Jensen–Shannon Divergence Based on Horizontal Visibility Graph for Complex Time Series

Abstract

In this paper, we propose Jensen–Shannon divergence (JSD) based on horizontal visibility graph (HVG) to measure the time series irreversibility for both stationary and non-stationary series efficiently. Numerical simulations are first conducted to show the validity of the proposed method and then empirical applications to the financial time series and traffic time series are investigated. It can be found that JSD shows better robustness than Kullback–Leibler divergence (KLD) on quantifying time series irreversibility and correctly distinguishes the different type of simulated series. For the empirical analysis, JSD based on HVG is able to detect the significant time irreversibility of stock indices and reveal the relationship between different stock indices. JSD results show the time irreversibility of speed time series for different detectors and present better accuracy and robustness than KLD. The hierarchical clustering based on their behavior of time irreversibility obtained by JSD classifies the detectors into four groups.