چگونه یک یک بازار سرمایه رابطه نزدیک با بازارهای دیگر داشته باشد؟بازنگری بر اساس آزمون واریانس برابر

The cointegration test cannot discriminate closer relationships from cointegrating relationships. In most applications, we must assess the degrees of cointegrating relationships, for example, to examine the comovement between international stock markets using the cointegration methodology. Lee et al. (2012) introduced a variance test of cointegration equilibrium errors to measure the similarity of these relationships. However, the key assumption of cross-sectional independence between a panel of two country-pair squared cointegrating equilibrium errors in their model is not desirable. The appearance of cross-sectional dependence of individual (stock) markets in a panel is a common existence. The current paper shows that the consideration of cross-sectional dependence and the method of estimating long-run variance are important. Our results, which extend the cross-sectional dependence of some Asian stock markets during the Asian financial crisis (1997–1998) documented by Lee et al. (2012), indicate that the similarity of background and business cooperation (or trading activities) are all crucial factors for determining the price patterns by the “equal variance test” proposed in this paper. The analysis of the 2007–2009 global financial crisis is included to confirm the robustness of the results.

Over the past two decades, researchers have paid increased attention to the comovement patterns among international stock markets. Early empirical studies investigated the comovement patterns among international stock markets based on a simple correlation analysis of returns or dynamic conditional correlation in the multivariate generalized autoregressive conditional heteroscedasticity (GARCH) framework.1 However, focusing on stock returns and returns volatility rather than equity prices may yield unstable and often conflicting short-term empirical results (Kasa, 1992, Manning, 2002 and Yang et al., 2006). Thus, the numerous studies that examine the comovement patterns among asset prices using either a bivariate or multivariate cointegration methodology can be used to complement the investigation of international stock markets (e.g., Kasa, 1992, Richards, 1995, Rangvid, 2001, Ghosh et al., 2005, Yang et al., 2006, Valadkhani and Chancharat, 2008 and Lee et al., 2012). Cointegration among stock markets can naturally result from the existence of a common feature among stock markets (Engle and Susmel, 1993). Based on this realization, a large number of authors have attempted to explain the factors underlying the comovement among stock markets. Most of the recent studies on this topic are devoted to determining the relative importance of both economic and geographical ties, but the cause of comovement remains enigmatic. Some studies tend to support the dominant importance of economic ties. For example, Johnson and Soenen (2002) showed that an increased export share by Asian economies to Japan and greater foreign direct investment from Japan to other Asian economies contributed to greater comovement. More recently, Didier et al. (2012) indicated that comovement in the stock market is driven largely by financial linkages. Fernández-Avilés et al. (2012) showed that stock market linkages are unrelated to geographical proximity. However, other authors have showed that both economic and geographical ties are important, or that geographical ties influence the pattern of stock prices. For example, Madaleno and Pinho (2012)reported results suggesting that geographically and economically closer markets exhibit a higher correlation and more short-run comovements. Lee et al. (2012) confirmed that geographic ties, not trading activities/business cooperation, would be reflected by most of the comovement patterns among stock markets. An assessment of the relationships among international stock markets is crucial to exploring the comovement patterns or the factors underlying the comovement of capital markets in the cointegration framework. Lee et al. (2012) proposed a residual-based variance test to discriminate closer relationships from cointegrating relationships by comparing the variances of the cointegrating equilibrium errors from the statistics calculated from the ordinary least squares (OLS)-estimated squared cointegrating residuals. This test can be treated as an extension of the concept of cointegration. Unlike analysis based on returns, such as correlation analysis, the degree of cointegration provides information on the long-term common trend. Alexander (1999) indicated that cointegration and correlation are related but are different concepts. A high correlation of returns does not necessarily imply a high cointegration in prices. Fig. 1 in Appendix B shows that the degree of cointegration can be measured by comparing the variances of cointegrating errors. Because the scale of the variables is a determining factor of the magnitude of the variances of cointegrating equilibrium errors, the variance tests should be used to compare the degrees of cointegrating relationships that contain a common dependent or independent variable. Nevertheless, in most applications, we must assess the degrees of cointegrating relationships