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Analysis of nonlinear time series using discrete generalized past entropy based on amplitude difference distribution of horizontal visibility graph

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  • Li, Sange
  • Shang, Pengjian

Abstract

In this paper, we propose discrete generalized past entropy based on amplitude difference distribution of horizontal visibility graph as a new complexity measure of nonlinear time series. We use amplitude difference distribution instead of degree distribution to extract information from the network constructed from the horizontal visibility graph, and combine amplitude difference distribution with discrete generalized past entropy to propose the new method. By analyzing the logistic map and Hénon map with the proposed method, we find the proposed method not only can assess systems well, but also has higher accuracy and sensitivity than the traditional method in characterizing dynamical systems. Furthermore, we apply the proposed method to the financial data: the six indices from Chinese mainland, Hong Kong and US. The result shows that the US market and the Hong Kong market are more developed than the Chinese mainland market, which is consistent with the reality.

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  • 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).
    • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s0960077921000400
    DOI: 10.1016/j.chaos.2021.110687
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    References listed on IDEAS

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    1. Gonçalves, Bruna Amin & Carpi, Laura & Rosso, Osvaldo A. & Ravetti, Martín G., 2016. "Time series characterization via horizontal visibility graph and Information Theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 464(C), pages 93-102.
    2. Bezsudnov, I.V. & Snarskii, A.A., 2014. "From the time series to the complex networks: The parametric natural visibility graph," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 53-60.
    3. Li, Ping & Wang, Bing-Hong, 2007. "Extracting hidden fluctuation patterns of Hang Seng stock index from network topologies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 378(2), pages 519-526.
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    Citations

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    Cited by:

    1. Bai, Shiwei & Niu, Min, 2022. "The visibility graph of n-bonacci sequence," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    2. Hu, Xiaohua & Niu, Min, 2023. "Degree distributions and motif profiles of Thue–Morse complex network," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    3. Lin, Guancen & Lin, Aijing, 2022. "Modified multiscale sample entropy and cross-sample entropy based on horizontal visibility graph," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    4. Chafi, Mohammadreza Shafiee & Narm, Hossein Gholizade & Kalat, Ali Akbarzadeh, 2023. "Chaotic and stochastic evaluation in Fluxgate magnetic sensors," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    5. 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).
    6. Wang, Fang & Wang, Lin & Chen, Yuming, 2022. "Multi-affine visible height correlation analysis for revealing rich structures of fractal time series," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    7. Ren, Weikai & Jin, Zhijun, 2023. "Phase space visibility graph," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    8. Hu, Xiaohua & Niu, Min, 2023. "Horizontal visibility graphs mapped from multifractal trinomial measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).
    9. 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 1-22, March.
    10. Gao, Meng & Ge, Ruijun, 2024. "Mapping time series into signed networks via horizontal visibility graph," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).

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