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					                           Prospects for Portfolio Investments

                         to Emerging European Stock Markets

                                   Dr. Theodore Syriopoulos 
                                   Department of Business Administration,
                               Technological Educational Institute, Larissa, and
                             Department of Shipping and Entrepreneurial Services,
                                    University of Aegean, Chios, Greece


The presence of short- and long-run linkages among major emerging Central European stock markets,
namely Poland, Czech Republic, Hungary, and Slovakia, as well as developed markets, particularly
Germany and the US, is investigated. An error correction vector autoregressive model is estimated to
detect cointegration relationships and the empirical findings support the presence of one cointegration
vector, indicating a stationary long-run relationship. Both domestic and external forces affect market
behavior, leading to long-run equilibriu m but the individual Central European markets tend to display
stronger lin kages with their mature counterparts rather than their neighbors. Long -run comovements
imply that the potential for diversifying risk and attaining superior portfolio returns by investing in
different Central European markets is rather limited for international investors.

                                     Paper Submitted for
                               the 2 Annual Conference of the
                         Hellenic Finance and Accounting Association

    Corresponding author: 12, Faid rou Str., 116 35 Athens, Greece.
    Tel.: 0030., 6944.911.787.
                                     Paper Submitted for
                               the 2 Annual Conference of the
                         Hellenic Finance and Accounting Association

                                    November 8th , 2003
                        Athens Universtity of Economics and Business

                           Prospects for Portfolio Investments

                         to Emerging European Stock Markets

                                   Dr. Theodore Syriopoulos 
                                   Department of Business Administration,
                               Technological Educational Institute, Larissa, and
                             Department of Shipping and Entrepreneurial Services,
                                    University of Aegean, Chios, Greece

    Corresponding author: 12, Faid rou Str., 116 35 Athens, Greece.
    Tel.: 0030., 6944.911.787.

1.       Introduction

As stock markets have gained a dominant role in equity funding and portfolio allocation decisions,

research examining possible stock market lin kages and interdependences has enriched recent literature.

Significant long-run relationships among different stock markets could be related to a range of reasons.

The presence of strong economic ties and policy coordination in various markets can indirectly link

stock price behavior over time. W ith technological advances and financial innovations, advancement of

international finance and trade, and regional and global cooperation, the geographical barriers among

various national stock markets become less clear (Gelos and Sahay, 2000). Adoption of measures

towards deregulation and market liberalizat ion, rapid development in communication s upport and

computerized trading systems, and increasing activities by mu ltinational corporations are factors

contributing to financial integration. The formation of co mmon trading blocks (e.g. EU, ASEA N,

NAFTA), and the development of integrated economic s ystems (EMU, euro) also foster closer linkages

of stock markets within the constituent states (Chen et al., 2002). These developments have in turn led

to an increase in capital flows across markets, enhancing the globalizat ion and integration process,

increasing accessibility, transparency and efficiency in t imely investment allocation decisions.

Long-run comovements between stock markets have important regional and global implications, as a

domestic economy cannot be insulated fro m external shocks and the scope for independent monetary

policy appears then limited. Cointegration has emerged as a powerful technique for investigating

common trends and long-run relationships and interdependencies among international stock markets,

and provides a sound methodology for modeling both short- and long-run dynamics in a system of

variables (e.g. Hamilton, 1994; Hendry, 1995; Enders, 1995; Campbell et al., 1997). If two or more

variables are co integrated, then stationary linear co mbinations of these variables may exis t even though

the variables themselves are individually non-stationary. Thus, variables that are cointegrated exhibit

stable long-run behavior. In the short-run, financial time series across markets may deviate fro m each

other, but market forces, investors ’ tastes and preferences, and government regulations will bring them

back to their long-run equilibriu m.

A significant part of past research focuses on major European stock markets, such as Corhay et al.

(1993), Choudhry (1996), Koutmos (1996), Serletis and King (1997), Steely and Steely (1999), Gerrits

and Yuce (1999), Dickinson (2000), Ejara (2001), and Yang et al. (2003) among others. A number of

studies investigate the Asian and Pacific stock markets, such as Hung and Cheug (1995), Cheug

(1995), Chauhdri (1996), Corhay et al. (1995), Janakiramanan and Lamba (1998), Roca et al. (1998),

Phylaktis and Ravazzolo (2001), Fan (2001), Sharma and Wongbangpo (2002), Yang et al. (2003),

Shamsuddin and Kim (2003), among others. A body of research examines the relationships among

international stock markets across regions, such as Eun and Shim (1989), Jeon and Chiang (1991),

Kasa (1992), Chan et al. (1992, 1997), Masih and Masih (1997), Ghosh et al. (1999), Huang et al.

