Abstract
In this paper, based on permutation patterns and Havrda–Charvat’s entropy, we propose a new measurement of complexity, weighted Havrda–Charvat’s entropy, to distinguish uncertainty for time series with the same order mode. First, we use logistic mapping to analyze the effect of similar data, length, noise, and weight on Havrda–Charvat’s entropy. Then we apply Havrda–Charvat’s entropy and weighted Havrda–Charvat’s entropy to stock market data including Shanghai Composite Index, CSI 300 index, Shenzhen Component Index, S&P500, DOW30 and NASDAQ. Results show that Havrda–Charvat’s entropy is helpful for distinguishing the uncertainty between similar data and it is robust to noise. Besides, the weighted Havrda–Charvat’s entropy values are of less deviation so as to make the analysis of complexity more convincing.
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