Testing time series irreversibility using complex network methods

TL;DR

This paper introduces new statistical tests based on complex network measures to detect time series irreversibility, applicable to short data sets and useful for identifying nonlinearity in various systems.

Contribution

It proposes a novel approach using visibility graph measures to test time-reversal symmetry without surrogate data, suitable for short time series.

Findings

Effective in detecting irreversibility in model systems

Identifies nonlinearity in neuro-physiological data

Does not require surrogate data

Abstract

The absence of time-reversal symmetry is a fundamental property of many nonlinear time series. Here, we propose a new set of statistical tests for time series irreversibility based on standard and horizontal visibility graphs. Specifically, we statistically compare the distributions of time-directed variants of the common complex network measures degree and local clustering coefficient. Our approach does not involve surrogate data and is applicable to relatively short time series. We demonstrate its performance for paradigmatic model systems with known time-reversal properties as well as for picking up signatures of nonlinearity in neuro-physiological data.