A novel and effective method for quantifying complexity of nonlinear time series

Abstract

In this work, we propose the discrete general cumulative residual Kullback-Leibler information(DGCKL)to measure the complexity of nonlinear time series. Theoretically, the novel method benefits from the core concept of distribution entropy (DistEn)and possesses the advantages of the general cumulative Kullback-Leibler information(GCKL), presenting significant superiorities in quantifying the complexity of time series. Furthermore, comparative experiments conducted on simulation data confirm thatDGCKLis robust to noise and inherits the excellent properties ofDistEn to extract the features of time series. In practical application, DGCKLis provided with the ability to detect the abnormal behaviors of the rail dynamic time series and identify the significant events in specific periods of stock indices. Supported by theoretical analysis, simulated research and experimental verifications, this work establishes DGCKLas a meaningful and practical model for quantifying the complexity of time series.