Complexity analysis of multiscale multivariate time series based on entropy plane via vector visibility graph

Abstract

Vector visibility graph (VVG) is an algorithm that transforms multivariate time series into directed complex networks. However, at present, the researches of VVG mainly focus on its degree distribution. Considering the limitation of using the degree distribution of vector visibility graph alone to analyze the complexity of multivariate time series, we use the normalized Shannon entropy and the statistical complexity measure to analyze the complexity of multivariate time series based on the results of the degree distribution. We introduce the multivariate multiscale entropy plane to measure the dynamical complexity of multivariate systems. The effectiveness of the proposed method is validated by numerical simulation from several kinds of systems. In addition, we also observe that it is immune to different levels of noise in a wide range. Then, it is applied to evaluate the dynamic classification of financial time series from stock markets. Our results indicate that this method is effective to research the physical structures of stock markets.