Measuring irreversibility via trend pattern lengths

In this work, we present a method to assess irreversibility in real-valued time series. Our approach introduces a novel measure based on the statistics of what we term “trend patterns.” By dividing a real-valued time series into subsequences that exhibit either increasing or decreasing trends, we define distributions representing the duration of uptrend and downtrend subsequences. When the process is reversible, these distributions should coincide. Consequently, we quantify the degree of irreversibility by measuring the statistical deviations between them. Our findings demonstrate the efficacy of this approach in identifying reversible and irreversible time series, even when working with not-so-long sample sizes. We have successfully applied this irreversibility index to real-world time series, particularly financial data sourced from cryptocurrency markets and heartbeat time series. Our analysis proves that the introduced method is effective in evaluating the irreversibility of real-valued time series without implementing any codification process.