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Permutation entropy analysis based on Gini–Simpson index for financial time series

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  • Jiang, Jun
  • Shang, Pengjian
  • Zhang, Zuoquan
  • Li, Xuemei

Abstract

In this paper, a new coefficient is proposed with the objective of quantifying the level of complexity for financial time series. For researching complexity measures from the view of entropy, we propose a new permutation entropy based on Gini–Simpson index (GPE). Logistic map is applied to simulate time series to show the accuracy of the GPE method, and expound the extreme robustness of our GPE by the results of simulated time series. Meanwhile, we compare the effect of the different order of GPE. And then we employ it to US and European and Chinese stock markets in order to reveal the inner mechanism hidden in the original financial time series. After comparison of these results of stock indexes, it can be concluded that the relevance of different stock markets are obvious. To study the complexity features and properties of financial time series, it can provide valuable information for understanding the inner mechanism of financial markets.

Suggested Citation

  • Jiang, Jun & Shang, Pengjian & Zhang, Zuoquan & Li, Xuemei, 2017. "Permutation entropy analysis based on Gini–Simpson index for financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 273-283.
    • Handle: RePEc:eee:phsmap:v:486:y:2017:i:c:p:273-283
    DOI: 10.1016/j.physa.2017.05.059
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    References listed on IDEAS

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    1. Kirman Alan & Teyssière Gilles, 2002. "Microeconomic Models for Long Memory in the Volatility of Financial Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 5(4), pages 1-23, January.
    2. LeBaron, Blake & Arthur, W. Brian & Palmer, Richard, 1999. "Time series properties of an artificial stock market," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1487-1516, September.
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    Cited by:

    1. Jiang, Jun & Shang, Pengjian & Zhang, Zuoquan & Li, Xuemei, 2018. "The multi-scale high-order statistical moments of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 474-488.
    2. Mohammad Arashi & Mohammad Mahdi Rounaghi, 2022. "Analysis of market efficiency and fractal feature of NASDAQ stock exchange: Time series modeling and forecasting of stock index using ARMA-GARCH model," Future Business Journal, Springer, vol. 8(1), pages 1-12, December.

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