Research on Correlation Analysis for Multidimensional Time Series Based on the Evolution Synchronization of Network Topology

Abstract

We apply the inherent dynamic consistency of a dynamic system as the basis for correlation analysis among different variables in a system. We use network analysis to measure the correlativity of multiple variables, find the interdependence between multiple variables with nonlinear interactions, and study the complex relationship between the stock index and trading volume. We explore the change pattern of the number of edges in the networks derived from the correlation among different time series by gradually increasing the length of the time series. We found that the evolution trend of the corresponding network edges is the same or similar for multiple series with the same dynamic properties or mutual effects, which is called network topology evolution synchronization (NTES). The correlation among time series can be determined by investigating the existence of NTES. Using this method, we detected that both the stock price and trading volume are chaotic series and have complex correlations with varying randomness caused by different markets and series lengths.