An empirical examination of international diversification benefits in Central European emerging equity markets.I. INTRODUCTION International portfolio diversification was started in with the decision of Morgan Guaranty As a verb, to agree to be responsible for the payment of another's debt or the performance of another's duty, liability, or obligation if that person does not perform as he or she is legally obligated to do; to assume the responsibility of a guarantor; to warrant. in 1974 to invest a part of its pension fund outside the United-States. At that time, the US market lived two successive decreases in 1973 and 1974, but outside the United-States, the returns had been very attractive. Accordingly, the investors have become increasingly more active in foreign capital markets. The investment in international financial market knows a spectacular increase. Recently, as a consequence of market liberalisation, financial markets tended to become more integrated. This integration process implies the increase of correlation between financial markets which can have negative effects on benefits from international diversification International diversification The attempt to reduce risk by investing in more than one nation. By diversifying across nations whose economic cycles are not perfectly correlated, investors can typically reduce the variability of their returns. . This later depends on markets correlations. If the correlation coefficients between markets are higher, the gains from international diversification are low. On the other hand, if the market correlation is low the gain is very important. The higher integration between developed markets led us to study the important potential of emerging markets for international portfolio diversification. However, the financial crises especially in Asia and Latin America Latin America, the Spanish-speaking, Portuguese-speaking, and French-speaking countries (except Canada) of North America, South America, Central America, and the West Indies. emerging markets led investors to search for other emerging markets (Flight to quality phenomenon) like the Central Europe Central Europe is the region lying between the variously and vaguely defined areas of Eastern and Western Europe. In addition, Northern, Southern and Southeastern Europe may variously delimit or overlap into Central Europe. emerging markets. Those markets can provide more opportunities to increase benefits from international diversification. The endeavour to bring these economies into line with the western European economies gives them an important priority and led investors to study these investment opportunities. This study examines the possible benefits from international diversification for the seven developed countries of United-States, Canada, United-Kingdom, France, Germany, Italy, and Japan in the three important emerging equity markets of Central Europe, those of the Czech Republic Czech Republic, Czech Česká Republika (2005 est. pop. 10,241,000), republic, 29,677 sq mi (78,864 sq km), central Europe. It is bordered by Slovakia on the east, Austria on the south, Germany on the west, and Poland on the north. , Hungary and Poland. The remainder of the paper is structured as follows; Section II discusses the relevant literature. Section III presents the methodology and the data. Section IV reports our empirical results and Section V contains our conclusions. II. LITERATURE REVIEW Advantages of International portfolio diversification are inversely related to the correlations between equity markets returns. The international diversification gains decline as the correlations between securities returns become increasingly positive. However, the existence of low correlations between national markets can provide significant benefits from international diversification. Numerous researches have recognized low correlation between international capital markets and highlight the substantial international diversification gains. The early literature in this field, like for example, Grubel (1968), Levy and Sarnat (1970), and Lessard (1973) finds that low correlation between developed and emerging equity markets proves that the benefits from international diversification is considerable for investors of industrial countries in emerging markets. Other recent studies document the importance of low correlation between developed and emerging markets for generating substantial benefits from international diversification (Eun and Resnick, 1984; Errunza and