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. Here, I introduce and analyse the complementary problem of its manipulation. In other words, I ask whether, given a time series, it can be manipulated to achieve desired irreversibility while maintaining its original dynamics. I 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. I further illustrate the relevance of this problem in the context of brain dynamics, determining that schizophrenic patients and control subjects are characterised by different “distances to irreversibility”. Finally, I discuss some open questions, including the meaning of such manipulation from both theoretical and applied viewpoints.