Manipulating Time Series Irreversibility Through Continuous Ordinal Patterns

Time irreversibility, i.e. the lack of invariance of a system under the operation of time reversal, has long attracted the attention of the statistical physics community; and has been shown to be a relevant marker of altered dynamics in many real-world problems. We here introduce and analyse the complementary problem of its manipulation. In other words, we ask whether, given a time series, this can be manipulated to achieve a desired irreversibility while maintaining the original dynamics. We show how this problem can be tackled using Continuous Ordinal Patterns, a non-linear transformation of a time series based on the local structure created by neighbouring values. We further illustrate the relevance of this problem in the context of brain dynamics, obtaining that schizophrenic patients and control subjects are characterised by different "distances to irreversibility". We finally discuss some open questions, including the meaning of such manipulation from both theoretical and applied viewpoints.