Abstract
This paper introduces a new statistical tool: dispersion Havrda–Charvat entropy plane, which is used to analyze the complexity characteristics of time series. The Havrda–Charvat entropy with one parameter can provide flexibility in applications and provide more information about time series. The dispersion entropy algorithm is a fast and powerful algorithm for evaluating time series, which has been proposed in recent years. The statistical complexity measure defined by Jensen–Shannon divergence reflects the chaotic degrees of complex systems. The dispersion Havrda–Charvat entropy plane is constructed using the above conceptions. The performance of the dispersion entropy plane is evaluated by simulated chaotic processes and fractional Brownian motions, and then we apply the method to stock data. This demonstrates that dispersion Havrda–Charvat entropy plane can distinguish the intensive properties of time series well and is a powerful method to classify stock markets. In addition, the multiscale measure is experimented, the results show that it can eliminate the noise contained in the data and effectively extract the information contained in time series with different time scales.
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