Price and Volatility Spillovers in the Case of Stock Markets Located in Different Time Zones

Transcription

1 Price and Volatility Spillovers in the Case of Stock Markets Located in Different Time Zones Joanna Olbrys ABSTRACT: This paper investigates the interdependence of price volatility across the U.S. stock market and two emerging markets: Poland and Hungary. Using daily data for countries located in different time zones, we point out the problems caused by the presence of nonsynchronous trading effects. To address this problem we use open-to-close logarithmic returns of major stock market indexes. The asymmetric impact of good and bad news is described by a multivariate exponential general autoregressive conditional heteroskedastic model. We investigate the sample from May 004 to December 011. The evidence is that the U.S. prices spill over to other markets. Our results show no pronounced volatility spillovers among the three examined markets. Moreover, we observe the presence of negative asymmetry in the case of all markets. KEY WORDS: asymmetry effect, market friction, multivariate EGARCH model. nonsynchronous trading, price and volatility spillovers. The transmission mechanism of price and volatility spillovers across stock markets is now one of the most active research areas in economics and finance. It is widely believed in the financial community that the initial signals for international spillovers come from the U.S. market. Price and volatility spillovers from the United States to the rest of the world are reported in many studies. Baumöhl and Výrost (010) perform Granger causality analysis on stock indexes from several Asian, European, and U.S. markets from different time zones. The results are evidence of U.S. dominance in the international stock markets. The results for the predictive general autoregressive conditional heteroskedastic (GARCH) factor models, obtained by Brzeszczynski and Welfe (007), show a very strong dependency between the Warsaw Stock Exchange main index WIG and the indexes from international markets, especially the DJIA, NASDAQ, DAX, and FTSE, in the period from 1998 to 00. Égert and Koc=enda (007) find links (on the intra-day level) among developed (the United States and the European Union) and emerging European markets going both ways. Eun and Shim (1989) interpreted nine time series of daily stock market returns using a vector autoregression (VAR) analysis in order to obtain insights into the interdependence structure of major national stock markets. The U.S. stock market is found to be the most influential market in the world. Hamao et al. (1990) find spillover effects from the U.S. and UK stock markets to the Japanese market in the period from April 1985 to March Koutmos and Booth (1995) investigate the transmission mechanism of price and volatility spillovers across the New York, Tokyo, and London stock markets in the period from September 1986 to December Li and Majerowska (008) investigate the linkages between the two emerging markets in Warsaw and Budapest and the developed markets in Frankfurt and New York in the Joanna Olbrys (j.olbrys@pb.edu.pl) is an assistant professor at the Faculty of Computer Science, Bialystok University of Technology, Poland. The author thanks two anonymous referees and Ali M. Kutan (the editor) for helpful comments and suggestions. Emerging Markets Finance & Trade / March April 013, Vol. 49, Supplement, pp M.E. Sharpe, Inc. All rights reserved. Permissions: ISSN X (print)/issn (online) DOI: /REE X490S08

2 146 Emerging Markets Finance & Trade period Among other things, they find a unidirectional return spillover from the United States to Poland, Hungary, and Germany. Martens and Poon (001) observe volatility spillover from the United States to the United Kingdom and France, as well as a reverse spillover, which was not documented before, in the period from August 1990 to November It is worthwhile to note that in the case of countries located in different time zones, international stock markets have different trading hours. We attribute this empirical problem to the friction in trading processes and we present it in detail in the following section. The main goal of this paper is to investigate the interdependence of price volatility across the developed, U.S. stock market and the two biggest emerging Central and Eastern European (CEE) markets, Warsaw and Budapest. Our paper contributes to the existing literature by focusing on the friction in trading processes, which may disrupt the analysis of stock market linkages in the case of countries located in different time zones. We propose a modified version of the multivariate exponential general autoregressive conditional heteroskedastic (EGARCH) model (Nelson 1991) in the case of the combination of two stock markets in countries located in the same time zone (i.e., the Polish and Hungarian markets) and one stock market from another time zone (i.e., the U.S. market). In our research, the whole period investigated runs from May 004 to December 011. From our point of view, it is worth stressing that Tse et al. (003) investigate the international information transmission between the U.S. and Polish stock markets in the period from January 1994 to February 003 by using the bivariate EGARCH model. Their results show no volatility spillover between these two markets. However, they observe a unidirectional mean spillover running from the United States to Poland. Our studies indicate that the U.S. prices spill over to other markets and our results show no volatility spillovers between the three markets investigated, thus confirming the previous findings of Tse et al. (003). Moreover, our results show pronounced negative asymmetry in the case of all investigated stock markets. For the Budapest, New York, and Warsaw markets, negative innovations increase volatility considerably more than positive innovations. Our findings suggest that these three stock markets are more sensitive to bad than to good news. The impact of bad and good news is described in terms of the multivariate EGARCH model, while Büttner and Hayo (010, 01), for example, advocate taking into consideration actual news (European Monetary Union [EMU] related news, news from the European Central Bank [ECB], etc.). Friction in Trading Processes In this paper, we perform an analysis of some empirical problems that can be attributed to the friction in trading processes. We understand frictions as various disturbances in the trading processes. It is worth stressing that the body of literature on empirical market microstructure has recently become quite extensive. High-frequency financial data are important in studying a variety of issues related to the trading processes and market microstructure (Tsay 010). For some purposes, aspects of the market microstructure such as nontrading or bid-ask spread effects can be safely ignored. However, for other purposes, market microstructure is central (Campbell et al. 1997). In 1980 Cohen et al. pointed to various frictions in the trading process that can lead to a distinction between true and observed returns. They focused on the fact that transaction prices differ from what they would otherwise be in a frictionless environment. It has been reported in the literature that some empirical phenomena can be attributed to frictions in the trading