(2000), Ratanapakorn and Sharma (2002), Chen et al. (2002), Swanson (2003), Chaudhuri and Wu

(2003), Bessler and Yang (2003), among others. Few only studies focus on the CE stock markets, such

as Jochum et al. (1999), Verchenko (2000), MacDonald (2001), Gilmo re and McManus (2003), and

Vo ronkova (2003). The majority of past empirical work investigating long -term stock market linkages

has concentrated main ly on mature rather than emerging stock markets, and has provided a range of

amb iguous and inconsistent conclusions, as statistical evidence supports the presence of cointegration

relationships in a number of markets whereas it rejects it in others. Further insight then is useful,

especially in emerg ing stock markets that appear to have low correlations with mature markets. The

conclusions have important imp licat ions for portfolio management decisions. If international stock

markets share common trends, this would imp ly that there are no particular gains to be made fro m

portfolio diversification, because the presence of common factors limits the amount o f independent

variation. Imp licit ly, shocks to the stock prices in integrated markets are temporary rather than

permanent, lead ing to predictable long-run stock prices. On the contrary, if financial markets do no

appear interrelated, profitable opportunities fro m international portfolio d iversification can be

exploited, lead ing to superior portfolio returns for long -term investors. It should be also noted, though,

that a number of studies calls into question the violation of the weak form of market efficien cy, due to

price predictability as implied by the presence of cointegration (Dwyer and Wallace, 1992; Cro wder,

1994, 1996; Engel, 1996; Caporalle and Pitt is, 1998).

The purpose of this study is to enrich research in possible interdependencies between transitional and

developed stock markets, exploring different market behaviors between emerging and mature

economies. The focus here is on long-run comovements of the emerging Central European (CE)

markets, departing fro m past practice that focuses main ly on d eveloped European markets, the US,

Asian-Pacific, and Latin A merican markets. The contribution of this study to the existing literature is

related to a range of innovative and interesting conclusions. The major CE stock markets are analyzed

in depth, in order to identify possible long-run comovements among the emerging markets of the

region as well as international mature markets, namely Germany and the US. As the relevant empirical

evidence appears to be thin and controversial, this effort intends to provide insight into the patterns of

long-run relationships among the individual CE stock markets and mature markets, the degree of asset

prices predictability and the prospects of a profitable portfolio diversificat ion to these markets. The

dynamic structure of international market integration based on innovation accounting is also analyzed,

as this topic has not been adequately investigated in relevant past studies. Central European markets are

characterized by stable performance of the domestic economies, hig her growth rates compared to ‘old’

European economies and relat ively low valuations (Havlik, 2003). A mong the CE stock markets,

Poland, the Czech Republic, Hungary, and Slovakia are considered the most developed, in terms of

capitalizat ion, turnover and number of traded securities (Hanousek and Filer, 2000; Pajuste, 2001;

Koke and Schroder, 2002). The efficient financial integration of the region with developed European

markets has important implications for the accession of the CE economies in the European Union (EU),

also affecting the long-term development prospects for Euroland as a whole. The reaction of these

markets to internal and external shocks has also considerable impact on the potential gains fro m

portfolio diversification to the region. If border effects still persist in the CE markets, portfolio

managers have an interest in investing in these markets in order to diversify their risk; otherwise

profitable opportunities for investor portfolios remain limited for such an allocation.

The statistical data used in this study consist of the daily stock index closing prices (expressed in local

currencies) of WIG (Po land), PX50 (the Czech Republic), BUX (Hungary), SAX (Slovakia), DAX

(Germany), and S&P500 (the US), over January 1, 1997 to September 20, 2003, totaling 1,747 daily

observations for each series. The rest of the paper is organized as follows. Section 2 outlines the

emp irical methodology, Section 3 presents the empirical results, and Section 4 concludes.

2.       Empirical Methodol ogy

Two distinct types of links between stock markets (indices) can be seen; the first one is typically

related to the ‘volatile behavior’ of stock indices and the second is related to the ‘trending behavior’ of

the series. In the first case, models based on estimating time-varying volatilit ies to investigate stock

price lin kages and the transmission of shocks from one market to another. In the latter case, emphasis is

placed on joint tests of market integration and comovements in the long -run. Interrelations and linkages

between the CE stock markets are studied here by estimat ion and testing for the presence and number

of cointegrating vectors. As explained, cointegration relat ionships allow fo r the description of stable

long-run stationary relationships among integrated variables, and are defined as independent linear

combinations of these non-stationary variables achieving stationarity. When a meaningful

interpretation can be attached to this linear combination, it imp lies that the series do not drift apart and

are moving together by some long-run equilibriu m relationship. Individual non-stationary times series

in a mu ltivariate system are driven by a reduced number of co mmon stochastic trends. A common

stochastic trend in a system of stock price indices can be interpreted to mean that the stochastic trend in

one individual stock price is related to the stochastic trend in some other individual stock price index.

Testing for Unit Roots

Cointegration tests require a certain stochastic structure of the individual time series involved. The

focus here will be placed on first order non-stationary integrated processes, I(1), which require first

differences to become weakly stationary. Thus, in order to test for the presence of stochastic non -

stationarity in the data, the integration order of the individual time series is first investigated, using

some well known unit root tests, such as the Augmented Dickey -Fuller (ADF) test (Dickey and Fuller,

1979, 1981), and the Ph illips and Perron (PP) non-parametric test (Perron, 1988; Phillips and Perron,

1988). These tests provide the appropriate tests statistics to determine whether a series contains a unit

root, unit root plus a drift, and/or unit root plus drift plus a time t rend. The mo re general ADF test

(including a d rift plus a time trend) is based on the following model:

                     Δyt = α + μ t + ρ yt-1 +   
                                                i 1
                                                       ψi Δ yt-i + εt   εt ~ i.i.d. (0, σ2 )   (1)
which is estimated by ordinary least squares. The null hypothesis in the ADF test is a unit root, ρ=0.

