Complexity analysis of multiscale multivariate time series based on entropy plane via vector visibility graph
- PDF / 1,149,590 Bytes
- 15 Pages / 547.087 x 737.008 pts Page_size
- 23 Downloads / 167 Views
ORIGINAL PAPER
Complexity analysis of multiscale multivariate time series based on entropy plane via vector visibility graph Binbin Shang · Pengjian Shang
Received: 24 June 2020 / Accepted: 17 September 2020 © Springer Nature B.V. 2020
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. Keywords Vector visibility graph · Entropy plane · Multivariate · Multiscale B. Shang (B) · P. Shang Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, People’s Republic of China e-mail: [email protected] P. Shang e-mail: [email protected]
1 Introduction The complexity analysis of time series from nonlinear dynamical systems is a hot issue in the scientific community [1]. In the past decade, a growing number of people show great interest in the interdisciplinary field of network science, which enables us to understand the nonlinear dynamics of complex systems in many fields. As a significant tool, complex network can not only explore the useful information contained in time series, but also reveal the highly nonlinear dynamic behavior that cannot be precisely characterized by theoretical models. The spatial connectivity is determined by the correlation of system states in time domain, the time series are transformed into complex networks, which supplies a practical framework for the study of time series in different subjects. In the last few years, plenty of methods have been proposed to transform time series into complex networks [2–11] and here are three methods in common use. The first one is the mapping from pseudoperiodic time series to complex networks, and each single node in the network corresponds to a period and the link between nodes is determined on the basis of the phase space distance between the corresponding periods [2,12]. Another network method is recursive network, which regards the single phase space vector as a node and the connection between nodes is determined by the distance of corresponding vector [8,13]. The third one is a significant method called visibility graph [9
Data Loading...