Padmanabhan, 1988; Meric and Meric, 1989; Bailey and Stulz, 1990; Divecha et al., 1992; and Phylaktis et Ravazzolo, 2005). Many factors can explain the low correlations and consequently the importance of emerging markets in international portfolio diversification strategies: barriers to foreign investment flows on emerging markets in order to preserve the control of national companies; the asymmetric information Asymmetric Information Information available to some people but not others. Notes: In other words, the asymmetric information is held by only one side, meaning someone is keeping a secret. on securities in emerging markets; strong controls of exchange and the lack in free trade of emerging markets with international markets. Several authors have used the cointegration techniques to examine the existence of linkages and long term co-movements between developed and emerging markets. They examine their effects on the benefits of international diversification for investment in emerging markets. Kasa (1992) and Arshanapalli and Doukas (1993) prove an evidence of bi-variate cointegration relationship between American and European equity markets. The existence of such linkage affects negatively the benefits of international diversification for US investors in those European markets. Harvey (1995b) finds that assets in emerging markets provides for American investors high expected returns and a low level of risk. He argues that the main interest of emerging markets for a portfolio manager rests in reducing the risk, but not in the enhancement of returns. This result gives an explanation to the low correlation between emerging markets, and with the global markets in comparison with the correlations between developed markets. DeFusco et al. (1996) show the non-existence of short-term and long-term linkages between the American market and thirteen emerging equity markets in the Pacific Basin, Latin America and the Mediterranean regions. They confirm that these markets are not cointegrated between them. They conclude that this segmentation between US market and these emerging markets in these three regions indicates the possible existence of international diversification benefits in short and long term across theses markets. Bekaert and Urias (1996) reject the assumption that equity indices in developed countries span the mean-variance frontier of all international equity indices. They prove the existence of gains from international diversification in emerging equity markets. De Santis and Gerard (1997) assess, by using the international capital asset pricing model Capital asset pricing model (CAPM) An economic theory that describes the relationship between risk and expected return, and serves as a model for the pricing of risky securities. (ICAPM ICAPM Intertemporal Capital Asset Pricing Model ), that the expected gain The expected gain (or expected return) is the weighted-average most likely outcome in gambling, probability theory, economics or finance. Discrete scenarios In gambling and probability theory, there is usually a discrete set of possible outcomes. from international diversification is on average 2.11 percent yearly for an American investor. Li et al. (2003) used Bayesian inference Bayesian inference is statistical inference in which evidence or observations are used to update or to newly infer the probability that a hypothesis may be true. The name "Bayesian" comes from the frequent use of Bayes' theorem in the inference process. approach to examine the impact of short-sale constraints on the existence and the magnitude of the gains from international diversification for American investors in eight emerging equity markets of four Latin American markets (Argentina, Brazil, Chile, and Mexico) and four South-East markets (Hong Kong Hong Kong (hŏng kŏng), Mandarin Xianggang, special administrative region of China, formerly a British crown colony (2005 est. pop. 6,899,000), land area 422 sq mi (1,092 sq km), adjacent to Guangdong prov. , South Korea, Singapore, and Thailand). They show that the benefits of international diversification remain substantial for American investors after imposing short-sale constraints on emerging equity markets but not after imposing short-sale constraints on G7 developed equity markets. The authors conclude that the integration of world equity markets reduces, but does not eliminate, the benefits of international diversification in emerging equity markets subject to short-sale constraints. These results reinforce