Asymptotic distribution of entropies and Fisher information measure of ordinal patterns with applications

Abstract

We present the asymptotic distribution of the Rényi and Tsallis/Havrda–Charvát entropies and the Fisher information measure of ordinal patterns embedding their serial correlation. We study the convergence behavior of the asymptotic variance for some types of dynamics and the permutation entropy to the limit distribution. These results lead to tests for comparing the underlying dynamics of two time series. We apply these tests to discriminate uniform white noise, logistic maps with Gaussian noise, fractional Brownian motion, and noise, with . We also applied these tests to cryptocurrency open prices data, with favorable results. We provide the R code that implements the functions.