Permutation extropy: a time series complexity measure

TL;DR

This paper introduces permutation extropy, a new complexity measure for time series that improves upon permutation entropy by better capturing chaos and complexity in various real-world data.

Contribution

The paper proposes permutation extropy, combining permutation entropy and extropy concepts, and demonstrates its effectiveness over permutation entropy in analyzing chaotic and real-world time series.

Findings

Permutation extropy outperforms permutation entropy in chaos detection.

It is robust, fast to compute, and invariant under monotonic transformations.

The measure provides better complexity assessment in financial and health data.

Abstract

On account of a greater need for understanding the complexity of time series like physiological time series, financial time series, and many more that enter into picture for their inculpation with real-world problems, several complexity parameters have already been proposed in the literature. Permutation entropy, Lyapunov exponents are such complexity parameters out of many. In this article, we introduce a new time series complexity parameter, that is, the permutation extropy. The failure of permutation entropy in correctly specifying complexity of some chaotic time series motivates us to come up with a better complexity parameter, hence we propose this permutation extropy measure. We try to combine the ideas behind the permutation entropy and extopy to construct this measure. We also validate our proposed measure using several chaotic maps like logistic map, Henon map and Burger map. We apply the proposed complexity parameter to study the complexity of financial time series of the stock market and time series constructed using WHO data, finding a better complexity specification than permutation entropy. The proposed measure is kind of robust, fast calculation and invariant with respect to monotonous nonlinear transformation like permutation entropy, but it gives us a better result in specifying complexity in some cases.