Ordinal pattern dependence and multivariate measures of dependence

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.