آنالیز رابطه نامتقارن زمان ـ تغییر بازارهای سهام جهانی

The time-shift asymmetric correlation analysis method is introduced for stock exchanges with different but non-overlapping trading hours to analyze the degree of global integration between stock markets of different countries and their influence on each other. Next-day correlation (NDC) and same-day correlation (SDC) coefficients are introduced. Correlations between major U.S. and Asia-Pacific stock market indices are analyzed. Most NDCs are statistically significant while most SDCs are insignificant. NDCs grow over time and the U.S. stock market plays a pacemaking role for the Asia-Pacific region. The correlation coefficients can be used as a measure of the degree of globalization for the corresponding countries.

As globalization progresses, economies of all countries have become more economically interdependent. However, different countries are engaged in this process to different degrees, which results in different impacts on their financial and securities markets. Correlations of stock market returns have been studied for decades (Atchinson et al., 1987, Bollerslev, 1990, Badrinath et al., 1995, Chan, 1993, Yu and Wu, 2001, Cohen et al., 1980, Conrad and Kaul, 1988, Ilina and Daragan, 2001a and Kumar and Dhankar, 2009; and many others) in the attempt to learn the market behavior for predicting trends and identifying hints for trading decisions. Stock market correlations have been attributed to information propagation including news and a variety of other factors that may impact the interrelations in the stock market on local or global scales. Delays in information propagation may cause a lead–lag relationship in different stock markets and in different segments of a single stock market. Autocorrelation and cross-correlation approaches were used to learn about such a relationship and its impact on trading behavior. Researchers have utilized a variety of models for analyzing the lead–lag relationship. Correlations between stock markets or within a given stock market have been analyzed utilizing model-free conventional statistics or special models to account for more complex relationships and effects like random information delays, noise, and others. Among the most popular models used in econometrics are Autoregressive Conditional Heteroskedasticity (ARCH) proposed by Engle (1982) and its modifications like Generalized Autoregressive Conditional Heteroskedasticity (GARCH) proposed by Bollerslev (1986) for analysis of market volatility. The GARCH model has led to a variety of modifications such as EGARCH – Exponential GARCH (Nelson, 1991), QGARCH – Quadratic GARCH (Sentana, 1995), GARCH-M – GARCH-in-mean (Hentschel, 1995), TGARCH – Threshold GARCH (Zakoian, 1994) and many others. Bollerslev et al. (1988) proposed a measure for determining the conditional covariance based on VECH representation, which would effectively become an ARMA model for the product of the error terms. To capture the asymmetric answer of the volatility by the different sign of the stock market shocks, Engle et al. (1990) proposed the AGARCH model. It is well known by now that cross-correlations of stock market returns vary over time (Makridakis and Wheelwright, 1974, Koch and Koch, 1991 and Knif and Pynnonen, 1999). Correlations increase as economic integration intensifies (Еrb et al., 1994, Longin and Solnik, 1995 and Goetzmann et al., 2005), but the correlations most likely are higher in bull markets and lower in the bear markets. Longin and Solnik (1995), Ang and Bekaert (2002), and Longin and Solnik (2001) showed that correlations between markets were going up during the periods of high volatility and correlation coefficients were higher than average when diversification was profitable. It was noticed that such a behavior of correlations leads to a quite insignificant return with portfolio diversification in a bear market (Baele, 2005). Multiple studies identified that correlations between international stock markets has a tendency to increase when returns decrease (King and Wadhwani, 1990, Lin et al., 1994, Solnik et al., 1996, Chesnay and Jondeau, 2001 and Baele, 2005). Richardson and Peterson (1999) have found that cross-correlation between large and small stocks takes place even after controlling for own-autocorrelation. The lead–lag phenomenon among returns of size-sorted portfolios may imply a complex information transmission between large and small firms and can be used as an important source for trading decisions. Chan (1993) suggested that own- and cross-autocorrelations among stock returns occur due to imperfection of market-to-market information that causes correlation pattern asymmetry. Lo and MacKinlay, 1990a and Lo and MacKinlay, 1990b documented asymmetric return caused by cross-correlations and nonsynchronous trading. Yu and Wu (2001) applied asymmetric cross-correlation analysis approach to identify “the differential quality of information between large and small firms.” It was suggested that the asymmetric cross-correlation between large and small firms is mainly caused by differences in the sensitivity of stock prices to market-wide information and cash flow information between those firms. Ilina and Daragan (2001a) noted that if any two indices are highly correlated, then diversification between them makes no sense because the diversification effect will be quite slim. They conducted correlation analysis for studying international stock market indices including S&P 500 (U.S.), DAX (Germany), FTSE (UK), TSE 300 (Canada), and Nikkei 225 (Japan) from 1990 to 2001 (Ilina and Daragan, 2001b). The study