The coupling analysis of stock market indices based on cross-permutation entropy

It is an interesting subject to analyze the coupling dependence between time series. Many information-theoretic methods have been proposed for this purpose. In this article, we propose a new permutation-based entropy for the detection of coupling structures between stock markets. It is inspired by inner composition alignment method that we use the number of crossing points instead of mode π in permutation entropy definition to define the probability distribution. The measure is named as cross-permutation entropy (CPE), and can be used to infer the cross-correlation properties as well as the direction of couplings. The capabilities of CPE to correctly infer couplings together with their directionality are compared against transfer entropy for artificial signals as well as stock market time series. The results show that CPE is efficient in the analysis of cross-correlation between signals. Besides, in the analysis of financial time series, we found the coupling between stock markets in a same country are generally stronger than what would be expected from different countries.