the "home bias puzzle" with respect to investments in emerging markets. Gilmore and McManus (2005) examine the diversification benefits for American investors in the emerging equity markets of Central Europe (Czech Republic, Hungary and Poland). They conclude that American investors can get a higher level of returns from diversifying their portfolio in Central European equity markets since there are not short-term and long-term linkages between theses markets and US market. Lagoarde and Lucey (2006) investigate the presence of international portfolio diversification benefits in the most important equity markets of the Middle East and North Africa (MENA) region. Their results show the presence of higher potential of international diversification benefits in this region, whether transaction are denominated in local currencies or in U.S dollars. Furthermore, the portfolio with minimum variance appears as the most promising optimization technique. In addition, portfolios based on local currencies seem to exhibit a higher degree of diversification, while the measure of risk seems to affect profitability less than the optimization model employed. Overall, they show that these under-estimated and under-investigated markets of MENA region should attract more portfolio flows in the future. Despite the existence of numerous studies about capital market integration between developed and emerging equity markets and their effects on the gains from international diversification, a little attention is given to the investment possibility in Central European equity markets. These markets were isolated under the communist regime for a long period from external influences until the 1990s, date of their reemergence on international financial arena. The increasing economic growth of these equity markets and their attempt to open their financial markets to foreign investment led us to spare them a particular attention. This research explores the issue of investment opportunities and the possible benefits from international diversification for seven industrial countries in the three main major Central European equity markets of Czech-Republic, Hungary and Poland; we use the recent development of cointegration theory. III. METHODOLOGY AND DATA A. Methodology We use the cointegration approach in order to study first the interdependence relationship between developed markets, and Central European emerging equity markets, and then, to examine the issue of likely benefits of international diversification in this region. The latter allows us to detect a long run co-movement between index series. This co-movement implies the integration between national markets which affect negatively the diversification benefits. The cointegration test examines the stationary of equity index series. In this way, all series must be non-stationary and integrated of the same order: it is a necessary condition for doing a cointegration analysis. Therefore, we use the Augmented Dickey Fuller (ADF (1) (Application Development Facility) An IBM programmer-oriented mainframe application generator that runs under IMS. (2) (Automatic Document Feeder) A paper stacker that feeds one sheet of paper at a time into the unit. ) and Phillips-Perron (PP) test. Appropriate lag lengths of vector autoregression Vector autoregression (VAR) is an econometric model used to capture the evolution and the interdependencies between multiple time series, generalizing the univariate AR models. used to determine the maximal order of integration were selected according to according to prep. 1. As stated or indicated by; on the authority of: according to historians. 2. In keeping with: according to instructions. 3. the Akaike Information Criterion Akaike's information criterion, developed by Hirotsugu Akaike under the name of "an information criterion" (AIC) in 1971 and proposed in Akaike (1974), is a measure of the goodness of fit of an estimated statistical model. It is grounded in the concept of entropy. (AIC) and Schwarz Criterion (SC). In order to determine whether the time series are cointegrated we resort to the Johansen test (1988). The latter allows us to know the number of cointegrated vector of the index series. The existence of long run relationship between series leads to the study of short run relationship by the VECM model. Finally, the Granger causality Granger causality is a technique for determining whether one time series is useful in forecasting another. Ordinarily, regressions reflect "mere" correlations, but