3 March April 013, Volume 49, Supplement 147 process (e.g., Brzeszczynski et al. 011; Dimson 1979; Fisher 1966; Hawawini 1980; Olbrys 011; Perry 1985; Scholes and Williams 1977). Some studies distinguish between two problems caused by nonsynchronous trading. The first problem, which we shall call the nonsynchronous trading effect I, occurs when we analyze one selected domestic stock market. The nonsynchronous trading effect induces potentially serious biases in the moments and co-moments of asset returns, such as their means, variances, covariances, betas, and autocorrelation and cross-autocorrelation coefficients (e.g., Campbell et al. 1997; Lo and MacKinlay 1990). The second and potentially serious problem is the nonsynchronous trading effect II, which is felt when we examine the relationships among stock markets in various countries. The national stock markets operate in different time zones with different opening and closing times, thereby making return observations nonsynchronous (Eun and Shim 1989). The differences in the return observations arise naturally from the fact that trading days in different countries are subject to different national and religious holidays, unexpected events, and so forth (Baumöhl and Výrost 010). Because this paper investigates the interdependence of price volatility across the Budapest, Warsaw, and U.S. stock markets, we have to deal with nonsynchronous trading effect II. Previous studies have attempted various methods to deal with this effect II. Some researchers use weekly or monthly data to avoid the nontrading problem (e.g., Drakos and Kutan 005; Kadlec and Patterson 1999; Masih and Masih 001). Such solutions, however, may lead to small sample sizes and cannot capture the information transmission in shorter (daily) time frames (Baumöhl and Výrost 010). Other papers present various daily data-matching processes. For example, Hamao et al. (1990) divide daily close-toclose returns into their close-to-open and open-to-close components. To examine how a nonsynchronous problem would affect the relationship between two markets, some researchers estimate suitable models (e.g., EGARCH) based on the open-to-close returns (see Koutmos and Booth 1995; Tse et al. 003). Martens and Poon (001) use prices recorded at 4:00 p.m. London time for the U.S., UK, and French indexes to study the daily dynamics of stock index returns. In Forbes and Rigobon (00), the stock market returns are calculated as rolling-average, two-day returns based on each country s aggregate stock market index. In many studies, the approach called a common trading window is very popular: the data are collected for the same dates across the stock markets, removing the data for those dates when any series has a missing value due to no trading (see, e.g., Égert and Koc=enda 011; Eun and Shim 1989; Li and Majerowska 008). Baumöhl and Výrost (010) perform the Granger causality analysis on stock market indexes from several markets and synchronize daily data using their own data-matching procedure. Data Description and Preliminary Statistics An event that had a significant impact on a group of eight CEE emerging markets was accession to the European Union on May 1, 004. These eight countries, in order of largest population size, are: Poland, Czech Republic, Hungary, Slovakia, Lithuania, Latvia, Slovenia, and Estonia. For this reason these eight economies are particularly interesting in many respects. Due to the significance of the accession, the period investigated in this study is May 1, 004, to December 31, 011. In this study, we use the two stock markets of Warsaw and Budapest to represent the CEE markets. It is worth stressing that it is not possible to investigate all the CEE stock markets (although such a study probably would be well founded) because of difficult access to daily data. Our analysis requires daily

