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Ordinal analysis of time series

Author

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  • Keller, K.
  • Sinn, M.

Abstract

In order to develop fast and robust methods for extracting qualitative information from non-linear time series, Bandt and Pompe have proposed to consider time series from the pure ordinal viewpoint. On the basis of counting ordinal patterns, which describe the up-and-down in a time series, they have introduced the concept of permutation entropy for quantifying the complexity of a system behind a time series. The permutation entropy only provides one detail of the ordinal structure of a time series. Here we present a method for extracting the whole ordinal information.

Suggested Citation

  • Keller, K. & Sinn, M., 2005. "Ordinal analysis of time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 356(1), pages 114-120.
    • Handle: RePEc:eee:phsmap:v:356:y:2005:i:1:p:114-120
    DOI: 10.1016/j.physa.2005.05.022
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    Citations

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    Cited by:

    1. Zunino, Luciano & Tabak, Benjamin M. & Serinaldi, Francesco & Zanin, Massimiliano & Pérez, Darío G. & Rosso, Osvaldo A., 2011. "Commodity predictability analysis with a permutation information theory approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(5), pages 876-890.
    2. 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.
    3. Bariviera, Aurelio F. & Guercio, M. Belén & Martinez, Lisana B. & Rosso, Osvaldo A., 2016. "Libor at crossroads: Stochastic switching detection using information theory quantifiers," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 172-182.
    4. Alexander Schnurr, 2015. "An Ordinal Pattern Approach to Detect and to Model Leverage Effects and Dependence Structures Between Financial Time Series," Papers 1502.07321, arXiv.org.
    5. Alexander Schnurr, 2014. "An ordinal pattern approach to detect and to model leverage effects and dependence structures between financial time series," Statistical Papers, Springer, vol. 55(4), pages 919-931, November.
    6. Liu, Yunxiao & Lin, Youfang & Jia, Ziyu & Wang, Jing & Ma, Yan, 2021. "A new dissimilarity measure based on ordinal pattern for analyzing physiological signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    7. Zunino, Luciano & Zanin, Massimiliano & Tabak, Benjamin M. & Pérez, Darío G. & Rosso, Osvaldo A., 2010. "Complexity-entropy causality plane: A useful approach to quantify the stock market inefficiency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(9), pages 1891-1901.
    8. Sinn, Mathieu & Keller, Karsten, 2011. "Estimation of ordinal pattern probabilities in Gaussian processes with stationary increments," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1781-1790, April.
    9. 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.
    10. Ji, Aiwen & Shang, Pengjian, 2019. "Analysis of financial time series through forbidden patterns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    11. 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.
    12. Annika Betken & Jannis Buchsteiner & Herold Dehling & Ines Münker & Alexander Schnurr & Jeannette H.C. Woerner, 2021. "Ordinal patterns in long‐range dependent time series," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 969-1000, September.
    13. Montani, Fernando & Deleglise, Emilia B. & Rosso, Osvaldo A., 2014. "Efficiency characterization of a large neuronal network: A causal information approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 58-70.
    14. De Micco, Luciana & Fernández, Juana Graciela & Larrondo, Hilda A. & Plastino, Angelo & Rosso, Osvaldo A., 2012. "Sampling period, statistical complexity, and chaotic attractors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2564-2575.
    15. 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.
    16. Zunino, Luciano & Zanin, Massimiliano & Tabak, Benjamin M. & Pérez, Darío G. & Rosso, Osvaldo A., 2009. "Forbidden patterns, permutation entropy and stock market inefficiency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2854-2864.
    17. 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.
    18. 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.
    19. Aurelio Fernandez Bariviera & María Belén Guercio & Lisana B. Martinez & Osvaldo A. Rosso, 2015. "The (in)visible hand in the Libor market: an information theory approach," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 88(8), pages 1-9, August.
    20. Shi, Wenbin & Shang, Pengjian & Xia, Jianan & Yeh, Chien-Hung, 2016. "The coupling analysis between stock market indices based on permutation measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 222-231.
    21. 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.
    22. 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.

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