The normalized bias (T(ρ^ )), where T is the sample size, or the t-test for ρ=0 is computed. For yt to be

stationary, ρ should be negative and significantly d ifferent fro m zero. Hypothesis tests concerning the

coefficients of non-stationary variables cannot be conducted using traditional t-tests or F-tests. Under

the null hypothesis of a unit root, the limit ing distributions of the test statistics are non -standard, since

the empirical mo ments of unit processes generally converge to random variables instead of constants.

Several assumptions concerning the determin istic components can also be tested using one-sided (F-

type) tests (critical values in Fuller, 1976). The limit ing distribution crucially depends on the

deterministic components of the univariate series. The optimal lag length for each of the autoreg ressive

processes of the unit root tests is settled by the structure that minimizes various Information Criteria,

such as the Akaike Informat ion Criterion (AIC) or the Shwarz Criterion (SC). Ph illips and Perron

(1988) have modified the ADF test (based on Equation (1) without lagged differences), as the ADF

tests are only valid under the crucial assumption of i.i.d. processes. In practice, it may be more realistic

to allow for some dependence among the εt ’s. In that case, the asymptotic distribution changes. Phillips

(1987), and Phillips and Perron (1988) have weakened the i.i.d. assumption by using a non -parametric

correction to allo w for some serial correlation and heteroskedasticity:

                                      yt = α0 + a yt-1 + ut          (2)

Unit root tests can efficiently apply, in case the data generating process is quite general (Harris, 1995).

The difference, then, between the two unit root tests (ADF vs. PP) lies in their treat ment of any

‘nuisance’ serial correlation. The PP test tends to be more robust to a wide range of serial correlations

and time -dependent heteroskedasticity. In the PP test, the null hypothesis is that a series is non -

stationary (i.e. difference stationary) if α = 1, hence, rejection of the unit root hypothesis is necessary

to support stationarity. As with the ADF test, the PP test requests specifying whether to include a

constant, a constant and a linear trend, or neither in the test regression. The asymptotic distribution of

the PP t-statistic is the same as the ADF t-statistic. In the computation of these modified PP -statistics,

the Newey and West (1987) non-negative long-run variance estimator is used and the truncation lag q

needs to be specified, that is the number of periods of serial correlat ion to include. The asymptotic

limit ing distribution is the same as that of the (τμ) tests tabulated by Fuller (1976). The sequential

testing procedure proposed by Perron (1988) is to start from a quite general specification with both

trend and constant terms. The first hypothesis to be tested is that of a random walk (unit root) with drift

against a trend stationary process. In case of non-rejection, the significance of the trend term is then

tested and so on. The final hypothesis to be tested (provided all the previous less restrictive hypotheses

have not been rejected) is the driftless random walk against the simple zero-mean stationary AR(1)


The Johansen Procedure

The implication that non-stationary variables can lead to spurious regressions, unless at least one

cointegration vector is present, means that some form of testing for cointegration in the time series

under study is mandatory. Recent empirical work departs fro m the earlier well known Engle -Granger

(1987) framework towards incorporating the Johansen procedure (Johansen, 1988, 1991, 1992, 1995;

Johansen and Juselius, 1990, 1992, 1994), in order to ease the consequences of the Engle-Granger

approach, if mo re than one cointegration relationships exist. It is useful, consequently, to extend the

single equation error-correct ion model (ECM ) to a mu ltivariate framework.

A maximu m likelihood (ML) approach to mult ivariate autoregressive models is used for estimating and

testing the number of cointegrating relationships and common stochastic trends among the components

of a vector zt of non-stationary variables, incorporating different short- and long-run dynamics. The

Johansen approach relies on the relat ionship between the rank of a matrix and its characteristic roots,

provides more robust results when more than two variables are included, circu mvents the use of two -

step estimators, has the advantage of taking into account the error structure of the underlying process,

and provides relatively powerfu l tests when the model is correct ly specified.

Defining a vector zt of n potentially endogenous variables, it is possible to specify the following data

generating process (d.g.p.) and model zt as an unrestricted vector autoregression (VAR) involving up to

k-lags of zt :

                 zt = A1 zt-1 + A2 zt-2 + … + Ak zt-k + u t         u t ~ IN (0, Σ)    (3)

where zt is a (n x 1) matrix, and each of Ai is a (n x n) matrix of parameters. This type of VA R models

has been advocated most notably by Sims (1980), as a way to estimate dynamic relationships among

jointly endogenous variables without imposing strong a priori restrictions, such as particular structural

relationships and / or the exogeneity of some of the variables (Harris, 1995). The system is in reduced

form with each variable in zt regressed on only lagged values of both itself and all the other variables in

the system.

