Assessing time series irreversibility through micro-scale trends

Abstract

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 an increasing attention during the last decades, thanks to the information it provides about the mechanisms underlying the observed dynamics. Following the need of analysing 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.