Detection of time reversibility in time series by ordinal patterns analysis

TL;DR

The paper introduces TiROP, a fast, data-driven method using ordinal patterns and Jensen-Shannon divergence to assess time-reversibility in time series, applicable to both synthetic and real data.

Contribution

It presents a novel, computationally efficient approach for detecting time-reversibility across multiple time scales without additional assumptions.

Findings

TiROP effectively detects non-linearity and irreversibility in diverse time series.

The method outperforms classical tests in speed and data requirements.

It offers potential for discovering reliable physiological biomarkers.

Abstract

Time irreversibility is a common signature of nonlinear processes, and a fundamental property of non-equilibrium systems driven by non-conservative forces. A time series is said to be reversible if its statistical properties are invariant regardless of the direction of time. Here we propose the Time Reversibility from Ordinal Patterns method (TiROP) to assess time-reversibility from an observed finite time series. TiROP captures the information of scalar observations in time forward, as well as its time-reversed counterpart by means of ordinal patterns. The method compares both underlying information contents by quantifying its (dis)-similarity via Jensen-Shannon divergence. The statistic is contrasted with a population of divergences coming from a set of surrogates to unveil the temporal nature and its involved time scales. We tested TiROP in different synthetic and real, linear and non linear time series, juxtaposed with results from the classical Ramsey's time reversibility test. Our results depict a novel, fast-computation, and fully data-driven methodology to assess time-reversibility at different time scales with no further assumptions over data. This approach adds new insights about the current non-linear analysis techniques, and also could shed light on determining new physiological biomarkers of high reliability and computational efficiency.