4 148 Emerging Markets Finance & Trade Figure 1. Exchange trading hours (CET) opening and closing prices of the stock markets. The raw data consist of daily opening and closing figures for major stock market indexes for Warsaw (WIG index), Budapest (BUX index) and New York (S&P500 index). We removed the data for those dates when any series has a missing value due to no trading. Thus all the data are collected for the same dates across the three markets, providing 1,850 observations for each series for the period beginning May 4, 004, and ending December 30, 011. Since Poland and Hungary are geographically close, they are within one time zone. As a consequence, the trading hours for the markets are about the same. Trading at the Warsaw Stock Exchange (WIG index) starts at 9:00 a.m. and finishes at 5:40 p.m. Central European Time (CET). Budapest (BUX index) trades from 9:0 a.m. to 5:00 p.m. CET, while the New York Stock Exchange (S&P500 index) trades from 3:30 p.m. to 10:00 p.m. CET. The trading overlap between the Warsaw and New York markets (as well as the Budapest and New York markets) is approximately equal to one and one-half hours, that is, late trading in Warsaw (or Budapest) corresponds to early trading in New York (see Figure 1). To simplify the analysis we assume that the Warsaw and New York markets (as well as the Budapest and New York markets) open and close sequentially (see Koutmos and Booth [1994] for the London, New York, and Tokyo markets). It is worth stressing that the use of ultra-high-frequency data probably would be well founded, but access to the intra-day data free of charge is very difficult in the case of the CEE markets. Therefore, to avoid this problem, we compute daily close-to-close, close-to-open, and open-to-close logarithmic returns for the three stock indexes. Following Hamao et al. (1990), we divide daily close-to-close (C C) logarithmic returns into their close-to-open (C O) and open-to-close (O C) components. Assuming that a daily close-to-close logarithmic return is equal to (C = C) = ln(c t /C t 1 ), a daily close-to-open logarithmic return is equal to (C O) = ln(o t /C t 1 ), and a daily open-to-close logarithmic return is equal to (O C) = ln(c t /O t ). We consequently obtain a daily close-to-close logarithmic return that can be expressed as Ot Ct Ot Ct Ct ln ln ln ln, C O C O C ( C C) = ( C O) + ( O C) = + = = t 1 t t 1 t t 1 where C t and C t 1 are the closing prices of days t and t 1, respectively, and O t is an opening price of day t. Table 1 reports summarized statistics for the close-to-close, close-to-open, and opento-close logarithmic returns for three stock indexes: S&P500, WIG, and BUX, as well as statistics testing for normality and interdependence. The sample means are not statistically different from zero. The measures for skewness and excess kurtosis show that all return series are negatively skewed and highly leptokurtic with respect to the normal distribution. Likewise, the Doornik Hansen (008) test rejects normality for each of the return series at the 5 percent level of significance. The Ljung Box (1978) statistic at the lag (1)

5 March April 013, Volume 49, Supplement 149 Table 1. Summarized statistics for the close-to-close, close-to-open, and open-to-close logarithmic returns for three stock indexes: S&P500, WIG, and BUX Number of observations Mean Standard deviation Skewness Excess kurtosis Doornik Hansen test LB(8) LB (8) S&P C C 1, * 9.63* 1,81.3* (0.0) S&P C O 1, * 1.6*,498.6* (0.0) S&P O C 1, * 9.55* 1,756.31* (0.0) WIG C C 1, * 3.18* 3,9.8* ( 10 7 ) WIG C O 1, * 6.85* 84.98* ( ) WIG O C 1, * 3.37* * ( ) BUX C C 1, * 5.89* * ( ) BUX C O 1, * 1.13*,409.73* (0.0) BUX O C 1, * 3.98* * ( ) 48.18* 1,395.8* 41.67* 44.1* 47.35* 1,394.57* 3.8* 57.01* 50.78* 93.64* * 58.44* 1,096.63* 74.10* 1,678.09* 3.6* * Source: Author s calculations (based on Gretl 1.9.7). Notes: The table is based on all sample observations during the period May 1, 004 December 31, 011. C C, C O, and O C stand for close-to-close, close-to-open, and open-to-close logarithmic returns for the three stock indexes (S&P500, WIG, BUX), respectively. The test statistic for skewness and excess kurtosis is the conventional t statistic. The Doornik Hansen (008) test has a χ distribution if the null hypothesis of normality is true. Numbers in parentheses are p values. LB(q) and LB (q) are the Ljung Box (1978) statistics for returns and squared returns, respectively, distributed as χ (q), q lnt, where T is the number of data points. The χ (8) critical value is (5 percent). * Significance at the 5 percent level.

