Assessing discrete time series irreversibility through detailed balance analysis

The analysis of the time irreversibility of time series has received increasing attention in the last decade, thanks to its potential for understanding the dynamics of normal and altered complex systems. While many metrics and tests have been proposed, these have mostly been focused on real-valued time series, in detriment of the analysis of symbolic sequences. We here present a simple test to assess the time irreversibility of the latter ones, based on a detailed balance evaluation; able to handle individual sequences or collections thereof; and that can further be conditioned to past symbols to extend the time scale of the evaluation. We test the proposed approach on symbolic sequences extracted from synthetic dynamical systems, written texts, and air transport operations. We further provide an open-source version of the test in a Python package.