Generalized Weighted Permutation Entropy

TL;DR

This paper introduces a generalized method called Generalized Weighted Permutation Entropy that combines permutation entropy and weighted permutation entropy, using a scaling parameter to analyze the complexity of various time series data.

Contribution

It proposes a new heuristic approach that extends existing entropy measures with a scaling parameter, enabling richer analysis of time series complexity.

Findings

Produces unique signatures for different data types in a 3D complexity-entropy-scale space.

Effectively distinguishes stochastic, chaotic, and real-world data.

Generalizes the complexity-entropy causality plane to a 3D causality box.

Abstract

A novel heuristic approach is proposed here for time series data analysis, dubbed Generalized weighted permutation entropy, which amalgamates and generalizes beyond their original scope two well established data analysis methods: Permutation entropy, and Weighted permutation entropy. The method introduces a scaling parameter to discern the disorder and complexity of ordinal patterns with small and large fluctuations. Using this scaling parameter, the complexity-entropy causality plane is generalized to the complexity-entropy-scale causality box. Simulations conducted on synthetic series generated by stochastic, chaotic, and random processes, as well as real world data, are shown to produce unique signatures in this three dimensional representation.