6 150 Emerging Markets Finance & Trade q lnt, where T is the number of data points (Tsay 010), calculated for both the return and the squared return series, indicates the presence of significant linear and nonlinear dependencies, respectively, except for the WIG O C series. The linear dependences may be due to the nonsynchronous trading effect I of the stocks that make up each index (see, e.g., Campbell et al. 1997; Lo and MacKinlay 1990). The nonlinear dependencies may be due to the autoregressive conditional heteroskedasticity (see, e.g., Booth et al. 1997; Koutmos and Booth 1995; Nelson 1991). Model Specification Most of the research on the interdependence and interaction of stock markets has focused on both conditional first and second moments. Some previous publications describe applications of univariate GARCH models. For example, Hamao et al. (1990) examine price spillovers (i.e., first-moment interdependencies) and volatility spillovers (i.e., second-moment interdependences) in the three major stock markets using the GARCH M (GARCH-in-mean) models. The use of a multivariate ARCH specification to model the conditional mean and volatility of stock prices is still not as widespread as the use of conventional univariate models (Égert and Koc=enda 011). Martens and Poon (001) stress that in the light of the existing literature, a multivariate GARCH approach is the only correct platform for studying the transmission mechanism between capital markets. Bauwens et al. (006) point out that a multivariate modeling framework leads to more relevant empirical models than separate univariate models do. Scheicher (001) models both returns and volatility of the national stock indexes of Hungary, Poland, and the Czech Republic during using a multivariate GARCH with a constant conditional correlation, but, as a matter of fact, the assumption of constant conditional correlation is unrealistic. Several studies find that the correlations are time-varying. For example, Li and Majerowska (008) use a multivariate asymmetric GARCH with time-varying variance-covariance, that is, the GARCH-BEKK model. They examine the cross-market volatility spillover effects from some developed markets to the emerging Polish and Hungarian markets. More recently, Büttner and Hayo (010) employed dynamic conditional correlation multivariate GARCH (DCC-MGARCH) models (Engle 00) to investigate conditional correlations between the three biggest Central and Eastern European Countries (CEEC-3) (i.e. Poland, Czech Republic, and Hungary) markets, in the period from 004 to 006. Since Nelson (1991) introduced the univariate exponential generalized autoregressive conditionally heteroskedastic model, some papers employ this model to capture the asymmetric effect of innovations on volatility. While the GARCH model is useful for capturing mild serial correlation and high kurtosis documented for daily stock returns, the multivariate EGARCH model is ideally suited to test the possibility of asymmetries in the volatility transmission mechanism because it allows innovations in the domestic and cross markets to exert an asymmetric impact on the volatility in a given market. In other words, news generated in one market is evaluated in terms of both size and sign by the next market to trade (Koutmos and Booth 1995). This advantage of the EGARCH model is particularly important in the case of international stock markets in countries located in different time zones. Nelson (1991) points out that researchers beginning with Fischer Black found evidence that stock returns are negatively correlated with changes in returns volatility, that is, volatility tends to rise in response to bad news (excess returns lower than expected) and to fall in response to good news (excess returns higher than expected). The impact of good news (market advances) and bad news

7 March April 013, Volume 49, Supplement 151 (market retreats) can be well described by a multivariate EGARCH model (Booth et al. 1997). Koutmos and Booth (1995) investigate the transmission mechanism of price and volatility spillovers across the New York, Tokyo, and London stock markets, which are in three different time zones, using the EGARCH approach. Jane and Ding (009) propose a multivariate extension of Nelson s univariate EGARCH model and compare their model with the existing one given by Koutmos and Booth (1995). Booth et al. (1997) provide evidence on price and volatility spillovers among four Scandinavian (Nordic) stock markets. Since Scandinavian countries are geographically close, they are within one time zone. Tse et al. (003) employ a bivariate EGARCH model that allows for both mean and variance spillovers between the U.S. and Polish stock markets. It is worthwhile to note that the estimation of the multivariate EGARCH model is particularly difficult due to large numbers of estimated parameters. Carvalhal and Vaz de Melo Mendes (008) stress that the EGARCH model is suitable for longer periods. The multivariate time series {R t } can be expressed as R t = μ t + ε t, () where μ t = E(R t F t 1 ) is the conditional expectation of R t given the past information F t 1, and e t is the innovation of the series at time t (Tsay 010). Process R t is assumed to be a multivariate time series such as a vector autoregressive moving average (VARMA) model with conditional expectation μ t. The μ t is presented as μ t = φ 0 + S p i=1φ i R t i S p j=1ψ j ε t j, (3) where p and q are nonnegative integers, φ 0 is a k dimensional vector of intercepts, and Φ i and Ψ j are the k k matrices of constant parameters (Jane and Ding 009). The conditional covariance matrix of ε t in Equation () given F t 1 is a k k positive-definite matrix H t = Cov(e t F t 1 ). Nelson s (1991) univariate EGARCH(p, q) model can be extended to the multivariate version as follows (Jane and Ding 009): q 1 I β B βq B 1 1 ln ( σt )= α Gz, p ( t 1) I α B a B 1 p (4) ε t = H t 1/ z t, ε t F t 1 ~ N k (0, H t ), z t ~ N k (0, I), G(z t ) = θ z t + g [ z t E( z t )]. In Equation (4), ln(σ t ) represents a vector of univariate ln(σ i,t), i = 1,..., k, α 0 is a vector of constants, α j and β l are k k diagonal matrices for j = 1,..., p, l = 1,...,(q 1), I is an identity matrix, and z t is a vector of z i,t, i = 1,..., k. In Equation (5), G(z t ) is a k dimensional random sequence, which is a function of both the magnitude and sign of z t, and θ and γ are k k parameter matrices. Since EGARCH(p, q) = EGARCH(1, 1) is a general setup, Equation (4) becomes (I α 1 B) ln (σ t ) = (I α1 B)α 0 + IG(z t 1 ). (6) Equation (6) can be rewritten using the matrix representation and then ln (s i, t) = a * i, 0 + a i, i ln(s i, t 1) + g i (z t 1 ), (7) where a * i,0 = (1 a i, i ) a i, 0, i = 1,,..., k. (5)

