The cross-correlations of stock markets based on DCCA and time-delay DCCA

In this paper, the Detrended Fluctuation Analysis (DFA) and Detrended Cross-Correlation Analysis (DCCA) are used to investigate the stock markets. The DFA method is a widely-used method for the determination and detection of long-range correlations in stock time series. DCCA is a recently developed method to quantify the cross-correlations of two non-stationary time series. We report the results of correlation and cross-correlation behaviors in US and Chinese stock markets by using the DFA and DCCA methods, respectively. The DCCA shows that there exists some crossovers in the cross-correlation fluctuation function versus time scale of stock absolute returns. The cross-correlations in Chinese stock markets are stronger than those between Chinese and US stock markets. After documenting the equal-time cross-correlations using DCCA method, we study the dynamics of cross-correlations of stock series based on a time-delay. The time-dependence of the underlying cross-correlations is monitored using a time window by step of 1 day. An interesting finding is that the cross-correlation exponents and crossovers demonstrate periodical uncertainty changing with the time-delay.