Multivariate generalized information entropy of financial time series

In order to explore the complexity of multivariate time series, we propose a novel method: multiscale multivariate weighted fractional entropy (MMWFE). The research results show that MMWFE is able to measure the complexity of multivariate data correctly and reflect more information contained in the time series. In this paper, the reliability of the proposed method is supported by simulations on generated and empirical data. We analyze simulated pink noise and white noise to test the validity of this method, and the result is consistent with the fact that pink noise is more complex than white noise. Meanwhile, MMWFE shows a better robustness. MMWFE is then employed to bivariate stock return and volume to explore the complexity of stock markets. It successfully distinguishes Asia, Europe and Americas markets. Finally, dynamic MMWFE is applied to explore the evolution of complexity for mining more information containing in nonlinear time series. (C) 2019 Elsevier B.V. All rights reserved.