Time Irreversibility of Complex Time Series with Detrended Cross-Correlation Analysis Based on Visibility Graph

In this paper, we introduce detrended cross-correlation analysis (DCCA) method into visibility graph (VG) algorithm and propose VGDCCA method to reflect the time series irreversibility from a new perspective. The validity and reliability of the proposed VGDCCA method is supported by numerical simulations on synthesized short-term correlated chaotic systems and long-term correlated fractal processes, and by the empirical analysis on stock indices and traffic parameter. The VGDCCA planes suggest that autoregressive fractionally integrated moving average (ARFIMA) and fractional Gaussian noise (FGN) series show time reversible behavior, whatever the long-term correlation of the series is or however strong the persistence or anti-persistence of the series is. Meanwhile, Logistic map with [Formula: see text] and Hénon map show more time irreversible behaviors than those of ARFIMA, FGN series and other Logistic maps. It can be found that the relationship between cross-correlation of ingoing degree sequence and outgoing degree sequence for the simulated series with different parameters is consistent with the complexity and autocorrelation behavior in the corresponding definition of the time series. For the empirical analysis, VGDCCA method declares the similarity and dissimilarity between stock indices on time series irreversibility and captures the time irreversibility of traffic time series recorded by the detectors in different locations.