Multiscale cross-sample entropy based on visibility graph for quantifying time series irreversibility

Abstract

In this paper, we propose VGMCSE method to obtain multiscale time series irreversibility and gain more information from time irreversibility analysis. The validity of VGMCSE method is illustrated by numerical simulations on synthesized data and then VGMCSE method is applied on traffic time series to give better understanding about the traffic system from the view of time series irreversibility. By means of the VGMCSE planes for all the simulated time series, it can be found that ARFIMA and FGN series are all time reversible, while Logistic map & Hénon map are time irreversible. The simulated series can be classified into two groups: (1) ARFIMA & FGN, (2) Logistic map & Hénon map by their time series irreversibility. It can be found that the relationship between asynchrony of ingoing degree sequence and outgoing degree sequence for the simulated series with different parameter is consistent with the complexity and autocorrelation behavior in the corresponding definition of the time series. However, it can be revealed that whether the series is long-term correlated or no matter how strong the persistence or anti-persistence is, the ARFIMA and FGN series are all time reversible, indicating time series irreversibility might have no direct connection with long-range dependence and stationarity of series. For the empirical analysis, the traffic time series recorded by detectors can be classified into three groups: (1) detector 2037, 2038, (2) detector 3055, (3) detector 2036, 2040, 3054, 3056, 3057, 4051, 4052, suggesting that there is more similar time irreversible behavior for speed and volume time series recorded by detectors with nearer positions, while the traffic time series of some special locations present different time irreversible behavior and these locations should be paid more attention and enhanced monitoring. VGMCSE method can not only show the asynchrony of ingoing degree sequence and outgoing degree sequence, but also detect the time series irreversibility for time series of complex system.