Distinguishing Stock Indices and Detecting Economic Crises Based on Weighted Symbolic Permutation Entropy

Abstract

Permutation entropy (PE) is evolved as an important way to reveal the intrinsic characteristics of complex systems. While PE does not consider that the amplitudes of identical order sequences might be different, weighted permutation entropy (WPE), the extended technique, weighs each vector to alleviate this problem. Furthermore, experimental investigation shows that symbolizing the time series contributes to detecting sudden dynamical changes. As an exemplary measure, we study weighted symbolic permutation entropy (WSPE) which is a combination of WPE and threshold-dependent symbolic entropy to mount the intrinsic information of four stock indices from China and America stock markets, and six sector indices of banking, aviation industry and pharmacy from China stock markets. One thing needs to be especially pointed out is that symbolic method we use in this work is not the most common method which divides time series into some small bins, but a two-step process, including symbolic process and coding process. The statistical analysis in stock indices shows that WSPE method is capable of distinguishing stock indices and detecting economic crises.