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. (Journal of Multivariate Analysis 123, 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 Betken et al. (Journal of Multivariate Analysis 186, 2021). Furthermore we show that ordinal pattern dependence satisfies a slightly modified set of axioms.

翻译：序数模式依赖性被引入以捕捉两个时间序列之间的协同单调行为。该概念具有依赖度量应具备的若干直观特征。以往认为序数模式依赖性满足Grothe等人（Journal of Multivariate Analysis 123, 2014）提出的多元相依性度量公理。本文指出这一结论并不成立，并揭示了Betken等人（Journal of Multivariate Analysis 186, 2021）论文中的错误。进一步证明序数模式依赖性满足一组经适度修正的公理体系。