identified the highest correlation between S&P 500 and the Canadian TSE 300 indices. The lowest correlation was found between S&P 500 and Japanese Nikkei 225 indices. A well-known gravity model frequently used for explanations of trade patterns can also be used for the explanation of stock market correlations (Flavin et al., 2002). Its essential conclusion is that geography does matter for goods markets while physical location and trading costs should be less of an issue in asset markets. It was found that geographical locations still matter when examining equity market linkages. In particular, the number of overlapping opening hours and sharing a common border tends to increase cross-country stock market correlation. Flavin et al. (2002) wrote “these results may stem from asymmetrical information and investor sentiment, lending some empirical support for these explanations of the international diversification puzzle.” Martens and Poon (2001) brought up the issue that the use of day-by-day close-to-close returns underestimates the correlation of returns because international stock markets in different countries have different trading hours. Growing interconnection of international stock markets and time-varying relationship of the returns was analyzed by Hu et al. (2008). They noted a dynamic relationship between major world stock markets over time and indicated a clear short-term continental integration of the selected markets which were replaced by a more complex global hedging behavior in the long run. However in their analysis Hu et al. (2008) did not take into account the differences in trading hours of different stock markets. Though the ARCH-family models have been successfully applied in the analysis of stock market correlations and volatility, many researchers prefer model-free statistical testing and correlation analysis (Ilina and Daragan, 2001a, Ilina and Daragan, 2001b, Aityan, 2007, Hong et al., 2007 and Ivanov-Schitz and Aityan, 2009). Michayluk et al. (2006) analyzed returns behavior and asymmetric volatility spillover effects and exceedance correlations in the example of real estate markets of different countries. They compared the correlations calculated on a daily basis when synchronously priced data were utilized with the correlations calculated on close-to-close returns and found that they are significantly different due to intraday information flows between both the markets. Li and Kazemi (2007) analyzed correlation asymmetry of daily returns of various hedge fund indices. In their research, they understood asymmetry as the correlation between two indices when both random variables were simultaneously above or below their means by more than their standard deviations. Chiang et al. (2007) and Centeno and Salido (2009) examined stock market asymmetric returns caused by positive and negative news and shocks. They found that negative news has a much stronger impact on returns than positive news. Thus researchers use term “correlation asymmetry” differently for a variety of different non-symmetric analyses. Some empirical studies suggested that monetary variables can also be used in the analysis of the dynamic interrelationship between securities markets. Sasaki et al. (1999) identified the significant impact of monetary and credit policies on the interrelationship between the securities markets. Black and Fraser (1995), Bracker et al. (1999), Bekaert and Harvey (2000), Bekaert et al. (2001), Wu (2001), Pretorius (2002), Liu et al. (2006), and Mukherjee and Mishra (2007) showed that the dynamics of stock markets integration depends on monetary parameters such as interest rates, foreign investment, trade, and inflation. Studies of correlations between stock markets have not been limited only to major markets. Da Costa et al. (2005) studied the correlations between developed and emerging markets. The scope of their analysis included emerging countries in Latin America such as Argentina, Brazil, Chile, Mexico, Asian countries such as South Korea, India, and Thailand, as well as developed countries such as the USA, Japan, and Great Britain. This study detected a growth of cross-correlations between the stock market indices in the 1980s and 1990s with a distinctive increase of the correlations in the 1990s as compared to the 1980s. The results suggested that efficiency of diversification in foreign markets decreases due to global integration. On the other hand, Kumar and Dhankar (2009) analyzed correlations between South Asian stock markets (India, Sri Lanka, Pakistan, and Bangladesh) and reported weak interdependency between these markets and global stock markets. The question arises: what did cause these studies to result in contradicting conclusions? Hamao et al. (1990) and Balaban et al. (2001) used the two-step GARCH model for studying stock markets interdependencies for intraday and overnight returns. They identified the intraday market shocks on the first step and used them for overnight returns on the second step. Different trading hours of different stock markets have been traditionally considered a disadvantage for correlation analysis (Martens and Poon, 2001) and major models like ARCH, GARCH, and others have been dealing with lead–lag relationships caused by real-time information delays mostly for overlapping trading hours. Martens and Poon (2001) showed that the use of close-to-close returns can underestimate return correlations for markets that trade at different times. Moreover, previous studies such as by Hamao et al. (1990) and Koutmos and Booth (1995), who utilized only opening and closing prices, have found it