8 15 Emerging Markets Finance & Trade In a similar way, Equation (5) can be rewritten using the summation notation: { } = ( ) = k + ( ) j= 1 gi zt θ z ij jt ij zjt E z,, γ, jt i j k,,,, 1,,...,. To accommodate the asymmetric relationship between stock returns and volatility changes, the value of g i (z t ) must be a function of both the magnitude and the sign of z t (Nelson 1991). Asymmetric effects of standardized innovations on volatility may be measured by partial derivatives for g i (z t ) as follows (Jane and Ding 009): g ( z ) i z t jt, θ = θ + γ, if z > 0 γ, if z < 0, i, j = 1,,..., k. ij, ij, jt, ij, ij, jt, The terms q i,j z j,t and g i,j [ z j,t E( z j,t )] in Equation (8) measure the sign and size effects, respectively. Relative asymmetry may be measured by the ratio q i, j g i, j / (q i, j + g i, j ). That is, (1) q i, j g i, j / (q i, j + g i, j ) > 1 for negative asymmetry; () q i, j g i, j / (q i, j + g i, j ) = 1 for symmetry; and (3) q i, j g i, j / (q i, j + g i, j ) < 1 for positive asymmetry. The total impact of spillover effects from market j to market i is measured by (q i, j + g i, j ), i j, for a unit increment of positive innovation, and by (q i, j g i, j ), i j, for a unit increment of negative innovation. The conditional covariance s i, j, t of e i, t and e j, t, given F t 1, can be denoted as s i, j, t = r i, j s i, t s j, t, for i, j = 1,,..., k, i j, (10) where r i, j is the constant conditional correlation between e i, t and e j, t, given F t 1. This quite strong assumption, suggested in Bollerslev (1990), significantly reduces the number of parameters to be estimated. Its validity should be assessed empirically. According to the assumption of constant conditional correlations, all variations over time in the conditional covariances are due to changes on each of the corresponding two conditional variances. To test for constant conditional correlations, one may use, for example, the method given by Bollerslev (1990). Let R i, t = 100 ln(c i, t /O i, t ) be the open-to-close percentage logarithmic return at time t for market i (i = 1,, 3, where 1 = New York, = Warsaw, and 3 = Budapest). Then the modified version of the multivariate EGARCH model used to describe price and volatility spillovers across the three markets may be written as follows: R 1, t = j 1,0 + j 1,1 R 1, t 1 + j 1, R, t + j 1,3 R 3, t + e 1, t, R, t = j,0 + j,1 R 1, t 1 + j, R, t 1 + j,3 R 3, t 1 + e, t, (11) R 3, t = j 3,0 + j 3,1 R 1, t 1 + j 3, R, t 1 + j 3,3 R 3, t 1 + e 3, t. ln ( )= + ( )+ + * σ1, t α10, α11ln σ1t 1 θ z t γ z t E z,, 11, 1, 1 11, 1, 1 1, t 1 { } 3 + θ jzj t + j zjt E( z jt ) 1,, γ1,,,, j= ( σ *, t )= 0,,, t 1 g zt 1 ln α α ln σ, * ln( σ3, t)= α30, + α33, ln( σ3, t 1)+ g3( z t 1). + ( )+ ( ) ( ) Note that on a given day t, because the Polish and Hungarian markets open before the U.S. market, daytime innovations from the Polish and Hungarian markets would have (8) (9) (1)

