Analyzing Financial Time Series by Dispersion Entropy Based on Hill’s Diversity Number

Abstract

In this paper, we propose dispersion entropy based on Hill’s diversity number (HDE) as a new method to characterize nonlinear time series such as financial time series. In order to test the performance of this new proposed method, we first apply HDE to characterize two synthetic models (logistic map, Hénon map), the results show that the proposed method can sensitively detect the changes in the state of systems, accurately distinguish different states of the system for different parameters and correctly characterize the complexity of systems. Furthermore, we apply the proposed method to analyze the financial time series obtained from the main indices from six different countries. Empirical results illustrate that the HDE can distinguish developed stock markets and emerging stock markets, and also reveal the intrinsic dynamical characteristics of financial time series.