence the volatility of theUS market negatively, inducing lower levels ofvolatility. Our VIRFs analysis of two historicalshocks, namely the 1987 crash and the 1997 Asianfinancial crash provided useful insights with respectto the size and persistence of volatility shocks.We specifically found evidence in favour of increasedamplitude and duration of volatility spillovers in thepost-1995 sample compared to the pre-1995 one.This intensity of shocks mainly stems from theincreased interdependence and persistence of theequity market volatilities documented in the recentera. Consequently, had a shock of similar magnitudeto the 1987 crash occurred in more recent years, thetime required for this shock to die out wouldhave been substantially longer compared to thepre-1995 period.

The finding of increased interdependence amongstthe equity markets of the G-7 countries, together withthe increased persistence of volatility shocks in themore recent years, is potentially bad news forportfolio managers who diversify over these markets.Increases in co-movement may serve to erode theperceived risk-return benefits promised by inter-national diversification strategies. Therefore, fundmanagers may need to pursue different policiesto offset this increased interdependence. One suchpolicy would be to increase the country coveragein the portfolio. To deliver comparable levels ofportfolio risk, investors should augment their currentG-7 portfolios with equity holdings of other markets.Fully diversified international portfolios will requiremore country indices. An alternative policy formanagers to pursue would be to increase theirhedging portfolios by acquiring more shortfuture positions or long put options on theunderlying assets.


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It is important to point out the limitations of ouranalysis. First, we perform the analysis by means ofbivariate GARCH models. A promising route forfurther investigation is the extension of this bivariateanalysis to a higher-order one, allowing for inter-actions among three or more countries. Second, weestimate a model that allows no asymmetries in thevolatility dynamics. It would be very interesting tomodify both the estimated model and the VIRFs toaccount for asymmetries in the transition of volatilityshocks. Third, it is important to note that ouranalysis examines volatility spillovers using overallvolatility, i.e. we do not decompose volatility into thesystematic and specific risk components. Such adecomposition would allow us to distinguish betweenthe sources of risk (see Cifarelli and Giannopoulos,2002). All these extensions will be the object of ourfuture work.

The method employed here can also be appliedto other cases that involve high frequency data,mainly financial data, to examine linkages anduncover the volatility dynamics between the seriesunder examination. Volatility spillovers betweenexchange rate markets or between stock marketsand exchange rates can be detected and quantifiedthrough the VIRFs.

Acknowledgements

We would like to thank the co-editor and threeanonymous referees for their constructive commentsand suggestions. We are grateful to T. Flavin,C. Hafner, N. Pittis, M. Roche, D. Serwa andparticipants at the 3rd INFINITY Conferenceand the Global Finance Conference 2005 forhelpful comments and suggestions. We thankT. Mavrogeorgis for excellent research assistantship.The authors thank the EU for financial supportunder the ‘PYTHAGORAS: Funding of researchgroups in the University of Piraeus’ through theGreek Ministry of National Education and ReligiousAffairs. The usual disclaimer applies.

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Integration at a cost: evidence from volatility impulse response functions

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