Clive Granger, who won a Nobel Prize in Economics, argued that there is an interpretation of a set of tests as test (1969) is used to identify the causality causality, in philosophy, the relationship between cause and effect. A distinction is often made between a cause that produces something new (e.g., a moth from a caterpillar) and one that produces a change in an existing substance (e.g. sense between index series. B. Data The data used in this study consist of daily price indices time series for three Central European emerging stock markets (Czech-Republic, Hungary and Poland), and seven developed stock markets (United-States, Canada, United-Kingdom, France, Germany, Italy, and Japan). The time period covers October 1, 2000, until September Until September is a 1984 romantic drama set in France. It stars Karen Allen as an American tourist in Paris who falls in love with a married Frenchman (Thierry Lhermitte). External links 30, 2006, which gives a total of 1565 observations for each market. Indices were obtained from the Morgan Stanley Capital International Morgan Stanley Capital International (MSCI) This firm publishes a number of well known benchmarks, such as the MSCI World Index. Data Base (MSCIDB (1)) and all the index series are in US dollars terms. We use stock prices in US dollars in order to eliminate the problem of exchange rate variations (especially between developed and emerging markets). IV. EMPIRICAL RESULTS A. Descriptive statistics descriptive statistics see statistics. Table 1 provides the descriptive statistics for daily stock returns of markets examined in this study: United-States, Canada, United-Kingdom, France, Germany, Italy, Japan, Czech-Republic, Hungary, and Poland. The Czech Republic stock index shows the higher average returns (0, 001472) than all other markets (the US market shows the low average returns (-0, 000173)). The maximum return varys between (0, 038562) in Canada stock market and (0, 08372) in the Hungarian market. The minimum return fluctuate between (-0, 08963) in the Canadian market to (-0, 05017) in the US. The German stock index shows the higher level of risk measured by the standard deviation (0, 016138), followed by Poland stock index for the emerging markets (0, 015985). The markets of Canada, United-Kingdom and United-States show the low level of risk (respectively: (0, 012472), (0, 012528) and (0, 012807)). The Kurtosis Kurtosis A statistical measure used to describe the distribution of observed data around the mean. Notes: Used generally in the statistical field, it describes trends in charts. and Skewness Skewness A statistical term used to describe a situation's asymmetry in relation to a normal distribution. Notes: A positive skew describes a distribution favoring the right tail, whereas a negative skew describes a distribution favoring the left tail. statistics indicate that index returns series are leptokurtic and have an asymmetric distribution that rejects significantly the null hypothesis null hypothesis, n theoretical assumption that a given therapy will have results not statistically different from another treatment. null hypothesis, n of normality for all the index returns series. B. Correlation Coefficients between Equity Return Series Table 2 reports the correlation coefficients between equity return series of developed and emerging equity markets for daily frequencies. The results show positive and higher correlation coefficients between developed markets. The higher correlation is noted between France and United-Kingdom markets (89, 84%) followed by the pair of Germany-France (88, 221%). The low correlation level is between Japan and Germany (12, 021%). We find low correlation coefficients between emerging and developed equity markets. They vary from (10, 126%) between US and Czech Republic market to (38, 681%) between Hungary and Czech Republic market. The correlation coefficients indicate that developed markets are more integrated between them, but they are segmented with the emerging equity markets of Central Europe in the short-term. This result shows that there are still some diversification benefits from investment in emerging equity markets of Central Europe in the short run. We investigate further through cointegration techniques whether theses short-term dependences are appropriate indicators for international diversification benefits in the long-term investment in Central European emerging equity markets. C. Unit Roots Tests for Stock Prices Unit root tests