9 March April 013, Volume 49, Supplement 153 a spillover effect on the U.S. market on the same day, and daytime innovations from the U.S. market would have a spillover effect on the Polish and Hungarian markets on the next day (see Equations (11) and (1)). To obtain parameter estimates by using the maximum likelihood method, we need the joint log-likelihood function under the distributional assumptions made previously. The log-likelihood function for the multivariate EGARCH model can be written as 1 1 T 1 L( Θ) = kt ln( π) ( ln Ht + εt H t εt), (13) where k is the number of dimensions, T is the number of observations, and Θ is the parameter vector to be estimated. t= 1 Empirical Results and Discussion Table reports the estimation results of the modified multivariate constant conditional correlation exponential AR(1)-CCC-EGARCH(1, 1) models (11) and (1) in the case of each of the major indexes of the three stock markets under study: New York (S&P500 index), Warsaw (WIG index), and Budapest (BUX index). Several results in Table are worth special notice. For one thing, all of the estimated conditional correlation coefficients are statistically significant. Moreover, Bollerslev (1990) indicates that the validity of the assumption of constant conditional correlations can be assessed by testing for serial correlation in the cross products of standardized residuals. Under the assumption of constant conditional correlations, the cross products of standardized residuals should be serially uncorrelated. As reported in Table, this suggested condition is met, except for the cross product of the standardized residuals z 1, t z 3, t (New York and Budapest). Simulation studies suggest that the choice of the lag q ln T, where T is the number of data points, provides good power performance (Tsay 010). The estimated Ljung Box statistics for standardized and squared standardized residuals show that the EGARCH model successfully accounts for all linear and nonlinear dependencies present in the return series (except LB (8) for New York, which is slightly higher than the critical value at the 5 percent level). Table provides evidence that the autoregressive coefficients j i, i are statistically significant, except the j 3, 3 for the Budapest market. The conditional variance is a function of past conditional variances and past innovations. The relevant coefficients a i, i, q i, i, and g i, i are statistically significant (except the a, for the Warsaw market). In addition, all of the g i, i coefficients are positive. For positive g i, i, if 1 < d i = (q i, i /g i, i ) < 0, then negative innovations have a higher impact than positive innovations on the volatility; if d i = 0, then the volatility increase resulting from positive innovations is smaller than the increase resulting from negative innovations; if 0 < d i < 1, then positive innovations can decrease volatility but negative innovations increase volatility (Jane and Ding 009). These asymmetry effects are present in Table. The degree of asymmetry is comparable in all markets. Our findings suggest that the three stock markets are more sensitive to bad than good news. Numerically, bad news for New York, Warsaw, and Budapest has 1.8, 1.3, and 1.10 times the impact of good news, respectively. In contrast to previous findings of an absence of asymmetric effects in Eastern Europe (see Scheicher 001), this study finds that a leverage effect is observed. However, our findings are consistent with those of Li and Majerowska (008).

10 154 Emerging Markets Finance & Trade Table. The modified multivariate AR(1)-CCC-EGARCH(1, 1) models (11) and (1), price and volatility spillovers (1,850 daily open-to-close percentage logarithmic returns) New York (i = 1) Warsaw (i = ) Budapest (i = 3) Price spillover parameters j i, * (0.000) j i,1 (New York) 0.14* (0.08) j i, (Warsaw) 0.036* (0.01) j i,3 (Budapest) 0.09* (0.017) Volatility spillover parameters a * i,0 0.94* (0.09) a i,i 0.418* (0.058) q i,1 (New York) 0.047* (0.001) q i, (Warsaw) 0.098* (0.041) q i,3 (Budapest) 0.05 (0.040) g i,1 (New York) 0.386* (0.035) g i, (Warsaw) (0.015) g i,3 (Budapest) (0.03) 0.043* (0.000) 0.051* (0.01) 0.003* (0.000) (0.015) 0.051* (0.000) 0.091* (0.06) 0.03* (0.009) (0.005) 0.13* (0.033) 0.604* (0.000) * (0.051) (0.000) (0.04) (0.057) 0.019* 0.100* (0.001) (0.049) * (0.046) (0.001) (0.040) (0.059) 0.179* (0.04) (0.07) * (0.04) (0.039) d i = q i,i /g i,i Relative asymmetry for market i q i,i g i,i /(q i,i + g i,i ) Conditional correlation r i,j between e i,t and e j,t r i, * (0.01) 0.309* (0.0) r i, * (0.016) r i,3 1 Diagnostics on standardized residuals and squared standardized residuals LB(8) LB (8) Diagnostics on cross products of the standardized residuals LB p (8) z 1,t z j,t, j > z,t z j,t, j > 9.6 Log-likelihood 17, Source: Author s calculations (using GAUSS 1, FANPAC MT 3.0). Notes: The table is based on all sample observations during the period May 4, 004 December 30, 011. The critical value of the correlation coefficient is equal to (5 percent). LB(q), LB (q), and LB p (q) are the Ljung Box (1978) statistics for standardized residuals, squared standardized residuals, and cross-standardized residuals, respectively, distributed as χ (q), q lnt, where T is the number of data points. The χ (8) critical value is (5 percent). Standard errors are in parentheses. * Significant at the 5 percent level.

