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Asymptotic distribution of entropies and Fisher information measure of ordinal patterns with applications

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  • Rey, Andrea
  • Frery, Alejandro C.
  • Gambini, Juliana
  • Lucini, Magdalena

Abstract

We present the asymptotic distribution of the Rényi and Tsallis/Havrda–Charvát entropies and the Fisher information measure of ordinal patterns embedding their serial correlation. We study the convergence behavior of the asymptotic variance for some types of dynamics and the permutation entropy to the limit distribution. These results lead to tests for comparing the underlying dynamics of two time series. We apply these tests to discriminate uniform white noise, logistic maps with Gaussian noise, fractional Brownian motion, and f−k noise, with k∈{0.5,1,1.5,2,2.5}. We also applied these tests to cryptocurrency open prices data, with favorable results. We provide the R code that implements the functions.

Suggested Citation

  • Rey, Andrea & Frery, Alejandro C. & Gambini, Juliana & Lucini, Magdalena, 2024. "Asymptotic distribution of entropies and Fisher information measure of ordinal patterns with applications," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:chsofr:v:188:y:2024:i:c:s0960077924010336
    DOI: 10.1016/j.chaos.2024.115481
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    References listed on IDEAS

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    1. Helmut Elsinger, 2010. "Independence Tests based on Symbolic Dynamics," Working Papers 165, Oesterreichische Nationalbank (Austrian Central Bank).
    2. Mariano Matilla‐García & José Miguel Rodríguez & Manuel Ruiz Marín, 2010. "A symbolic test for testing independence between time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(2), pages 76-85, March.
    3. Weiß, Christian H. & Ruiz Marín, Manuel & Keller, Karsten & Matilla-García, Mariano, 2022. "Non-parametric analysis of serial dependence in time series using ordinal patterns," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    4. Matilla-Garci­a, Mariano & Ruiz Mari­n, Manuel, 2008. "A non-parametric independence test using permutation entropy," Journal of Econometrics, Elsevier, vol. 144(1), pages 139-155, May.
    5. Miguel Henry & George Judge, 2019. "Permutation Entropy and Information Recovery in Nonlinear Dynamic Economic Time Series," Econometrics, MDPI, vol. 7(1), pages 1-16, March.
    6. Spichak, David & Aragoneses, Andrés, 2022. "Exploiting the impact of ordering patterns in the Fisher-Shannon complexity plane," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    7. Eduarda T. C. Chagas & Marcelo Queiroz‐Oliveira & Osvaldo A. Rosso & Heitor S. Ramos & Cristopher G. S. Freitas & Alejandro C. Frery, 2022. "White Noise Test from Ordinal Patterns in the Entropy–Complexity Plane," International Statistical Review, International Statistical Institute, vol. 90(2), pages 374-396, August.
    8. Matilla-Garcia, Mariano, 2007. "A non-parametric test for independence based on symbolic dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 31(12), pages 3889-3903, December.
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