developed by Phillips (19874), Perron Per´ron n. 1. (Arch.) An out-of-door flight of steps, as in a garden, leading to a terrace or to an upper story; - usually applied to mediævel or later structures of some architectural pretensions. (19885) and augmented by Dickey-Fuller (1981) (Extension of Dickey and Fuller, 19796) are used for examining the time series stationary. The presence of unit root in time series of stock prices indicates that series are non-stationary 1. Augmented Dickey-Fuller (ADF) Tests Under alternative hypothesis alternative hypothesis Epidemiology A hypothesis to be adopted if a null hypothesis proves implausible, where exposure is linked to disease. See Hypothesis testing. Cf Null hypothesis. [absolute value of [[phi].sub.1]] [??] 1, augmented Dickey-Fuller (ADF) tests are based on estimation by ordinary least-squares OLS OLS Ordinary Least Squares OLS Online Library System OLS Ottawa Linux Symposium OLS Operation Lifeline Sudan OLS Operational Linescan System OLS Online Service OLS Organizational Leadership and Supervision OLS On Line Support OLS Online System regression of the three following models. -Model 1 Standard (7): [DELTA][Y.sub.t] = [rho][Y.sub.t-1] - [p.summation over(j=2)][[phi].sub.j][DELTA][Y.sub.t-j+1] + [[epsilon].sub.t] -Model 2 with intercept (8): [DELTA][Y.sub.t] = [rho][Y.sub.t-1] - [p.summation over(j=2)][[phi].sub.j][DELTA][Y.sub.t- j+1] + c + [[epsilon].sub.t] -Model 3 with intercept and trend (9): [DELTA][Y.sub.t] = [rho][Y.sub.t-1] - [p.summation over(j=2)][[phi].sub.j][DELTA][Y.sub.t-j+1] + c + bt + [[epsilon].sub.t] 2. The Phillips-Perron (PP) Test The Augmented Dickey Fuller (ADF) test assumes that errors are statistically independent and have a constant variance. To overcome this limitation, Phillips and Perron (1988) developed an alternative test which represents a generalization of the Dickey-Fuller test In statistics, the Dickey-Fuller test tests whether a unit root is present in an autoregressive model. It is named after the statisticians D. A. Dickey and W. A. Fuller, who developed the test in the 1970s. Explanation A simple AR(1) model is . The advantage of Phillips-Perron test consists of allowing the error disturbances to be weakly dependent and heterogeneously distributed. The Phillips-Perron (1988) model is as follows: [Y.sub.t] = [[alpha].sub.0] + [[alpha].sub.1] [Y.sub.t-1] + [[alpha].sub.2](t - T/2) + [[mu].sub.t] Where T is the observations number and the disturbance term [[mu].sub.t] is such that E([[mu].sub.t]) = 0. The ordinary least squares method least squares method Statistical method for finding a line or curve—the line of best fit—that best represents a correspondence between two measured quantities (e.g., height and weight of a group of college students). is used to estimate the equation. The t-statistic of the [[alpha].sub.1] coefficient is corrected for serial correlation in [[mu].sub.t] using the Newey-West (10) procedure for adjusting the standard errors. The results for the ADF and PP unit root tests applied to the levels and first differences of each series of daily price indices (available on request). For the series in level, the null hypothesis of a unit root cannot be rejected at the tree confidence level. On the other hand, the series in first difference reject the null hypothesis of unit root. This result indicates that all the series of daily price indices is stationary in first difference and consequently they follow I(1) processes (integrated of order one, I(1)). D. Johansen Cointegration Test The Johansen 1988 method relies on the relationship between the rank of a matrix and its characteristic roots (or eigenvalues eigenvalues statistical term meaning latent root. ). Let [X.sub.t] be a vector of n time series variables, each of which is integrated of order (1) and assume that [X.sub.t] can be modelled by a vector autoregression (VAR): [X.sub.t] = [A.sub.1][X.sub.t-1] + .... + [A.sub.p] [X.sub.t-p] + [[epsilon].sub.t] (1) Rewrite the VAR as: [[DELTA][X.sub.t] = [PI][X.sub.t-1][summation][GAMMA][DELTA][X.sub.t-1] + [[epsilon].sub.t] (2) where [PI] = [summation][A.sub.i] - I, [[GAMMA].sub.i] = - [summation][A.sub.i]. If the coefficient matrix In linear algebra, the coefficient matrix refers to a matrix consisting of the coefficients of the variables in a set of linear equations. Example In general, a system with m linear equations and n unknowns can be written as * First, if [PI] is of full rank, all elements of X are stationary and none of the series has a unit