Chin. Phys. Lett.  2020, Vol. 37 Issue (9): 090501    DOI: 10.1088/0256-307X/37/9/090501
Rescaled Range Permutation Entropy: A Method for Quantifying the Dynamical Complexity of Extreme Volatility in Chaotic Time Series
Jia-Chen Zhang , Wei-Kai Ren , and Ning-De Jin*
School of electrical and information engineering, Tianjin University, Tianjin 300072, China
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Jia-Chen Zhang , Wei-Kai Ren , and Ning-De Jin 2020 Chin. Phys. Lett. 37 090501
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Abstract Information entropy, as a quantitative measure of complexity in nonlinear systems, has been widely researched in a variety of contexts. With the development of a nonlinear dynamic, the entropy is faced with severe challenges in dealing with those signals exhibiting extreme volatility. In order to address this problem of weighted permutation entropy, which may result in the inaccurate estimation of extreme volatility, we propose a rescaled range permutation entropy, which selects the ratio of range and standard deviation as the weight of different fragments in the time series, thereby effectively extracting the maximum volatility. By analyzing typical nonlinear systems, we investigate the sensitivities of four methods in chaotic time series where extreme volatility occurs. Compared with sample entropy, fuzzy entropy, and weighted permutation entropy, this rescaled range permutation entropy leads to a significant discernibility, which provides a new method for distinguishing the complexity of nonlinear systems with extreme volatility.
Received: 13 May 2020      Published: 01 September 2020
PACS:  05.45.-a (Nonlinear dynamics and chaos)  
  05.45.Tp (Time series analysis)  
  89.70.Cf (Entropy and other measures of information)  
Fund: Supported by the National Natural Science Foundation of China (Grant Nos. 51527805 and 11572220).
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Jia-Chen Zhang 
Wei-Kai Ren 
and Ning-De Jin
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