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Non-parametric analysis of serial dependence in time series using ordinal patterns

Author

Listed:
  • Weiß, Christian H.
  • Ruiz Marín, Manuel
  • Keller, Karsten
  • Matilla-García, Mariano

Abstract

A list of new tests for serial dependence based on ordinal patterns is provided. These new methods rely exclusively on the order structure of the data sets. Hence, the novel tests are stable under monotone transformations of the time series and robust against small perturbations or measurement errors. The standard asymptotic distributions are given, and their finite sample behavior under linear and non-linear departures from the null of independence are studied. Moreover, it is proved that under mild conditions, any ordinal-pattern-based test is nuisance free, which is appealing for modeling, as these tests can eventually be used as misspecification tests. This property is also analyzed for finite samples and illustrated through an empirical application. Much of the discussion is based on a detailed combinatorial analysis of ordinal pattern probabilities.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:csdana:v:168:y:2022:i:c:s0167947321002152
    DOI: 10.1016/j.csda.2021.107381
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    References listed on IDEAS

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    1. 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.
    2. Matilla-García, Mariano & Marín, Manuel Ruiz & Dore, Mohammed I., 2014. "A permutation entropy based test for causality: The volume–stock price relation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 280-288.
    3. M. Victoria Caballero-Pintado & Mariano Matilla-García & Manuel Ruiz Marín, 2019. "Symbolic correlation integral," Econometric Reviews, Taylor & Francis Journals, vol. 38(5), pages 533-556, May.
    4. Alexander Schnurr & Herold Dehling, 2017. "Testing for Structural Breaks via Ordinal Pattern Dependence," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 706-720, April.
    5. Matilla-García, Mariano & Ruiz Marín, Manuel, 2009. "Detection of non-linear structure in time series," Economics Letters, Elsevier, vol. 105(1), pages 1-6, October.
    6. 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.
    7. Ingo Klein & Monika Doll, 2021. "Tests on asymmetry for ordered categorical variables," Journal of Applied Statistics, Taylor & Francis Journals, vol. 48(7), pages 1180-1198, May.
    8. Amendola, Alessandra & Candila, Vincenzo & Gallo, Giampiero M., 2021. "Choosing the frequency of volatility components within the Double Asymmetric GARCH–MIDAS–X model," Econometrics and Statistics, Elsevier, vol. 20(C), pages 12-28.
    9. 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.
    Full references (including those not matched with items on IDEAS)

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