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Ambiguities in Bandt–Pompe’s methodology for local entropic quantifiers

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  • Olivares, Felipe
  • Plastino, Angelo
  • Rosso, Osvaldo A.

Abstract

The Bandt–Pompe (BP) prescription for building up probability densities [C. Bandt, B. Pompe, Permutation entropy: a natural complexity measure for time series, Phys. Rev. Lett. 88 (2002) 174102] constituted a significant advance in the treatment of time-series. However, as we show here, ambiguities arise in applying the BP technique with reference to the permutation of ordinal patterns. This happens if one wishes to employ the BP-probability density to construct local entropic quantifiers that would characterize time-series generated by nonlinear dynamical systems. Explicit evidence of this fact is presented by comparing two different procedures, frequently found in the literature, that generate sequences of ordinal patterns. In opposition to the case of global quantifiers in the orthodox Shannon fashion, the proper order of the pertinent symbols turns out to be not uniquely predetermined for local entropic indicators. We advance the idea of employing the Fisher–Shannon information plane as a tool to resolve the ambiguity and give illustrative examples.

Suggested Citation

  • Olivares, Felipe & Plastino, Angelo & Rosso, Osvaldo A., 2012. "Ambiguities in Bandt–Pompe’s methodology for local entropic quantifiers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2518-2526.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:8:p:2518-2526
    DOI: 10.1016/j.physa.2011.12.033
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Rosso, Osvaldo A. & De Micco, Luciana & Plastino, A. & Larrondo, Hilda A., 2010. "Info-quantifiers’ map-characterization revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4604-4612.
    4. Keller, K. & Sinn, M., 2005. "Ordinal analysis of time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 356(1), pages 114-120.
    5. Saco, Patricia M. & Carpi, Laura C. & Figliola, Alejandra & Serrano, Eduardo & Rosso, Osvaldo A., 2010. "Entropy analysis of the dynamics of El Niño/Southern Oscillation during the Holocene," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 5022-5027.
    6. De Micco, L. & González, C.M. & Larrondo, H.A. & Martin, M.T. & Plastino, A. & Rosso, O.A., 2008. "Randomizing nonlinear maps via symbolic dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3373-3383.
    7. O. A. Rosso & C. Masoller, 2009. "Detecting and quantifying temporal correlations in stochastic resonance via information theory measures," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 69(1), pages 37-43, May.
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    Cited by:

    1. Spichak, David & Aragoneses, Andrés, 2022. "Exploiting the impact of ordering patterns in the Fisher-Shannon complexity plane," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    2. Bariviera, Aurelio F. & Font-Ferrer, Alejandro & Sorrosal-Forradellas, M. Teresa & Rosso, Osvaldo A., 2019. "An information theory perspective on the informational efficiency of gold price," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    3. Redelico, Francisco O. & Traversaro, Francisco & Oyarzabal, Nicolás & Vilaboa, Ivan & Rosso, Osvaldo A., 2017. "Evaluation of the status of rotary machines by time causal Information Theory quantifiers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 321-329.
    4. Aurelio F. Bariviera & M. Belen Guercio & Lisana B. Martinez & Osvaldo A. Rosso, 2015. "A permutation Information Theory tour through different interest rate maturities: the Libor case," Papers 1509.00217, arXiv.org.

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