between a panel of two pairs of countries which contains a common country, satisfying the requirement of including a common dependent or independent variable in the relationship. Therefore measuring the degree of cointegration by conducting the variance test can be a useful complement to the analysis of comovement patterns among international stock markets based on correlations of returns. Full-size image (22 K) Fig. 1. The variances of cointegrating errors and the degree of cointegration. Figure options However, the variance test proposed by Lee et al. (2012) has some limitations. The appearance of cross-sectional dependence of individual time series in a panel is a common existence. According to Lee et al. (2012), the key assumption of cross-sectional independence between a panel of two country-pair squared cointegrating equilibrium errors is not desirable. Some common unobservable factors or omitted variables can lead to cross-sectionally dependent cointegrating equilibrium errors, especially for country-pair regressions, hence lead to cross-section dependence between squared cointegrating equilibrium errors. In one extreme case, even cross-sectional independent cointegrating errors can induce cross-correlated squared cointegrating equilibrium errors among the panel data. Consequently, it may be necessary to relax the assumption by allowing for cross-sectional dependence between squared cointegrating equilibrium errors. Another drawback of the test proposed by Lee et al. (2012) is that it uses White (1980) heteroscedasticity-autocorrelation consistent (HAC) estimator to estimate variance–covariance of squared cointegrating equilibrium errors. The use of a HAC estimator involves the specification of a kernel and a truncation lag or bandwidth. The bandwidth choice determines the fraction of the available covariance information that goes into the calculation of the long run variances. Kiefer et al. (2000) showed that even if a data-dependent method is used to choose the truncation lag (bandwidth), arbitrary choices of the truncation lag are inevitable. Furthermore, HAC has a poor finite sample performance, (see, for example, Kiefer et al., 2000, Kiefer and Vogelsang, 2005, Phillips et al., 2006 and Phillips et al., 2007). Kiefer et al. (2000) proposed an alternative method of constructing robust test statistics; in this method, estimates of the variance–covariance matrix are not explicitly required to construct the test. This approach requires a nonsingular data-dependent stochastic transformation to the OLS estimates. Therefore, arbitrary choices of the truncation lags in HAC can be avoided, and the test based on KVB approach is asymptotically invariant to serial correlation/heteroskedasticity nuisance parameters. Furthermore, Ray and Savin (2008) and Ray et al. (2009) showed that the HAC-based method has an unsatisfactory size control, whereas the KVB-based approach provides a substantially more accurate approximation to the finite sample distribution. The method proposed in this paper improves the variance test proposed by Lee et al. (2012) in two ways. First, we allow the cross-sectional dependence between squared cointegrating equilibrium errors. To achieve this, we employ the concept of the near-epoch dependence (NED) on a mixing process because, under suitable size of the underlying mixing and moment restrictions, NED is general enough to enable the application of the central limit theorem to the squared cointegrating equilibrium errors. The NED approach can also accommodate a variety of possible process of the squared cointegrating equilibrium errors, such as GARCH(p,q). This accommodation is important given the considerable evidence that the conditional variance–covariance matrix in financial time series can be described as a GARCH-type model. Second, the method proposed in this paper reconstructs Lee et al.'s (2012) variance test by using the KVB approach. The proposed test has the advantage of being simple and intuitive. The limit distribution of the proposed test is free of nuisance parameters, and the critical values of the proposed test are also tabulated. The simulations presented in this study indicate that the finite performance of Lee et al. (2012) test is sensitive to the serial correlation of cointegrating errors and cross-sectional dependence between cointegrating errors, whereas the proposed test in this paper has favorable finite sample performance. 2 Hence, the proposed test can be expected to yield more robust empirical results. The test proposed in this paper was used to reexamine the comovement patterns among stock markets including Taiwan, the United States, and other Asian markets during the 1997 Asian financial crisis, which were examined by Lee et al. (2012). Lee et al.