Modeling coskewness with zero correlation and correlation with zero coskewness

Carole Bernard, Jinghui Chen and Steven Vanduffel

Abstract

This paper shows that care needs to be taken when making statements on potential links between correlation and coskewness. Specifically, we show that it is possible to observe any possible values of coskewness among symmetric random variables but zero pairwise correlations of these variables. Conversely, it is also possible to have zero coskewness and any level of correlation. We then generalize this result to the case of arbitrary marginal distributions, showing the absence of a general link between rank correlation and standardized rank coskewness.