Equation (3) can be reformu lated into a vector error -correction (VECM ) form:

                      Δzt = Γ1 Δzt-1 + Γ2 Δzt-2 + …+ Γk-1 Δzt-k+1 + Π zt-k + u t     or

                                        k 1
                                Δzt =   
                                        i 1
                                               Γi Δzt-i + Π zt-k + u t    (4)

where Γi = -(I - A1 - … - Ai ), (i = 1,…, k -1), Γi are interim mu ltipliers, and Π = -(I - A1 - … - Ak). This

way, the system contains information on both the short- and long-run adjustment to changes in zt , via

the estimates of Γi ^ and Π^ respectively; the Π matrix, specifically, contains information on the long-run

relationships. Granger’s representation theorem asserts that if the coefficient mat rix Π has reduced rank

r < n, there exist (n x r) matrices α and β each with ran k r such that Π = α β´, and β´zt is stationary.

It is assumed in fact that Π can be deco mposed into Π = α β´, where α and β can both be reduced in

dimension to (n x r). The short-run structure of stock market integration involves two parts, α, and Γi .

The matrix α defines the error correction (speed of) adjustment through which the system is pulled

back to its long-run equilibriu m. The matrix ( Γi … Γk-1 ) defines the short-run adjustment to changes in

the variables, while β is a matrix of long-run coefficients, such that the term β´zt-1 (embedded in

Equation (4)), represents up to (n - 1) cointegration vectors in the multivariate model (wh ich ensure

that the zt converge to their long-run steady state solutions). It has been recognized, however, that like

in a standard VA R model, the indiv idual coefficients of the ECM are hard to interpret, and innovation

accounting may be a better description of the short-run dynamic structure (e.g. Sims, 1980; Lutkephol

and Reimers, 1992).

Assuming zt is a vector of non-stationary I(1) variables, then all the terms in (4) which involve Δzt-i are

I(0), while Πzt-k must also be stationary for u t ~ I(0) to be ‘white noise’. There are three instances when

this requirement, that Πzt-k ~ I(0), is met : (i) when all the variables in zt are in fact stationary, zt ~ I(0)

(Π has full rank), wh ich imp lies that there is no problem of spurious regression and the appropriate

modeling strategy is to estimate the standard Sims -type VA R in levels (i.e. Equation (3)); (ii) when

there is no cointegration at all, imply ing that there are no linear comb inations of the zt that are I(0), and

consequently Π is an (n x n) matrix of zeros (rank Π = 0, the matrix is null) - the appropriate model

then is a VAR in first differences involving no long -run elements; (iii) when there exist up to (n - 1)

cointegration relationships: β´zt-k ~ I(0). In this case, r < (n - 1) cointegration vectors exist in β (i.e. r

columns of β form r linearly independent combinations of the variables in zt , each of which is

stationary), together with (n - r) non-stationary vectors (i.e. (n – r) columns of β form I(1) common

stochastic trends). Only the cointegration vectors in β enter (4), otherwise Πzt-k would not be I(0),

which implies that the last (n - r) colu mns of α are insignificantly s mall (i.e. effect ively zero). Thus, the

typical problem of determining how many r < (n - 1) cointegration vectors exist in β, is equivalent to

testing which columns of α are zero. Testing, then, for cointegration amounts to consideration of the

rank of Π, that is, finding the number of r linearly independent columns in Π (cointegrating vectors).

The Johansen approach provides estimates of α and β using the ‘reduced rank regression’ procedure

(Harris, 1995).

The ML estimate of a basis of the cointegrating space is given by the empirical canonical variates of zt-k

with respect to Δzt corrected for the short-run dynamics and possible deterministic co mponents. The

number of significant canonical correlations gives the number of cointegrating relationships. Their

significance can be tested by means of a sequence of likelihood ratio (LR) tests whose limit ing

distribution is expressed in terms of vector Brownian motions (Johansen, 1988, 1991). Two test

statistics can be used for the hypothesis of the existence of r cointegrating vectors. First, the so-called

‘trace test’, i.e. the LR test statistic for the hypothesis that there are at most r distinct cointegrating

vectors against a general alternative, given by:

                                 λtrace (r) = -2 log (Q) = -T    
                                                                i  r 1
                                                                           log (1 – λ^i )

where i = r+1,…,n, are the (n - r) s mallest squared canonical correlations , r = 0, 1, 2,…, n - 1, and λtrace

(r) = 0, when all λi = 0. Asymptotic critical values are provided by Osterwald -Lenu m (1992).

Alternatively, the ‘maximum eigenvalue’ test can be used to compare the null hypothesis of r

cointegrating vectors against the alternative of (r + 1) cointegrating vectors. The LR test statistic for

this hypothesis is given by:

                                λmax (r, r+1) = -2 log (Q) = -T log (1 - λ ^r+1)

where r = 0, 1, 2,…, n - 1, and if the estimated value of the characteristic root is close to zero, λmax will

be small. The limiting distribution of 2log(Q), which is a function of a (n - r) dimensional vector

Bro wnian mot ion, is not independent of the unknown drift term. Critical values have been tabulated for

various hypotheses concerning the behavior of the deterministic co mponents (Johansen and Juselius,

1990). The distributions of both the trace and the eigenvalue tests in the case without drift have broader

tails than in the case with drift. Emp irical applications should therefore carefully investigate t he

presence or absence of trends in the long run. To test for the presence of an intercept in the

cointegrating vector as opposed to the unrestricted drift, a likelihood ratio test can be implemented.

