Weighted link entropy and multiscale weighted link entropy for complex time series

Abstract

In this paper, weighted link entropy (WLE) and multiscale weighted link entropy (MWLE) are proposed as novel measures to quantify complexity of nonlinear time series. MWLE is different from traditional weighted permutation entropy (WPE) in that its proposal is based on the combination of symbolic ordinal analysis and networks. Besides, the analysis of MWLE takes into account multiple time scales inherent in complex systems. The advantages of the proposed methods are investigated by simulations on synthetic signals and real-world data. Based on the study of synthetic data, we find that a significant advantage of WLE is its reduced sensitivity to noise. WLE shows the trend of more chaotic of system as the variance of Gaussian white noise increases. In addition, WLE has a wider range of variations when the system is in a chaotic state and can detect minute changes of complexity in complex systems as control parameters vary. To further show the utility of MWLE and WLE methods, we provide new evidences of their application in financial time series. By comparing WLE with the mean and variance of closing price data, WLE can predict the occurrence of financial crisis in advance. Furthermore, MWLE is capable of helping mark off different regions of stock markets, detecting their multiscale structure and reflects more information containing in financial time series.