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Weighted multiscale Rényi permutation entropy of nonlinear time series

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  • Chen, Shijian
  • Shang, Pengjian
  • Wu, Yue

Abstract

In this paper, based on Rényi permutation entropy (RPE), which has been recently suggested as a relative measure of complexity in nonlinear systems, we propose multiscale Rényi permutation entropy (MRPE) and weighted multiscale Rényi permutation entropy (WMRPE) to quantify the complexity of nonlinear time series over multiple time scales. First, we apply MPRE and WMPRE to the synthetic data and make a comparison of modified methods and RPE. Meanwhile, the influence of the change of parameters is discussed. Besides, we interpret the necessity of considering not only multiscale but also weight by taking the amplitude into account. Then MRPE and WMRPE methods are employed to the closing prices of financial stock markets from different areas. By observing the curves of WMRPE and analyzing the common statistics, stock markets are divided into 4 groups: (1) DJI, S&P500, and HSI, (2) NASDAQ and FTSE100, (3) DAX40 and CAC40, and (4) ShangZheng and ShenCheng. Results show that the standard deviations of weighted methods are smaller, showing WMRPE is able to ensure the results more robust. Besides, WMPRE can provide abundant dynamical properties of complex systems, and demonstrate the intrinsic mechanism.

Suggested Citation

  • Chen, Shijian & Shang, Pengjian & Wu, Yue, 2018. "Weighted multiscale Rényi permutation entropy of nonlinear time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 548-570.
    • Handle: RePEc:eee:phsmap:v:496:y:2018:i:c:p:548-570
    DOI: 10.1016/j.physa.2017.12.140
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    References listed on IDEAS

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    1. Jing Wang & Pengjian Shang & Xiaojun Zhao & Jianan Xia, 2013. "Multiscale Entropy Analysis Of Traffic Time Series," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 24(02), pages 1-14.
    2. Thuraisingham, Ranjit A. & Gottwald, Georg A., 2006. "On multiscale entropy analysis for physiological data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 323-332.
    3. Martin, M.T. & Plastino, A. & Rosso, O.A., 2006. "Generalized statistical complexity measures: Geometrical and analytical properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(2), pages 439-462.
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    Citations

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    Cited by:

    1. Han, Yun-Feng & Jin, Ning-De & Zhai, Lu-Sheng & Ren, Ying-Yu & He, Yuan-Sheng, 2019. "An investigation of oil–water two-phase flow instability using multivariate multi-scale weighted permutation entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 518(C), pages 131-144.
    2. Mukherjee, Sayan & Banerjee, Santo & Rondoni, Lamberto, 2018. "Dispersive graded entropy on computing dynamical complexity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 131-140.
    3. Zhou, Qin & Shang, Pengjian, 2020. "Weighted multiscale cumulative residual Rényi permutation entropy of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    4. Wang, Gangjin & Wei, Daijun & Li, Xiangbo & Wang, Ningkui, 2023. "A novel method for local anomaly detection of time series based on multi entropy fusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(C).
    5. Chen, Shijian & Shang, Pengjian & Wu, Yue, 2019. "Multivariate multiscale fractional order weighted permutation entropy of nonlinear time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 217-231.

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