Asymptotically the statistic:

                                       -T    
                                            i  r 1
                                                       [ log (1 - λi* ) – log (1 - λi) ]

has a χ2 distribution with (n - r) degrees of freedom, and λi * and λi denote the ordered characteristic

roots of the restricted and unrestricted Π matrix respectively. If the restriction is not binding, all values

of log(1- λi *) and log(1-λ i) should be equivalent. As a result, small values of the test statistic imp ly that

it is ad missible to include the intercept in the cointegrating vector. However, the presence of the

intercept in the cointegrating vector increases the likelihood of finding a stationary linear comb ination

of the n variables. Thus, a large value of λ* r+1 , implies that the restriction artificially inflates the number

of cointegrating vectors (Enders, 1995). Once the number of co integrating relationships has been

determined, it is possible to test particular hypotheses concerning α and β using standard χ2 distributed

LR tests.

It should be noted that cointegrating vectors are obtained from the reduced form of a system where all

of the variables are assumed to be jointly endogenous (Dickey et al., 1991). Thus, cointegrating vectors

cannot be interpreted as representing structural equations. However, cointegrating vectors may be due

to constraints that an economic structure imposes on the long -run relationship between the jointly

endogenous variables

3.       Empirical Results

Contemporaneous Correlations

Regressing non-stationary variables on each other can lead to potentially misleading inferences about

the estimated parameters resulting to the problem of spurious regressions . Before testing for

cointegration, therefore, the order of integration of stock prices must be determined. As a preliminary

step, the CE stock prices were transformed into natural logs, their integrated properties were

investigated and their graphical representations were inspected. Most of the CE stock markets (indices)

under study appear to possess some deterministic trend co mponent or might even be characterized as

trend-stationary processes (Figure 1). A range of descriptive statistics of the CE stock markets is

analyzed (Table 1). The negative skewness apparent in some stock markets imp lies that the distribution

of the series (around the mean) has a long left tail, whereas the relevant Jarque -Bera statistics indicate

rejection of the normality hypothes is.

        Table 1: Stock Market Descripti ve Statistics
                          S&P500       DAX          WIG          PX50          BUX         SAX
        Mean                7.010      8.465       9.656         6.157         8.891       4.736
        Median              7.018      8.518       9.646         6.167         8.917       4.709
        Maximu m            7.331      8.995      10.038         6.538         9.256       5.341
        Minimu m            6.603      7.698       9.257         5.756         8.236       4.251
        Std. Deviat ion     0.186      0.287       0.139         0.148         0.167       0.299
        Skewness           -0.152     -0.330       0.218         -0.118       -0.781       0.347
        Kurtosis            1.957      2.266       2.940         2.706         4.009       1.883

        Jarque-Bera           95.913      70.812     14.125      10.363      252.024      125.833
        Probability           0.0000      0.0000     0.0009      0.0056      0.00000      0.00000

        Observations           1,747       1,747      1,747       1,747       1,747        1,747
        The following indices correspond to the respective stock market: S&P500: US; DAX: Germany;
        WIG: Poland; PX50: Czech Republic; BUX: Hungary; SAX: Slovakia.

The contemporaneous correlations matrix of the four CE stock indices as well as the German and the

US stock indices is also studied (Table 2). The stock indices of Poland, Hungary, and the Czech

Republic indicate relat ively high and positive pairwise correlat ions (WIG / PX50: 0.82, WIG / BUX:

0.63, PX50 / BUX: 0.52), and the same holds for Germany and the US (S&P500 / DAX: 0.91). The

SAX Index, however, shows high negative correlation with the mature markets (SAX / S&P500: -0.87,

SAX / DAX: -0.78) and low correlation with most of the neighboring CE markets. Overall, the

correlation coefficients appear rather low, indicating weak (short-term) contemporaneous interactions

between these markets. These findings may be associated to the relatively short active life of the CE

stock markets since their reopening (early 1990s), and the absence of substantial market depth, in terms

of number of listed companies, capitalization and turnover.

             Table 2: Contemporaneous Correlations Matrix
                         S&P500     DAX         WIG       PX50                 BUX         SAX
             S&P500        1.000
             DAX           0.908    1.000
             WIG           0.369    0.405       1.000
             PX50         -0.002    0.010       0.818     1.000
             BUX           0.331    0.318       0.629     0.521               1.000
             SAX          -0.874    -0.776     -0.096     0.210               -0.137       1.000

Unit Roots

In order to test for the presence of stochastic non-stationarity in the data, the integration order of the

individual time series is investigated using the ADF and PP tests for the presence of unit roots. The

selection of optimal lags is determined by minimizing AIC, and is set at four lags for the ADF test and

at seven lags for the PP test. Both the ADF and PP tests are considered with and without trend. The null

hypothesis in each test is that each of the price series contains a unit root (i.e., testing the series as I(1)

against I(0)); it should be rejected if the test s tatistics are less than the critical value. The results from

the ADF and PP tests indicate that, for every stock price index series, the null hypothesis of a unit root

is not rejected at the 5% significance level by both tests (Table 3). To verify that the order of

integration is I(1), the presence of a unit root in the first difference of the stock price indices was also

tested but no unit roots in first differenced series was found.

