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Contrasting stochasticity with chaos in a permutation Lempel–Ziv complexity — Shannon entropy plane

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  • Mateos, Diego M.
  • Zozor, Steeve
  • Olivares, Felipe

Abstract

This paper aims at introducing the Lempel–Ziv permutation complexity vs. permutation entropy plane (EC-plane) as a tool to analyze time series with diverse dynamical nature. These two quantities use the Bandt and Pompe representation to quantify a continuous-state time series. The main strength of this approach lies in the fact that this plane combines two different perspectives to study a signal, one being purely statistic (the permutation entropy) and the other being algorithmic (the Lempel–Ziv complexity). The results allow us to conclude that the EC-plane constitutes an appropriate framework for: (i) characterizing non-linear chaotic maps, (ii) distinguishing deterministic from stochastic processes and (iii) to discriminate between fractional Brownian motion, fractional Gaussian noise and K-noise.

Suggested Citation

  • Mateos, Diego M. & Zozor, Steeve & Olivares, Felipe, 2020. "Contrasting stochasticity with chaos in a permutation Lempel–Ziv complexity — Shannon entropy plane," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    • Handle: RePEc:eee:phsmap:v:554:y:2020:i:c:s0378437120303125
    DOI: 10.1016/j.physa.2020.124640
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    References listed on IDEAS

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    1. Burton G. Malkiel, 2003. "The Efficient Market Hypothesis and Its Critics," Working Papers 111, Princeton University, Department of Economics, Center for Economic Policy Studies..
    2. Rosso, Osvaldo A. & Craig, Hugh & Moscato, Pablo, 2009. "Shakespeare and other English Renaissance authors as characterized by Information Theory complexity quantifiers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(6), pages 916-926.
    3. repec:pri:cepsud:91malkiel is not listed on IDEAS
    4. M. Beben & A. Orłowski, 2001. "Correlations in financial time series: established versus emerging markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 20(4), pages 527-530, April.
    5. Zunino, L. & Pérez, D.G. & Kowalski, A. & Martín, M.T. & Garavaglia, M. & Plastino, A. & Rosso, O.A., 2008. "Fractional Brownian motion, fractional Gaussian noise, and Tsallis permutation entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(24), pages 6057-6068.
    6. Di Matteo, T. & Aste, T. & Dacorogna, M.M., 2003. "Scaling behaviors in differently developed markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 183-188.
    7. Olivares, Felipe & Zunino, Luciano & Rosso, Osvaldo A., 2016. "Quantifying long-range correlations with a multiscale ordinal pattern approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 283-294.
    8. Rosso, Osvaldo A. & Carpi, Laura C. & Saco, Patricia M. & Gómez Ravetti, Martín & Plastino, Angelo & Larrondo, Hilda A., 2012. "Causality and the entropy–complexity plane: Robustness and missing ordinal patterns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 42-55.
    9. Tarnopolski, Mariusz, 2016. "On the relationship between the Hurst exponent, the ratio of the mean square successive difference to the variance, and the number of turning points," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 662-673.
    10. Lamberti, P.W & Martin, M.T & Plastino, A & Rosso, O.A, 2004. "Intensive entropic non-triviality measure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 334(1), pages 119-131.
    11. Burton G. Malkiel, 2003. "The Efficient Market Hypothesis and Its Critics," Journal of Economic Perspectives, American Economic Association, vol. 17(1), pages 59-82, Winter.
    12. Aurelio F. Bariviera & Luciano Zunino & Osvaldo A. Rosso, 2018. "An analysis of high-frequency cryptocurrencies prices dynamics using permutation-information-theory quantifiers," Papers 1808.01926, arXiv.org.
    13. Osvaldo Rosso & Felipe Olivares & Luciano Zunino & Luciana Micco & André Aquino & Angelo Plastino & Hilda Larrondo, 2013. "Characterization of chaotic maps using the permutation Bandt-Pompe probability distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 86(4), pages 1-13, April.
    14. 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.
    15. Burton G. Malkiel, 2003. "The Efficient Market Hypothesis and Its Critics," Working Papers 111, Princeton University, Department of Economics, Center for Economic Policy Studies..
    16. Zozor, S. & Ravier, P. & Buttelli, O., 2005. "On Lempel–Ziv complexity for multidimensional data analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 345(1), pages 285-302.
    17. Rajković, Milan, 2000. "Extracting meaningful information from financial data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 383-395.
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    Cited by:

    1. Mateos, Diego M. & Gómez-Ramírez, Jaime & Rosso, Osvaldo A., 2021. "Using time causal quantifiers to characterize sleep stages," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    2. Šapina, Matej & Karmakar, Chandan Kumar & Kramarić, Karolina & Kośmider, Marcin & Garcin, Matthieu & Brdarić, Dario & Milas, Krešimir & Yearwood, John, 2021. "Lempel-Ziv complexity of the pNNx statistics – an application to neonatal stress," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

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    Keywords

    Chaos; Noises; Entropy; Complexity; FBM; FGN;
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