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Order Patterns in Time Series

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  • Chstoph Bandt
  • Faten Shiha

Abstract

. Recent use of order patterns in time‐series analysis shows the need for a corresponding theory. We determine probabilities of order patterns in Gaussian and autoregressive moving‐average (ARMA) processes. Two order functions are introduced which characterize a time series in a way similar to autocorrelation. For stationary ergodic processes, all finite‐dimensional distributions are obtained from the one‐dimensional distribution plus the order structure of a typical time series.

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  • Chstoph Bandt & Faten Shiha, 2007. "Order Patterns in Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(5), pages 646-665, September.
    • Handle: RePEc:bla:jtsera:v:28:y:2007:i:5:p:646-665
    DOI: 10.1111/j.1467-9892.2007.00528.x
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    7. Aurelio F. Bariviera & Luciano Zunino & M. Belen Guercio & Lisana B. Martinez & Osvaldo A. Rosso, 2015. "Efficiency and credit ratings: a permutation-information-theory analysis," Papers 1509.01839, arXiv.org.
    8. Christoph Bandt, 2020. "Order patterns, their variation and change points in financial time series and Brownian motion," Statistical Papers, Springer, vol. 61(4), pages 1565-1588, August.
    9. 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.
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    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. 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.
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    15. 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.
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    17. Fernando López & Mariano Matilla-García & Jesús Mur & Manuel Ruiz Marín, 2021. "Statistical Tests of Symbolic Dynamics," Mathematics, MDPI, vol. 9(8), pages 1-21, April.
    18. 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.
    19. Ji, Aiwen & Shang, Pengjian, 2019. "Analysis of financial time series through forbidden patterns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
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    21. Schnurr, Alexander & Fischer, Svenja, 2022. "Generalized ordinal patterns allowing for ties and their applications in hydrology," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
    22. Jauregui, M. & Zunino, L. & Lenzi, E.K. & Mendes, R.S. & Ribeiro, H.V., 2018. "Characterization of time series via Rényi complexity–entropy curves," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 498(C), pages 74-85.
    23. Domenico Piccolo & Rosaria Simone, 2019. "Rejoinder to the discussion of “The class of cub models: statistical foundations, inferential issues and empirical evidence”," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(3), pages 477-493, September.

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