Characterization of Time Series Via R\'enyi Complexity-Entropy Curves

TL;DR

This paper introduces Re9nyi complexity-entropy curves as a new tool for analyzing time series, effectively distinguishing between chaotic, stochastic, and periodic signals by examining the curvature of these curves.

Contribution

It extends the complexity-entropy analysis framework by incorporating Re9nyi entropy, providing a novel parametric curve for improved time series classification.

Findings

Re9nyi complexity-entropy curves differentiate chaotic, stochastic, and periodic time series.

Curves with positive curvature indicate stochastic processes.

Curves with negative curvature indicate chaotic processes.

Abstract

One of the most useful tools for distinguishing between chaotic and stochastic time series is the so-called complexity-entropy causality plane. This diagram involves two complexity measures: the Shannon entropy and the statistical complexity. Recently, this idea has been generalized by considering the Tsallis monoparametric generalization of the Shannon entropy, yielding complexity-entropy curves. These curves have proven to enhance the discrimination among different time series related to stochastic and chaotic processes of numerical and experimental nature. Here we further explore these complexity-entropy curves in the context of the R\'enyi entropy, which is another monoparametric generalization of the Shannon entropy. By combining the R\'enyi entropy with the proper generalization of the statistical complexity, we associate a parametric curve (the R\'enyi complexity-entropy curve) with a given time series. We explore this approach in a series of numerical and experimental applications, demonstrating the usefulness of this new technique for time series analysis. We show that the R\'enyi complexity-entropy curves enable the differentiation among time series of chaotic, stochastic, and periodic nature. In particular, time series of stochastic nature are associated with curves displaying positive curvature in a neighborhood of their initial points, whereas curves related to chaotic phenomena have a negative curvature; finally, periodic time series are represented by vertical straight lines.