11 March April 013, Volume 49, Supplement 155 Table also presents details about price and volatility spillovers. Coefficients j i, j for i j measure the extent of price spillover across markets. All but two of the relevant coefficients j i, j are statistically significant. These coefficients indicate that the U.S. prices spill over to other markets. Volatility spillovers across the markets are measured by g i, j for i j. A significant positive g i, j coupled with a negative q i, j implies that negative innovations in the market j have a higher impact on the volatility of the market i than positive innovations do, that is, the volatility spillover mechanism is asymmetric. It can be seen from Table that we do not observe such pairs of estimates for i j. Our results show no volatility spillovers between the three markets investigated, which is consistent with the results obtained by Tse et al. (003) for the U.S. and the Polish markets in the period January 1994 February 003. However, it is worthwhile to note that there is ample evidence of spillovers among the CEE markets (Poland, the Czech Republic, Hungary) and from the U.S. and European markets to the CE markets (see, e.g., Hanousek and Koc=enda 011; Hanousek et al. 009). Conclusion To summarize, based on the empirical analysis it can be concluded that the modified version of the multivariate exponential AR(1)-CCC-EGARCH(1, 1) model is quite suitable for the explanation of price and volatility spillovers across stock markets that are located in different time zones and are affected by the nonsynchronous trading effect II. We agree with Baumöhl and Výrost s (010) comment that the use of a wide range of time-series models could be questionable if the nonsynchronocities are not accounted for, especially because the current implementations of these models in most econometric software inherently assume synchronous data. Moreover, we observe the presence of pronounced negative asymmetric effects in the case of all markets in the sample period May 4, 004 December 30, 011. The results show no pronounced volatility spillover among the three analyzed markets; however, there is evidence that the U.S. prices spill over to other markets. A possible direction for further investigation would be the exploration of the linkages between markets in different time zones, such that the nonsynchronous trading effect II is an issue, using various modified multivariate GARCH models, such as the multivariate asymmetric GARCH with time-varying variance-covariance (the BEKK model proposed by Engle and Kroner 1995), the asymmetric dynamic covariance (ADC) model presented in Kroner and Ng (1998) or the dynamic conditional correlation GARCH (DCC-GARCH) model introduced by Engle (00). References Baumöhl, E., and T. Výrost Stock Market Integration: Granger Causality Testing with Respect to Nonsynchronous Trading Effects. Finance a Uver: Czech Journal of Economics and Finance 60, no. 5: Bauwens, L.; S. Laurent; and J.V.K. Rombouts Multivariate GARCH Models: A Survey. Journal of Applied Econometrics 1, no. 1: Bollerslev, T Modelling the Coherence in Short-Run Nominal Exchange Rates: A Multivariate Generalized ARCH Model. Review of Economics and Statistics 7, no. 3: Booth, G.G.; T. Martikainen; and Y. Tse Price and Volatility Spillovers in Scandinavian Stock Markets. Journal of Banking & Finance 1, no. 6: Brzeszczynski, J., and A. Welfe Are There Benefits from Trading Strategy Based on the Returns Spillovers to the Emerging Stock Markets? Evidence from Poland. Emerging Markets Finance & Trade 43, no. 4 (July August): 74 9.

