IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v203y2024ics0047259x24000447.html
   My bibliography  Save this article

Ordinal pattern dependence and multivariate measures of dependence

Author

Listed:
  • Silbernagel, Angelika
  • Schnurr, Alexander

Abstract

Ordinal pattern dependence has been introduced in order to capture co-monotonic behavior between two time series. This concept has several features one would intuitively demand from a dependence measure. It was believed that ordinal pattern dependence satisfies the axioms which Grothe et al. (2014) proclaimed for a multivariate measure of dependence. In the present article we show that this is not true and that there is a mistake in the article by Betken et al. (2021). Furthermore, we show that ordinal pattern dependence satisfies a slightly modified set of axioms.

Suggested Citation

  • Silbernagel, Angelika & Schnurr, Alexander, 2024. "Ordinal pattern dependence and multivariate measures of dependence," Journal of Multivariate Analysis, Elsevier, vol. 203(C).
    • Handle: RePEc:eee:jmvana:v:203:y:2024:i:c:s0047259x24000447
    DOI: 10.1016/j.jmva.2024.105337
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X24000447
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2024.105337?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Betken, Annika & Dehling, Herold & Nüßgen, Ines & Schnurr, Alexander, 2021. "Ordinal pattern dependence as a multivariate dependence measure," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    2. 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).
    3. 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.
    4. 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.
    5. Schnurr, Alexander & Fischer, Svenja, 2022. "Generalized ordinal patterns allowing for ties and their applications in hydrology," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
    6. Grothe, Oliver & Schnieders, Julius & Segers, Johan, 2014. "Measuring association and dependence between random vectors," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 96-110.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Schnurr, Alexander & Fischer, Svenja, 2022. "Generalized ordinal patterns allowing for ties and their applications in hydrology," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
    2. Betken, Annika & Dehling, Herold & Nüßgen, Ines & Schnurr, Alexander, 2021. "Ordinal pattern dependence as a multivariate dependence measure," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    3. Christoph Bandt, 2019. "Order patterns, their variation and change points in financial time series and Brownian motion," Papers 1910.09978, arXiv.org.
    4. 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.
    5. 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.
    6. 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.
    7. Liebscher Eckhard, 2017. "Copula-Based Dependence Measures For Piecewise Monotonicity," Dependence Modeling, De Gruyter, vol. 5(1), pages 198-220, August.
    8. 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).
    9. Majid Asadi & Somayeh Zarezadeh, 2020. "A unified approach to constructing correlation coefficients between random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(6), pages 657-676, August.
    10. Liebscher, Eckhard, 2021. "Kendall regression coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    11. Mordant, Gilles & Segers, Johan, 2022. "Measuring dependence between random vectors via optimal transport," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    12. Yanqin Fan & Marc Henry, 2020. "Vector copulas," Papers 2009.06558, arXiv.org, revised Apr 2021.
    13. Bergamelli, Michele & Bianchi, Annamaria & Khalaf, Lynda & Urga, Giovanni, 2019. "Combining p-values to test for multiple structural breaks in cointegrated regressions," Journal of Econometrics, Elsevier, vol. 211(2), pages 461-482.
    14. Fuchs, Sebastian & Di Lascio, F. Marta L. & Durante, Fabrizio, 2021. "Dissimilarity functions for rank-invariant hierarchical clustering of continuous variables," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    15. De Keyser, Steven & Gijbels, Irène, 2024. "Parametric dependence between random vectors via copula-based divergence measures," Journal of Multivariate Analysis, Elsevier, vol. 203(C).
    16. Liebscher Eckhard, 2014. "Copula-based dependence measures," Dependence Modeling, De Gruyter, vol. 2(1), pages 1-16, October.
    17. Fan, Yanqin & Henry, Marc, 2023. "Vector copulas," Journal of Econometrics, Elsevier, vol. 234(1), pages 128-150.
    18. Lingyue Zhang & Dawei Lu & Xiaoguang Wang, 2020. "Measuring and testing interdependence among random vectors based on Spearman’s $$\rho $$ ρ and Kendall’s $$\tau $$ τ," Computational Statistics, Springer, vol. 35(4), pages 1685-1713, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:203:y:2024:i:c:s0047259x24000447. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.