Abstract
The complexity of time series has become necessary to understand the dynamics of the control system. In this paper, the multivariate multiscale distribution entropy (MMSDE) is introduced as a new method to assess the complexity of dynamical systems such as financial systems, physiological systems, etc. Distribution entropy (DE) takes full advantage of the information hidden in the state–space by the estimation of the probability density of distances among vectors. Based on this, MMSDE can quantify the complexity of multivariate time series from multiple time scales. We test the performance of this method with simulated data. Results show that MMSDE has less dependence on parameters and the test of short time series is very effective. As for the real data, we explore the high dimensional series that are composed of opening price, closing price, volume of stocks data including US stock indices and Chinese stock indices. MMSDE can quantify the change in the complexity of the stock market data. In addition, we get richer information from MMSDE and gain some features about the difference between the U.S. and Chinese stock indexes.
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