root. * Second, if the rank of [PI] = 0, there are no combinations which are stationary and there are no cointegrating vectors. * Third, if the rank of [PI] is r such that 0 [??] r [??] k, then the X variables are cointegrated and there exist r cointegrating vectors. Eq. (1) can be modified to allow for an intercept and a linear trend. The number of distinct cointegrating vectors can be obtained by determining the significance of the characteristic roots of [PI]. To identify the number of characteristic roots that are not different from unity, we use two statistics: the trace test and the maximum eigenvalue eigenvalue In mathematical analysis, one of a set of discrete values of a parameter, k, in an equation of the form Lx = kx. Such characteristic equations are particularly useful in solving differential equations, integral equations, and systems of test given by: [[lambda].sub.trace](r) = - T[summation]ln(1 - [[lambda].sub.i]) (3) [[lambda].sub.max] (r, r + 1) = - Tln(1 - [[lambda].sub.r+1]) (4) where [[lambda].sub.i] equals the estimated values of the characteristic roots (eigenvalues) obtained from the estimated [PI] matrix, r is the number of cointegrating vectors, and T is the number of usable observations. The trace test evaluates the null hypothesis that the number of distinct cointegrating vectors is less than or equal to r against a general alternative. The maximum eigenvalue test examines the number of cointegrating vectors. If the variables in [X.sub.t] are not cointegrated, the rank of [PI] is equal to zero and all the characteristic roots are equal to zero. Given that ln(1)=0, each of the expressions ln(1 - [[lambda].sub.i]) will equal zero in that case. Critical values for the test are provided by Johansen and Juselius (1990) (11) and by Osterwald-Lenum (1992) (12). We use the Johansen (1988) cointegration test to investigate the existence of long-run relationship between developed equity markets and Central European emerging equity markets. The lag structures of vector autoregression model were chosen according to the Akaike Information Criterion (AIC) and Schwarz Criterion (SC). A multilateral Johansen test was applied to the Central European equity markets as a group. Our results (available on request) table 4 indicate no evidence for a multilateral cointegration relationship between these markets. This reveals the absence of long-run stable equilibrium (Mech.) the kind of equilibrium of a body so placed that if disturbed it returns to its former position, as in the case when the center of gravity is below the point or axis of support; - opposed to The Johansen bivariate bi·var·i·ate adj. Mathematics Having two variables: bivariate binomial distribution. Adj. 1. cointegration tests between emerging markets (of central Europe) and the G7 developed markets (available on request), show the absence of bilateral cointegration relationship between the groups of those markets. This result implies the segmentation of this emerging European market with developed markets. These conclusions confirm the results in Gilmore and McManus (2002) (for the Emerging markets of central Europe). They report the segmentation of this group of markets especially with the US market. Hence, US investors with longer-term investment horizons can benefit from diversifying into the Central European equity markets. These results can be explained first by the recent emergence of these markets (on international financial arena) after their liberation from the communist regime in the 1990. Second, they can be explained by the weak of economic and financial relationship between the economy of this country as a group and with the economy of developed country. Other factors can explain the segmentation between developed and the emerging markets of central Europe. First, emerging markets of central Europe opened their economy under some conditions, which are very different from those of the United States United States, officially United States of America, republic (2005 est. pop. 295,734,000), 3,539,227 sq mi (9,166,598 sq km), North America. The United States is the world's third largest country in population and the fourth largest country in area. and Western Europe Western Europe The countries of western Europe, especially those that are allied with the United States and Canada in the North Atlantic Treaty Organization (established 1949 and usually known as NATO). . This period has been characterised by the transition from planned economies to market economies and