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A new complexity measure: Modified discrete generalized past entropy based on grain exponent

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  • Li, Sange
  • Shang, Pengjian

Abstract

In this paper, we propose the modified discrete generalized past entropy based on grain exponent (GE-MDGPE), to analyze complex dynamical systems. Gao et al. proposed discrete generalized past entropy based on oscillation-based grain exponent (O-DGPE) method in 2019, which has been proved to be a good measure of uncertainty of time series. Whereas, it still has some drawbacks, such as the effectiveness of O-DGPE is not good when characterizing some special systems. In order to solve these drawbacks, we therefore generalize O-DGPE method to put forward GE-MDGPE which can better characterize complex systems. While using two artificial model (logistic map, Hénon map) to qualify the proposed method, we find that the method can characterize the system more accurately than O-DPGE, and can distinguish the periodic system and chaotic system effectively and sensitively. Moreover, we discuss the influence of parameters β and j on the proposed method. At last, we apply the proposed method to analyze the financial series which are extracting from six indices: three U.S. stock indices and three Chinese stock indices. The results show that the method can clearly distinguish the stock markets of different levels of development, and the U.S. market and the Hong Kong market are more mature than the Chinese mainland market.

Suggested Citation

  • Li, Sange & Shang, Pengjian, 2022. "A new complexity measure: Modified discrete generalized past entropy based on grain exponent," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001382
    DOI: 10.1016/j.chaos.2022.111928
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    References listed on IDEAS

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    1. Li, Sange & Shang, Pengjian, 2021. "Analysis of nonlinear time series using discrete generalized past entropy based on amplitude difference distribution of horizontal visibility graph," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Mao, Xuegeng & Shang, Pengjian & Xu, Meng & Peng, Chung-Kang, 2020. "Measuring time series based on multiscale dispersion Lempel–Ziv complexity and dispersion entropy plane," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    3. Zhang, Boyi & Shang, Pengjian & Zhou, Qin, 2021. "The identification of fractional order systems by multiscale multivariate analysis," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    4. Qin, Guyue & Shang, Pengjian, 2021. "Analysis of time series using a new entropy plane based on past entropy," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
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    1. J. Alberto Conejero & Andrei Velichko & Òscar Garibo-i-Orts & Yuriy Izotov & Viet-Thanh Pham, 2024. "Exploring the Entropy-Based Classification of Time Series Using Visibility Graphs from Chaotic Maps," Mathematics, MDPI, vol. 12(7), pages 1-23, March.

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