Cross-correlations and structures of stock markets based on multiscale MF-DXA and PCA

Based on the daily closing prices of US and Chinese stock markets, we conduct empirical analysis of the cross-correlations and multiscale distances among the US stock markets and China stock markets using the proposed multiscale multifractal detrended cross-correlation analysis method (MSMF-DXA). It is demonstrated that stock markets appear to be far more complex than hitherto reported in the studies using a fixed time scale. In order to identify and compare the interactions and structures of stock markets during financial crisis, as well as in the pre-crisis and post-crisis periods, all the entire samples are divided into four sub-periods. We are thus able to deeply examine the dynamics of linkages among stock markets during different considered periods by MSMF-DXA and principal component analysis technology. The empirical results indicate that both two financial crises cause the increase of international transmission of stock markets, but the global financial crisis and Asian financial crisis lead to different effects in stock markets. It is indicated that the markets are more correlated during global financial crisis compared to Asian financial crisis. The cross-correlations, especially for the markets within different geographic region, increased significantly during the crisis. It is shown that stock markets can be described by the first and second principal component during normal and crisis period, respectively. The results presented in this paper are useful to interpret the multiscale properties of stock markets and describe the dynamics of interactions among considered stock markets.