difficult to differentiate between contemporaneous and lagged spillover pricing effects from one market to another. They suggested that to avoid such a problem in correlation analysis, data must be synchronized by time, i.e. for every correlation pair the data must be observed at the same time. In this paper, we propose a model-free time-shift asymmetric correlation analysis for studying correlations and the interdependency of international stock markets that have no overlap of trading hours. We analyze close-to-close stock market returns for the markets with non-overlapping trading hours taking into account that each market operates with the information available by the market close of the other stock market. For this reason, we need neither the detailed information about delays of intraday information propagation nor the detailed information about any specifically accurate intraday time-lags for autocorrelations. We are not using explicit time-lags and explicit cross-autocorrelations because the time difference between the close of one market and the open of another market may vary due to occasionally shortened operating time on some markets, weekends, and holidays. In our approach, we only use the fact that one market works with the information of another previously closed market. The time between the close of one market and the open of another market for markets with non-overlapping trading hours is sufficient for the information from one market to reach another market. This fact allows us to use a simple model-free approach rather than a more complicated approach with ARCH/GARCH family models to identify a lead–lag relationship between the markets. The proposed approach helps overcome the disadvantage of using non-overlapping trading hours and turns it into a source of valuable information. This approach also helps identify which stock market is setting the pace and which ones are following the trend in the global environment. Though traditional correlation analysis does not identify the cause-and-effect relationship, the proposed time-shift asymmetric correlation analysis is able to solve this challenge utilizing the fact that stock exchanges in different countries operate at different times and with recent information about other stock markets with earlier trading hours (Aityan, 2007). Particularly, such an approach is quite efficient for cross-analysis of the U.S. and Asia-Pacific stock markets, where the U.S. stock markets are already closed at the time of trading on the Asia-Pacific stock markets, and vice versa. We suggest that correlation coefficients calculated between daily rates of return for stock market indices of different countries adequately reflect the degree of integration of the appropriate economies and can be used as a measure of globalization.

The analysis of SDC and NDC coefficients between U.S. stock indices—including Dow Jones Industrial Average (DJI) and Nasdaq Composite (IXIC)—and Asia-Pacific stock indices—including N225, KS11, STI. HSI, TWII, SSEC, KLSE, and JKSE—shows that NDC are statistically significant for all Asia-Pacific indices considered with the exception of SSEC. In contrast, analysis shows that most SDC are typically statistically insignificant, with a few exceptions for KLSE and LKSE in the years of recession and economic instability. The values of SDC are lower than the values of the corresponding NDC. The values of NDC were between 0.4 and 0.6 in 2007 for all indices except SSEC. In the last 2 years the NDC for DJI-N225 rose above 0.6, but the NDC for other indices decreased to 0.3–04. Such a drop can be explained by the typical reduction of correlations during global financial instability. Both SDC and NDC for DJI-SSEC are statistically insignificant and below 0.4 in value. The fact that the NDC are statistically significant and are higher than the corresponding SDC—which are mostly insignificant—allows us to conclude that the U.S. stock market plays a pacesetting role at least on the scale of the U.S. and Asia-Pacific region, with the exception of the stock market of mainland China (SSEC). The introduction of SDC and NDC made such a conclusion possible, while the traditional correlation analysis does not identify cause-and-effect relationship. The analysis of NDC and SDC coefficients suggests that Asian stock markets are more likely following the U.S. market while the U.S. market behaves more independently of the Asian stock markets. As it becomes evident from the results of this paper, the time-shift asymmetric correlation method with SDC and NDC helps better identify pairs of data for corellation analysis of the markets with different non-overlapping trading hours. Traditionally, researchers used only SDC matching pairs for close-to-close correlation analysis that, as was shown in this paper, leads to statistically insignificant results and underestimated correlation coefficients (Hamao et al., 1990, Koutmos and Booth, 1995, Martens and Poon, 2001 and Michayluk et al., 2006; and others), while NDC coefficients show stronger correlations with very high statistical significance. As we have suggested in this paper, correlation coefficients between stock market indices can be used as a measure of global integration for the corresponding countries. Low correlations between Chinese Shanghai Composite (SSEC) and U.S. Dow Jones (DJI) and Nasdaq Composite (IXIC) indicate that China, though it plays one of the leading roles in the global economy, has an even bigger internal market that offsets its complete integration in the global economy and its dependence on the global financial and economic instabilities.