(2012) indicated that the main reason for focusing on Taiwan is that much trade has taken place between Taiwan and countries other than those in the Asian region (e.g., the United States) over the past several decades. Therefore, focusing on the relationships between Taiwan and other Asian markets enables the exploration of the relative importance of both economic and geographical ties. The results of this study are in sharp contrast with those reported by Lee et al. (2012) even though both studies draw from the same data. First, we find closer relationships between Taiwan and the Philippines, Australia, the United States, and Thailand than between Taiwan and other countries considered during the 1997 Asian financial crisis. By contrast, Lee et al. (2012) did not find that Taiwan had any close relationships with other country for this stage. Second, this paper does not show a closer relationship between Taiwan and Malaysia than between Taiwan and other countries, including the United States for the post-crisis period, whereas Lee et al. (2012) found a closer relationship here. Thus, our results support the existence of the same extent of comovements among these selected markets after the 1997 Asian financial crisis. Therefore, after considering the lack of a cointegration relationship before the 1997 crisis, and the cointegrating relationships are confirmed and the extent of the comovement among the selected stock markets shows no significant difference in the post-crisis period, we conclude that the linkage among stock markets was strengthened after the Asian financial crisis. The relatively close relationship between Taiwan and the United States during this crisis confirms the leadership and influence of the US economy, whereas geographic ties cannot be rejected in considering the close relationships between Taiwan and its adjacent markets, such as Hong Kong, Singapore, South Korea, and Malaysia, during and after the 1997 crisis. It is also shown that our empirical results are robust for the 2007–2009 financial crisis when the analysis is extended to the sample period July 1, 2007 to December 31, 2012. The remainder of the paper is organized as follows. Section 2 presents the test methodology, and presents the null distribution of the proposed test. This section also presents tabulated critical values of the proposed test. Section 3 presents empirical results. Finally, Section 4 provides the concluding remarks. Throughout this paper, View the MathML source→d denotes convergence in distribution; View the MathML source→a.s. denotes almost sure convergence; [Tr] denotes the largest integer not exceeding Tr, and ║.║p denotes (E│.│p)1/p.

To improve the knowledge of the level of cointegration relationship, this paper introduces a new generalized test that is based on the test proposed by Lee et al. (2012). The absence of this ability to answer how the level of comovement is for the traditional cointegration analysis including Engle–Granger procedure and Johansen and Juselius approach shows the importance of the variance tests. The ability to assess the closeness of the cointegrating relationships makes the variance tests relevant to applying to various issues, such as constructing portfolios among international stock markets. By allowing cross-sectional dependence between the squared cointegrating equilibrium errors, the proposed variance test provides further insights into the power of a hypothesis test, and is more adequate for the real-world analysis of the cointegration relationship than that in Lee et al. (2012). We extend the variance test of Lee et al. (2012) and re-examine empirical tests of the price linkages and the degree of comovement between Taiwan and other countries in the event of the 1997 Asian financial crisis. One important feature of the proposed set-up is that it is robust to a variety of possible squared cointegrating equilibrium errors, such as GARCH(p,q). Another advantage of the proposed variance test is that it does not require an estimation of the variance, σm2, by employing the KVB approach. The results of this study show that the proposed test is more robust because it is asymptotically invariant to serial correlation/heteroscadasticity nuisance parameters in σm2. We also show that the consideration of plausible dependence between capital markets raises questions about the validity of inferences based on the test proposed by Lee et al. (2012), which may lead to different empirical results. Even though the data source, sample period, and sample countries used in this study are the same as those used by Lee et al. (2012), this study presents different results. We cannot find enough evidence to support the conclusion in Lee et al. (2012)that adjacent regions with similar backgrounds in terms of their capital markets will reflect price patterns. Our results are robust when we focus on the 2007–2009 financial crisis. In summary, the empirical results of this study find closer relationships between Taiwan and other markets (i.e., the Philippines, the United States, and Australia) during the 1997 Asian financial crisis. Combining the cointegration test with the proposed equal variance test, we conclude that the linkage among stock markets was strengthened after the Asian financial crisis. The leading role of the United States stock market in Taiwan is founded in this paper, and geographical ties cannot be rejected. The findings of this study favor that frequent business cooperation and trading activities may be crucial factors in international stock price patterns. Future studies an employ our methodology to examine the degree of economic integration or convergence between developed and developing economies, or to assess the performance of mutual funds relative to a reference index.