Functional decomposition and estimation of irreversibility in time series via machine learning

This paper introduces a method to estimate irreversibility in multivariate time series based on the well-known mapping to a binary classification problem. Our approach utilizes gradient boosting as a binary classifier, thus providing a model-free, nonlinear, and multivariate analysis while requiring minimal calibration of the classifier. An additional functionality of the proposed methodology is to easily dissect the contributions to the irreversibility of subsets of variable interactions, for instance, those operating at different time scales. The pipeline is divided into three phases: trajectory encoding, Markovian order identification, and irreversibility estimation via the classifier; the latter could be refined by hypothesis testing and quantification of variable interactions' contributions to irreversibility. When applied to financial markets, our findings reveal a distinctive shift: During stable periods, irreversibility is mainly related to short-term patterns, whereas in unstable periods, these short-term patterns are disrupted, leaving only contributions from stable, long-term ones.