Assessing time series irreversibility through micro-scale trends

Time irreversibility, defined as the lack of invariance of the statistical properties of a system or time series under the operation of time reversal, has received increasing attention during the last few decades, thanks to the information it provides about the mechanisms underlying the observed dynamics. Following the need of analyzing real-world time series, many irreversibility metrics and tests have been proposed, each one associated with different requirements in terms of, e.g., minimum time series length or computational cost. We here build upon previously proposed tests based on the concept of permutation patterns but deviating from them through the inclusion of information about the amplitude of the signal and how this evolves over time. We show, by means of synthetic time series, that the results yielded by this method are complementary to the ones obtained by using permutation patterns alone, thus suggesting that “one irreversibility metric does not fit all.” We further apply the proposed metric to the analysis of two real-world data sets. Given a system, or more generally a time series representing the observable dynamics of a system, the first step is usually to try to characterize it through one or more metrics. Among these, tests assessing the irreversible nature of a time series are gaining attention. Irreversibility is found when the statistical properties of a process are not the same as the statistical properties of the time-reversed data; it thus formalizes the intuitive idea that a time series can be recognized from its time-reversed version. Irreversibility stems both from non-linearities and memory in the dynamics and represents the entropy production of a system out of equilibrium; in short, it can be used to infer information about the physical processes generating a time series, even when these are not directly accessible. We here leverage on a previously proposed metric to estimate the irreversibility of a time series through the concept of permutation patterns, introducing information about the amplitude of the signal and how this changes over time. Most notably, we show that the proposed metric and the original one are complementary; i.e., their relative performance depends on the characteristics of the system under study.This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 851255). M.Z. acknowledges the Spanish State Research Agency through the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (No. MDM-2017-0711)