Cumulative Tsallis entropy based on multi-scale permuted distribution of financial time series

Abstract

A method based on multi-scale permuted distribution Cumulative Tsallis entropy (MPDCTE) is proposed in this paper to measure the complexity and dissimilarity between sequences. It avoids the influence of permutation on spatial distribution, and uses the calculation of spatial distance matrix in distributed entropy to effectively measure the complexity of time series. We apply the MPDCTE method to the simulation data, verify the effectiveness of the method, discuss the influence of the parameters, and compare it with the traditional entropy metric. The results show that This method is insensitive to parameter changes and has a low dependence on data length. The dependencies all show superiority. Finally, it was applied to the real financial market, and we selected 9 stocks in the world to analyze. The MPDCTE method clearly divided the stocks by analyzing the sequence, which is consistent with the phenomenon of the financial market.