Time reversibility from visibility graphs of non-stationary processes

TL;DR

This paper introduces a visibility graph-based method to quantify time irreversibility in both stationary and non-stationary time series, enabling analysis of memory and non-equilibrium dynamics without detrending.

Contribution

It proposes a new definition of time irreversibility using visibility graphs, applicable to non-stationary processes, and demonstrates its effectiveness through rigorous analysis and simulations.

Findings

Visibility graphs can quantify irreversibility in non-stationary signals.

The method distinguishes between different degrees of irreversibility.

It provides a practical tool for analyzing memory and off-equilibrium dynamics.

Abstract

Visibility algorithms are a family of methods to map time series into networks, with the aim of describing the structure of time series and their underlying dynamical properties in graph-theoretical terms. Here we explore some properties of both natural and horizontal visibility graphs associated to several non-stationary processes, and we pay particular attention to their capacity to assess time irreversibility. Non-stationary signals are (infinitely) irreversible by definition (independently of whether the process is Markovian or producing entropy at a positive rate), and thus the link between entropy production and time series irreversibility has only been explored in non-equilibrium stationary states. Here we show that the visibility formalism naturally induces a new working definition of time irreversibility, which allows to quantify several degrees of irreversibility for stationary and non-stationary series, yielding finite values that can be used to efficiently assess the presence of memory and off-equilibrium dynamics in non-stationary processes without needs to differentiate or detrend them. We provide rigorous results complemented by extensive numerical simulations on several classes of stochastic processes.