Testing time series irreversibility using complex network methods

¹ Potsdam Institute for Climate Impact Research - P.O. Box 601203, 14412 Potsdam, Germany, EU
² Department of Physics, Humboldt University Berlin - Newtonstr. 15, 12489 Berlin, Germany, EU
³ Stockholm Resilience Centre, Stockholm University - Kräftriket 2B, 11419 Stockholm, Sweden, EU
⁴ Institute for Complex Systems and Mathematical Biology, University of Aberdeen - Aberdeen AB24 3FX, UK, EU

^(a) donges@pik-potsdam.de

Received: 6 November 2012
Accepted: 20 March 2013

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.