Entropy of Difference

TL;DR

The paper introduces the entropy of difference (ED), a new complexity measure for time series that uses the sign of differences, requiring less data and allowing divergence estimation with Kullback-Leibler.

Contribution

It presents a novel entropy measure based on difference signs, improving efficiency and enabling divergence analysis compared to existing methods.

Findings

ED reduces the sample size needed for estimation

Allows use of Kullback-Leibler divergence for comparison

Performs comparably to permutation entropy in complexity assessment

Abstract

Here, we propose a new tool to estimate the complexity of a time series: the entropy of difference (ED). The method is based solely on the sign of the difference between neighboring values in a time series. This makes it possible to describe the signal as efficiently as prior proposed parameters such as permutation entropy (PE) or modified permutation entropy (mPE), but (1) reduces the size of the sample that is necessary to estimate the parameter value, and (2) enables the use of the Kullback-Leibler divergence to estimate the distance between the time series data and random signals.