Multiscale Irreversibility Analysis of Time Series Based on Permutation Jensen–Shannon Distance

In this study, we propose a multiscale permutation Jensen–Shannon distance (MPJSD) to measure irreversibility of complex time series. The new quantifier is based on symbolic permutation pattern and Jensen–Shannon distance. As an alternative, the new method offers the best characterization of the underlying irreversibility on different scales. The ARFIMA process and three dissipative chaotic systems are used to verify the effectiveness of the new method. The numerical results indicate that the MPJSD can unveil subtle and interesting findings on different scales and the permutation Jensen–Shannon distance (PJSD) is scale-dependent. Furthermore, we apply the approach to detect the multiscale irreversibility of ECG and financial data. The underlying irreversible nature of the investigated series is well discriminated. The method here introduced gives a new way to distinguish different degrees of irreversibility.