by extensive waves of privatization privatization: see nationalization. privatization Transfer of government services or assets to the private sector. State-owned assets may be sold to private owners, or statutory restrictions on competition between privately and publicly owned of state-owned companies. Each central European country has tried to liberalize lib·er·al·ize v. lib·er·al·ized, lib·er·al·iz·ing, lib·er·al·iz·es v.tr. To make liberal or more liberal: "Our standards of private conduct have been greatly liberalized . . . their economy and opened their frontier to international capital flows to attract global investors but they are not yet fully integrated into the international economy. So, it is not surprising that their equity markets would not provide evidence of long-term co-movements with the G7 developed market. V. CONCLUSION This paper examines the relationship between the G7 developed capital markets and the emerging markets of Central Europe. Bivariate and multivariate cointegration techniques (Johansen cointegration test (1988)) are used in our analysis. Central European markets started a process of liberalisation of their economies in the beginning of the 1990, to start their integration of European Union. This liberalisation process allows these countries to attract foreign investors and to increase the international capital flows to these markets. The results of cointegration tests showed that the emerging markets of central Europe are segmented as a group and are segmented with the G7 developed markets. The results of our tests reveal that emerging markets can provide substantial gains from international diversification especially for the investors of industrialised Adj. 1. industrialised - made industrial; converted to industrialism; "industrialized areas" industrialized industrial - having highly developed industries; "the industrial revolution"; "an industrial nation" countries. We are extending these tests to other countries. REFERENCES Arshanapalli, B., and J. Doukas, 1993, "International Stock Market Linkages: Evidence from the Pre- and Post-October 1987 Period", Journal of Banking and Finance, 17, 193-208. Bailey, W., and R.M. Stulz, 1990, "Benefits of International Diversification: the Case of Pacific Basin Stock Markets", Journal of Portfolio Management, 16, 57-61. Bekaert, G., and M.S. Urias, 1996, "Diversification, Integration, and Emerging Market Closed-end Funds", Journal of Finance, 51, 835-870. De Santis, G., and B. 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Sarnat, 1970, "International Diversification in Investment Portfolios", American Economic Review, 60, 668- 675. Li, K., A. Sarkar Sarkar could mean:
Meric, I., and G. Meric, 1989, "Potential Gains from International Portfolio Diversification and Inter-temporal Stability and Seasonality in International Stock Market Relationships", Journal of Banking and Finance, 13, 627-640. Philips, P.C., and P. Perron, 1988, "Testing for a Unit Root in Time Series Regression", Biometrika, 57, 335-346. Phylaktis, K., and F. Ravazzaolo, 2005, "Stock Market Linkages in Emerging Markets: Implications for International Portfolio Diversification", Journal of International Financial Markets, Institution, and Money, 15, 91-106. ENDNOTES (1.) Morgan Stanley Capital International (www.msci.com). (2.) Index returns are estimated as the log-relative of daily prices for October 1, 2000, through September 30, 2006 using the MSCI indices for all markets in the sample: [Return.sub.t] = Ln([I.sub.t]/[I.sub.t-1]). (3.) The Jarque-Bera statistic tests the null hypothesis of a normal distribution and is distributed as a [chi square chi square (kī), n a nonparametric statistic used with discrete data in the form of frequency count (nominal data) or percentages or proportions that can be reduced to frequencies. ] with 2 d.f.. Jarque. C. M et Bera. A. K, 1984, "Efficient Tests for Normality Homoscedasticity and Independence of Regression Residuals", Economic Letter, 6, 255-259. (4.) Phillips, P. C. B., 1987, "Time Series Regression with a Unit Root", Econometrica, 55, 277-301. (5.) Perron, P., 1988, "Trends and Random Walks in Macroeconomic mac·ro·ec·o·nom·ics n. (used with a sing. verb) The study of the overall aspects and workings of a national economy, such as income, output, and the interrelationship among diverse economic sectors. Time Series: Further Evidence from a New Approach", Journal of Economic Dynamics and Control, 12, 297- 332. (6.) Dickey, D. and W. Fuller, 1979, "Distribution