Generalized entropy plane based on multiscale weighted multivariate dispersion entropy for financial time series

Abstract

Abstract In recent years, complexity-entropy causality plane, Shannon-Fisher information plane and Renyi-Tsalli entropy plane methods have been proposed to study one-dimensional nonlinear complex systems and widely applied in many fields. However, it is much less common for these definitions to extend to two-dimensional or higher-dimensional data. Dispersion entropy shows superior performance in complex system analysis. We propose the above three generalized entropy plane methods based on multivariate dispersion entropy (MDE) and weighted multivariate dispersion entropy (WMDE) to evaluate the complexity of two-dimensional data. The performance of these methods is compared by analyzing the simulated data. Applying these methods to the study of multivariate stock time series, the complexity-entropy causality plane shows more great performance, not only obtains the classification of the stock market indices, but distinguishes the development states of different stock market indices. At the same time, we also propose multiscale multivariate dispersion entropy (MMDE) and multiscale weighted multivariate dispersion entropy (MWMDE), and reveal the ordinal structure of stock market indices from the view of multiscale.