Cross-sample entropy statistic as a measure of synchronism and cross-correlation of stock markets

In this paper, we employ cross-sample entropy (cross-SampEn), transfer entropy, and detrended cross-correlation analysis (DCCA) measurement to investigate the relationship between time series among different stock markets. Cross-SampEn method is used to compare the returns of every two stock index time series to assess their degree of asynchrony. Transfer entropy is applied to measure the information flow between two financial time series and this model-free approach in principle allows us to detect statistical dependencies of all types. We use DCCA method to quantify the cross-correlations of two non-stationary time series. We report the results of synchronism and cross-correlation behaviors in US and Chinese stock markets in periods 1991-1998 (before the Asian currency crisis) and 1999-2008 (after the Asian currency crises) by using cross-SampEn, transfer entropy and DCCA methods, respectively. The results, through the contrast description of the three methods, show that the synchronism and cross-correlation become higher after the Asian currency crises, especially for the three Chinese stock index time series. Among all these consequences, ShangZheng and ShenCheng show the strongest synchronism, information transfer and cross-correlation. While the three US stock markets show a good cross-correlation and information transfer, but less synchronism before the Asian currency crisis.