of the Estimators for Autoregressive Time Series with a Unit Root", Journal of the American Statistical Association Established in 1888 and published quarterly in March, June, September, and December, the Journal of the American Statistical Association (JASA) has long been considered the premier journal of statistical science. , 74, 427-431. (7.) [[gamma].sub.t] is a pure random walk if [rho] = 0. (8.) [[gamma].sub.t] is a random walk with a drift if [rho] = 0. (9.) [[gamma].sub.t] is a random walk with a drift and linear time trend if [rho] = 0. (10.) Newey, W. and K. West, 1987, "Hypothesis Testing hypothesis testing In statistics, a method for testing how accurately a mathematical model based on one set of data predicts the nature of other data sets generated by the same process. with Efficient Method of Moments Estimation", International Economic Review, 28, 777-787 (11.) Johansen, S. and K. Juselius, 1990, "Maximum Likelihood Estimation and Inferences on Cointegration with Applications to the Demand for Money". Oxford Bulletin of Economics and Statistics, 52, 169-210. (12.) Osterwald-Lenum, M., 1992, "A Note with Quantiles of the Asymptotic Distribution In mathematics and statistics, an asymptotic distribution is a hypothetical distribution that is in a sense the "limiting" distribution of a sequence of distributions. A distribution is an ordered set of random variables
for i of the Maximum Likelihood Conintegration Rank Test Statistics", Oxford Bulletin of Economics and Statistics, 54, 461-472. Kais Fadhlaoui, (a) Makram Bellalah, (b) Armand Dherry, (c) Mhamed Zouaouii (d) (a) PhD Student in Finance University of Amiens, CRIISEA-France, University of Picardie--Jules Verne CRIISEA Cathedral University Pole 10, Placette Lafleur P.O. Box 271680 027--AMIENS CEDEX 1-France, kais.fadhlaoui@yahoo.fr (b) Assistant Professor University of Amiens, CRIISEA-France, University of Picardie--Jules Verne CRIISEA Cathedral University Pole 10, Placette Lafleur P.O. Box 271680 027--AMIENS CEDEX 1-France, makram.bellalah@u-picardie.fr (c) Professor of Finance, ESG ESG Enterprise Strategy Group (Veritas) ESG Emergency Shelter Grant (Florida, USA) ESG Expeditionary Strike Group ESG Electronic Service Guide (used in DVB) Paris Paris Graduate School of Management, 25 Saint-Ambroise Street 75011 PARIS--France, aderhy@esg.fr (d) Professor of Management, ESC See escape character and escape key. See also ESC/P. ESC - escape Tunis, Tunisia P.O. BOX 145 Manar 2, 2092 Tunis-Tunisia mhz@planet.tn
Table 1
Summary statistics of daily equity [return.sup.2] series
Statistic US Canada UK France
Mean -0,000173 0,000179 0,000048 0,00000386
Median 0,000394 0,000594 0,000004 0,000327
Maximum 0,06428 0,038562 0,047372 0,05897
Minimum -0,05017 -0,08963 -0,05452 -0,06382
Standard Deviation 0,012807 0,012472 0,012528 0,014938
Skewness 0,13854 -0,91837 -0,38674 -0,11837
Kurtosis 5,32546 7,8539 63,692 5,14836
Jarque.Bera 364,9372 2216,438 428,6039 287,5639
Probability 0 0 0 0
N 1565 1565 1565 1565
Statistic Germany Italy Japan
Mean -0,0000473 0,00016 -0,0000739
Median 0,000374 0,000628 -0,0000318
Maximum 0,06986 0,06572 0,04938
Minimum -0,07567 -0,06127 -0,07027
Standard Deviation 0,016138 0,013772 0,014893
Skewness -0,14621 -0,56738 -0,15718
Kurtosis 5,10326 6,7382 4,93872
Jarque.Bera 276,8372 463,137 182,7639
Probability 0 0 0
N 1565 1565 1565
Czech
Statistic Republic Hungary Poland
Mean 0,001472 0,001138 0,000631
Median 0,001427 0,001038 0,000683
Maximum 0,05679 0,08372 0,05862
Minimum -0,07268 -0,07849 -0,05283
Standard Deviation 0,01562 0,015831 0,015985
Skewness -0,28603 -0,1773 0,078329
Kurtosis 4,87382 4,9821 443,082
Jarque.Bera 139,8452 188,1483 26,84372
Probability 0 0 0
N 1565 1565 1565
The Jarque-Bera [test.sup.3] for normality rejects the null
hypothesis that all the stock index and return series follow
a normal distribution.
Table 2
Correlation coefficients between daily equity return series
US Canada UK France Germany
US 100% 74,4% 65,1% 54,0% 68,2%
Canada 100% 47,4% 49,3% 62,3%
UK 100% 89,9% 78,6%
France 100% 88,2%
Germany 100%
Italy
Japan
Czech Republic
Hungary
Poland
Czech
Italy Japan Republic Hungary Poland
US 39,4% 13,6% 10,1% 13,7% 15,1%
Canada 33,8% 16,8% 19,3% 21,2% 20,1%
UK 69,3% 20,2% 21,4% 12,2% 22,1%
France 81,1% 19,0% 23,6% 27,0% 14,5%
Germany 76,7% 12,0% 18,2% 23,5% 21,2%
Italy 100% 15,6% 22,4% 24,4% 35,5%
Japan 100% 17,5% 18,5% 14,4%
Czech Republic 100% 38,7% 36,6%
Hungary 100% 37,8%
Poland 100%
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