Comparing different approaches to compute Permutation Entropy with coarse time series

Abstract

Abstract: Bandt and Pompe introduced Permutation Entropy as a complexity measure and has been widely used in time series analysis and in many fields of nonlinear dynamics. In theory these time series come from a process that generates continuous values, and if equal values exists in a neighborhood, xt∗ = xt , t∗ ̸= t, they can be neglected with no consequences because their probability of occurrence is insignificant. Since then, this measure has been modified and extended, in particular in cases when the amount of equal values in the time series is large due to the observational method, and cannot be neglected. We test the new Data Driven Method of Imputation that cope with this type of time series without modifying the essence of the Bandt and Pompe Probability Distribution Function and compare it with the Modified Permutation Entropy, a complexity measure that assumes that equal values are not from artifacts of observations but they are typical of the data generator process. The Data Driven Method of Imputation proves to outperform the Modified Permutation Entropy.