Rate of Decay of the Tail Dependence Coefficient for the Skew t Distribution

Abstract

We examine the rate of decay to zero of the tail dependence coefficient of the bivariate skew t distribution which is obtained via normal variance-mean mixture in a case where there is no asymptotic tail dependence. Our result helps to explain the difference in performance in model fitting between this skew t distribution and the one based on the variance mixing of the bivariate skew-normal distribution. This t distribution always displays asymptotic tail dependence, as happens in the symmetric case which is common to both models.