Ordinal pattern dependence as a multivariate dependence measure

Annika Betken, Herold Dehling, Ines Nüßgen, Alexander Schnurr*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

In this article, we show that the recently introduced ordinal pattern dependence fits into the axiomatic framework of general multivariate dependence measures, i.e., measures of dependence between two multivariate random objects. Furthermore, we consider multivariate generalizations of established univariate dependence measures like Kendall's τ, Spearman's ρ and Pearson's correlation coefficient. Among these, only multivariate Kendall's τ proves to take the dynamical dependence of random vectors stemming from multidimensional time series into account. Consequently, the article focuses on a comparison of ordinal pattern dependence and multivariate Kendall's τ in this context. To this end, limit theorems for multivariate Kendall's τ are established under the assumption of near-epoch dependent data-generating time series. We analyze how ordinal pattern dependence compares to multivariate Kendall's τ and Pearson's correlation coefficient on theoretical grounds. Additionally, a simulation study illustrates differences in the kind of dependencies that are revealed by multivariate Kendall's τ and ordinal pattern dependence.

Original languageEnglish
Article number104798
JournalJournal of multivariate analysis
Volume186
DOIs
Publication statusPublished - Nov 2021

Keywords

  • Concordance ordering
  • Limit theorems
  • Multivariate dependence
  • Ordinal pattern
  • Ordinal pattern dependence
  • Time series

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