                  Table 3: Uni t Root Tests
                                             ADF Test                          PP Test
                                        Without     With                 Without       With
                                         Trend     Trend                 Trend        Trend
                  S&P500                -2.153     -2.115                -2.216       -2.166
                  DAX                   -1.668     -2.004                -1.699       -2.030
                  WIG                   -2.280     -2.222                -2.390       -2.352
                  PX50                  -1.877     -1.729                -1.696       -1.541
                  BUX                   -3.110     -3.155                -3.299       -3.316
                  SAX                   -1.059     -0.702                -1.022       -0.676

                  Critical values - without trend: -3.437 at the 1% level; -2.864 at the 5% level;
                  -2.568 at the10% level. Critical values - with trend: -3.969 at the 1% level;
                   -3.415 at the 5% level; -3.129 at the 10% level.
                  MacKinnon (1991) critical values for rejection of hypothesis of a unit root.

Cointegration Vectors

As the null hypothesis of unit roots cannot be rejected, multivariate models can be built to enable

investigation of the presence or absence of cointegrating relationships in the data set. Departing fro m

the bivariate cointegration regressions in the Engle-Granger framewo rk, a vector error cointegration

model (VECM ) such as in Equation (4) is estimated to consider the six series jo intly, according to the

procedure advanced by Johansen (1989, 1991). The six stock markets are modeled as in Equation (4)

and the order the stock indices are entered into the VAR model is based on their market capitalizat ion

(all other orderings are also analyzed in supplementary models). The choice of optimal lags is given by

consideration of minimizing the AIC and absence of autocorrelation in the VA R residuals; four lags for

the levels of variables are included. Three alternative models are compared and contrasted: (a) a model

with a constant restricted to the cointegrating space; (b) a model with unrestricted constant; and (c) a

model with a linear trend in the cointegration vector.

Table 4: Model S pecification
Null            Eigenvalues                                λtrace test                   critical values at 95%
       Model 1 Model 2 Model 3                Model 1      Model 2       Model 3     Model 1 Model 2 Model 3
r= 0    0.0242     0.0242     0.0243          105.42        104.13       117.10      102.14        94.15     114.90
r< 1    0.0133     0.0130     0.0148           62.81         61.53        74.23       76.07        68.52      87.31
r< 2    0.0120     0.0117     0.0118           39.41         38.76        48.28       53.12        47.21      62.99
r< 3    0.0055     0.0054     0.0064           18.33         18.17        27.59       34.91        29.68      42.44
r< 4    0.0046     0.0045     0.0049           8.86           8.72        16.49       19.96        15.41      25.32
r< 5    0.0005     0.0006     0.0045           0.82           0.81        7.88        9.24         3.76       12.25

H1(r) against H 1(n)
Model 1: model with a constant restricted to the cointegrating space
Model 2: model with unrestricted constant
Model 3: model with a linear trend in the cointegration vector

           Table 5: Tests for the Number of Cointegrating Vectors
            Null                   λmax test                   critical values at 95%
            n -r     Model 1       Model 2    Model 3     Model 1      Model 2      Model 3
           r= 0       42.61          42.60     42.87       40.30         39.37       43.97
           r= 1       23.41          22.77     25.95       34.40         33.46       37.52
           r= 2       21.08          20.59     20.68       28.14         27.07       31.46
           r= 3        9.47          9.45      11.10       22.00         20.97       25.54
           r= 4        8.04          7.90       8.61       15.67         14.07       18.96
           r= 5        0.82          0.81       7.88        9.24         3.76        12.25

           H 1(r) against H 1(r+1)
           Model 1: model with a constant restricted to the cointegrating space
           Model 2: model with unrestricted constant
           Model 3: model with a linear trend in the cointegration vector
           Critical values are obtained from Ostenwald-Lemum (1992).

The results of the λmax and λtrace tests are reported in Tables 4, and 5 respectively. The empirical

findings indicate the presence of one cointegrating vector in the markets under study, in all three

versions of the model. The null hypothesis that the four CE stock markets, Germany, and the US are

not cointegrated (r = 0) against the alternative of one or more cointegrating vectors (r > 0) is rejected,

since the λmax(0) statistic exceeds the critical value at the 5% significance level. However, the λmax and

λtrace statistics suggest no more than one cointegrating vector, since H0 of r < 1 is not rejected, as λ max(1)

is less than the critical value at the 5% significance level. The normalized cointegration vector fro m the

three versions of the model is included in Table 6. The relative magnitude of the coefficients of the

cointegrating vector is informat ive on the respective role of the individual stock markets in the group.

