Time reversibility from visibility graphs of non-stationary processes

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.

References in corpus (3)

• From time series to complex networks: the visibility graph
• Random walks with preferential relocations to places visited in the past and their application to biology
• On the degree distribution of horizontal visibility graphs associated to Markov processes and dynamical systems: diagrammatic and variational approaches

Cited by in corpus (15)

• Complex network approaches to nonlinear time series analysis
• Network structure of multivariate time series
• Sequential visibility-graph motifs
• Detection of time reversibility in time series by ordinal patterns analysis
• Sequential motif profile of natural visibility graphs
• Visibility graphs and symbolic dynamics
• Visibility graphs of random scalar fields and spatial data
• The arrow of time across five centuries of classical music
• Time irreversibility and amplitude irreversibility measures for nonequilibrium processes
• Coherent structures at the origin of time irreversibility in wall turbulence
• Estimating entropy rate from censored symbolic time series: a test for time-irreversibility
• Permutation time irreversibility in sleep electroencephalograms: Dependence on sleep stage and the effect of equal values
• Comparative analysis of time irreversibility and amplitude irreversibility based on joint permutation
• Irreversibility of symbolic time series: a cautionary tale
• Identifying statistical indicators of temporal asymmetry using a data-driven approach