12 156 Emerging Markets Finance & Trade Brzeszczynski, J.; J. Gajdka; and T. Schabek The Role of Stock Size and Trading Intensity in the Magnitude of the Interval Effect in Beta Estimation: Empirical Evidence from the Polish Capital Market. Emerging Markets Finance & Trade 47, no. 1 (January February): Büttner, D., and B. Hayo News and Correlations of CEEC-3 Financial Markets. Economic Modelling 7, no. 5: EMU-Related News and Financial Markets in the Czech Republic, Hungary and Poland. Applied Economics 44, no. 31: Campbell, J.Y.; A.W. Lo; and A.C. MacKinlay The Econometrics of Financial Markets. Princeton: Princeton University Press. Carvalhal, A., and B. Vaz de Melo Mendes Evaluating the Forecast Accuracy of Emerging Market Stock Returns. Emerging Markets Finance & Trade 44, no. 1 (January February): Cohen, K.J.; G.A. Hawawini; S.F. Maier; R.A. Schwartz; and D.K. Whitcomb Implications of Microstructure Theory for Empirical Research on Stock Price Behaviour. Journal of Finance 35, no. : Dimson, E Risk Measurement When Shares Are Subject to Infrequent Trading. Journal of Financial Economics 7, no. : Doornik, J.A., and H. Hansen An Omnibus Test for Univariate and Multivariate Normality. Oxford Bulletin of Economics and Statistics 70, supp. 1: Drakos, K., and A.M. Kutan Why Do Financial Markets Move Together? Eastern European Economics 43, no. 4 (July August): 5 6. Égert, B., and E. Koc=enda Interdependence Between Eastern and Western European Stock Markets: Evidence from Intraday Data. Economic Systems 31, no. : Time-Varying Synchronization of European Stock Markets. Empirical Economics 40, no. : Engle, R.F. 00. Dynamic Conditional Correlation: A Simple Class of Multivariate GARCH Models. Journal of Business and Economic Statistics 0, no. 3: Engle, R.F., and K.F. Kroner Multivariate Simultaneous Generalized ARCH. Economic Theory 11, no. 1: Eun, C.S., and S. Shim International Transmission of Stock Market Movements. Journal of Financial and Quantitative Analysis 4, no. : Fisher, L Some New Stock Market Indexes. Journal of Business 39, no. 1: Forbes, K.J., and R. Rigobon. 00. No Contagion, Only Interdependence: Measuring Stock Market Comovements. Journal of Finance 57, no. 5: Hamao, Y.; R.W. Masulis; and V. Ng Correlations in Price Changes and Volatility Across International Stock Markets. Review of Financial Studies 3, no. : Hanousek, J., and E. Koc=enda Foreign News and Spillovers in Emerging European Stock Markets. Review of International Economics 19, no. 1: Hanousek, J.; E. Koc=enda; and A.M. Kutan The Reaction of Asset Prices to Macroeconomic Announcements in New EU Markets: Evidence from Intraday Data. Journal of Financial Stability 5, no. : Hawawini, G.A The Intertemporal Cross Price Behavior of Common Stocks: Evidence and Implications. Journal of Financial Research 3, no. : Jane, T.D., and C.G. Ding On the Multivariate EGARCH Model. Applied Economics Letters 16, no. 17: Kadlec, G.B., and D.M. Patterson A Transactions Data Analysis of Nonsynchronous Trading. Review of Financial Studies 1, no. 3: Koutmos, G., and G.G. Booth Asymmetric Volatility Transmission in International Stock Markets. Journal of International Money and Finance 14, no. 6: Kroner, K.F., and V.K. Ng Modeling Asymmetric Comovements of Asset Returns. Review of Financial Studies 11, no. 4: Li, H., and E. Majerowska Testing Stock Market Linkages for Poland and Hungary: A Multivariate GARCH Approach. Research in International Business and Finance, no. 3: Ljung, G., and G.E.P. Box On a Measure of Lack of Fit in Time Series Models. Biometrika 65, no. : 67 7.

13 March April 013, Volume 49, Supplement 157 Lo, A.W., and A.C. MacKinlay An Econometric Analysis of Nonsynchronous Trading. Journal of Econometrics 45, nos. 1 : Martens, M., and S.H. Poon Returns Synchronization and Daily Correlation Dynamics Between International Stock Markets. Journal of Banking and Finance 5, no. 10: Masih, R., and A.M.M. Masih Long and Short Term Dynamic Causal Transmission Amongst International Stock Markets. Journal of International Money and Finance 0, no. 4: Nelson, D.B Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica 59, no. : Olbrys, J The Intertemporal Cross Price Behavior and the Fisher Effect on the Warsaw Stock Exchange. Ekonometria 31: Theory and Applications of Quantitative Methods, Prace Naukowe UE we Wrocławiu 194: Perry, P.R Portfolio Serial Correlation and Nonsynchronous Trading. Journal of Financial and Quantitative Analysis 0, no. 4: Scheicher, M The Comovements of Stock Markets in Hungary, Poland and the Czech Republic. International Journal of Finance and Economics 6, no. 1: Scholes, M., and J. Williams Estimating Betas from Nonsynchronous Data. Journal of Financial Economics 5, no. 3: Tsay, R.S Analysis of Financial Time Series. New York: Wiley. Tse, Y.; C. Wu; and A. Young Asymmetric Information Transmission Between a Transition Economy and the U.S. Market: Evidence from the Warsaw Stock Exchange. Global Finance Journal 14, no. 3: To order reprints, call ; outside the United States, call

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