The results indicate positive long-run relationship for Germany, Czech Republic, and Slovakia and

negative long-run linkages for Hungary and Poland. The comovements in these subgroups may be

related to their extensive trade and financial linkages respectively. Stock price fluctuations in the

mature markets, especially in the US, appear to have a significant impact on the emerging CE stock


Table 6: Normalized Cointegrating Vector
Model 1     S&P500      DAX          WIG                    PX50         BUX        SAX             C         TREND
             1.000      0.939       -4.075                  3.163       -0.102      0.817         1.953         -
                       (0.828)     (0.574)                 (0.058)     (0.278)     (0.383)       (0.955)

Model 2        S&P500         DAX             WIG           PX50         BUX        SAX             C         TREND
                1.000         0.936          -4.064         3.152       -0.098      0.815         1.907         -
                             (0.823)        (0.559)        (0.045)     (0.277)     (0.381)

Model 3        S&P500         DAX             WIG           PX50         BUX        SAX             C         TREND
                1.000         1.273          -4.800         3.861       -0.314      0.972         2.909       0.00008
                             (0.824)        (0.623)        (0.014)     (0.504)     (0.599)                    (0.0002)

Model 1: model with a constant restricted to the cointegrating space
Model 2: model with unrestricted constant
Model 3: model with a linear trend in the cointegration vector
Asymptotic standard errors in parentheses.

       The presence of one cointegrating vector implies that the stock indices of the six markets under study

       share a long-run equilibriu m. An important aspect of international financial globalization is that market

       prices are interrelated and price movements in one national stock market are expected to affect stock

       prices in other international markets, through efficient informat ion, easy accessibility and timely

       portfolio management. The CE (Poland, the Czech Republic, Hungary, Slovakia) s tock markets, as

       well as the German, and the US stock markets share a common stochastic trend with long -run

       movements of national stock prices. The presence of equilibriu m relationships could be attributed to

       the growing inflow of foreign portfolio investments in the CE markets and the common economic path

       of their economies. Both domestic and external forces affect the CE stock markets, leading to their

       long-run equilibriu m. This outcome, however, imp lies that investors with long holding periods, who

       diversify their portfolios across the CE stock markets, should expect only modest portfolio gains from

       such an investment allocation.

       Innovation Accounting Analysis

       The decomposition of forecast error variance of each market provides an alternative view of t he system

       dynamics and gives a quantitative measure of the interdependences among the CE, German, and US

       stock markets. Variance decomposition breaks down variation in an endogenous variable into the

       component shocks to the endogenous variables in the VA R model and gives information about the

       relative importance of each random innovation to the variables in the model. In other words, this

method indicates the magnitude of a movement in one market that can be explained by other markets,

in terms of the percentage of the forecast error variance of that market. The variance decomposition

results of 1-day, 5-day, 10-day, and 20-day horizon ahead forecast error variances of each stock index

into fractions that are attributable to innovations in each of the six ma rkets under study, based on the

estimated ECM, are summarized in Table 7. These findings provide further support to the presence of

long-run stock market linkages. At a 20-day horizon, for instance, the proportion of domestic stock

index variance that can be collectively attributable to the CE neighboring index innovations ranges

fro m 1.03% for Slovakia, to 3.25%, 15.20%, and 21.57% for Poland, Hungary, and the Czech

Republic, respectively. The proportion of domestic stock index variance that can be attribu table to the

mature market innovations ranges from 0.84% for Slovakia, to 14.67%, 24.99%, and 25.81% for the

Czech Republic, Hungary, and Poland, respectively. With the exception of Slovakia, a significant part

of the international shocks to the CE markets , and to Germany as well, is attributable to the US stock

market; this impact is stronger especially for Po land (21.74%), and Hungary (16.39%). Hence,

statistical evidence indicates that stock movements in the US predo minantly (and in Germany, to a

lesser extent) drive fluctuations in the Central European markets. The influential ro le of the US market

is also depicted by the fact that no individual market can exp lain any significant part of the US error

variance, a conclusion in line with previous studies (e.g. Ratanapakorn and Sharma, 2002). Overall, the

emp irical findings suggest that both domestic and external forces affect CE markets, leading them to

equilibriu m in the long-run. The individual CE stock markets appear relatively closer lin ked and more

influenced by movements in the developed markets of the US and Germany rather than by their other

CE neighbors in the group. The reaction of the CE markets to international shocks may be related to the

fact that, according to recent estimates, foreign investors are involved in approximately 70% of trading

in Budapest Stock Exchange, 30% in Warsaw Stock Exchange, and a lower percentage in Prague Stock

Exchange (Hanousek and Filer, 2000).

  Table 7: Decomposition of Index Innovations
  Stock Index   Horizon
                                    Percentage of forecast error variance by innovations in:
                              S&P500        DAX         WIG          PX50        BUX         SAX
  S&P500           1          100.000       0.000       0.000        0.000       0.000      0.000
                   5           99.431       0.371       0.033        0.014       0.058      0.093
                   10          99.356       0.390       0.020        0.032       0.069      0.133
                   20          99.279       0.380       0.023        0.074       0.069      0.174
  DAX              1           29.002      70.998       0.000        0.000       0.000      0.000
                   5           47.528      52.306       0.035        0.030       0.027      0.075
                   10          49.347      50.482       0.021        0.022       0.021      0.108
                   20          50.260      49.532       0.032        0.012       0.016      0.148
  WIG              1            3.350       2.449      94.201        0.000       0.000      0.000
                   5           17.323       2.913      78.542        0.925       0.289      0.009
                   10          19.246       3.390      75.379        1.630       0.339      0.016
                   20          21.741       4.070      70.938        2.841       0.347      0.062
  PX50             1            3.617       5.764       5.037       85.582       0.000      0.000
                   5            9.952       5.569       7.481       76.530       0.410      0.057
                   10          10.232       5.421      11.693       71.995       0.625      0.034
                   20           9.792       4.866      20.679       63.772       0.844      0.048
  BUX              1            3.844       9.453       9.293        4.346      73.064      0.000
                   5           15.464       8.693       8.089        5.940      61.689      0.126
                   10          16.222       8.735       8.324        6.127      60.455      0.137
                   20          16.387       8.603       9.229        5.851      59.809      0.121
  SAX              1            0.100       0.034       0.246        0.018       0.054     99.549
                   5            0.683       0.013       0.180        0.046       0.056     99.021
                   10           0.803       0.011       0.318        0.094       0.064     98.708
                   20           0.823       0.018       0.733        0.219       0.079     98.128

Impulse responses trace out the responsiveness of the dependent variable in the VAR to shocks to each

of the variables. For each variab le fro m each equation separately, a unit shock is applied to the error,

and the persistence of the effects upon the VAR system over time is noted. Provided that the system is

stable, the shock should gradually die away (Brooks, 2002). If the effect of a shock in one of the

variables does not die out in the long-run (even if no further shocks occur), it shifts the system to a new

equilibriu m, and it is called the permanent effect. If, on the other hand, the system returns to its

previous equilibriu m value after some time, it is called the transitory effect. A fast adjustment to the

previous equilibriu m indicates strong cointegration relationships in the long -run, as deviations from

equilibriu m are short lived (Ratanapakorn and Sharma, 2002). Hence, the pattern of the impulse

response of each CE stock market index to a shock in the US and German stock markets (which appear

to be the most influential markets for the CE region) is examined, in order to obtain additional insight

into the structure of the CE stock market linkages. For that, the impulse responses based on the

simu lated responses of the estimated VAR system are produced. The plots of the time path of impulse
responses of each stock index to one standard deviation shock of the US and German stock indices are

inspected for a range of time horizons (not shown). The findings from the impulse response analysis

indicate a rather slow response of the CE stock markets to a shock induced by the US or German

markets, imp lying that the CE markets react in a rather stable pattern. The contemporaneous impact of

shocks on the CE markets appears rather weak. The mature stock markets appear more integrated with

each other, as deviations from equilibriu m are restored relat ively fast.

4. Conclusions

This study investigates the short- and long-run linkages among stock indices of major transitional

Central European markets, namely Po land, Czech Republic, Hungary, Slovakia, and developed

markets, particu larly Germany, and the US. The emp irical findings enrich the thin body of the literature

focusing on emerg ing economies and the CE markets in particu lar. As Central European states are on

the way to join the European Union, the examination of possible long -run interdependencies and

comovements of these markets with major international stock markets remains a crucial issue. An error

correction vector autoregressive model is estimated to detect cointegration relationships, and the

emp irical findings support the presence of one cointegration vector, indicating a stationary long -run

relationship. Both domestic and external forces affect the CE stock markets, leading to their long -run

equilibriu m.

The CE markets tend to display stronger linkages with their mature counterparts, whereas the

interdependencies between the individual CE markets and the other CE neighbors appear rather weak.

These findings may be related to the relatively short active life of the CE stock markets since their

reopening in the early 1990s, and the absence of substantial market depth, in terms of number of listed

companies, capitalization and turnover. There is, on the other hand, growing inflow of foreign portfolio

investments and international investors have increased trading activity in the CE stock markets. The

Czech market, followed by Hungary, and Poland, exhib its the h ighest proportion of domestic stock

index variance that can be collectively attributable to the CE neighboring index innovations. The Polish

and Hungarian stock markets are more sensitive to shocks stemming fro m mature markets. The US

market holds a leading role, as it can induce strong movements in the CE markets but is not influenced

by them. The Slovakian stock market appears to exhibit a more autonomous behavior relative to its CE

peers. A rather slow response of the CE markets to a shock in the mature markets is indicated, and the

contemporaneous impact of shocks on the CE markets appears rather weak. The US and German

markets appear more integrated, as deviations from equilibriu m are restored relatively fast. The

presence of cointegrating relationships , however, has important implications for portfolio management.

Long-run comovements imp ly that the potential for diversify ing risk and attaining superior portfolio

returns by investing in different CE markets is rather limited fo r international investors.

To conclude, the Central European markets follow a co mmon path of development and become

gradually more integrated with the international mature markets. These linkages are anticipated to

strengthen in the mediu m term, as the Central Eu ropean economies are on the way to fully join the

European Union as member states by 2004. In order to attain economic convergence, the CE states are

bound to remove trade and investment barriers and proceed to tighter policy coordination with the

Euro zone. These developments will eventually lead to the introduction of the euro as the common

currency of the CE states, as well as to new challenges for the enlarged Euroland.


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      Figure 1: Central European, US, German Stock Indices

9.4                                                    9.2


8.8                                                    8.4


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                        LB U X                                               LD A X

6.6                                                    5.4




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                        LP X 50                                              LS A X

7.4                                                   10.2

7.2                                                   10.0

7.0                                                    9.8

6.8                                                    9.6

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                       LS P 500                                              LW IG


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