Asymmetric Dependence, Tail Dependence, and the Time Interval over Which the Variables Are Measured

The effect of time interval on the linear correlation coefficient between random variables is well documented in the literature. In this paper, we investigate the time interval effect on asymmetric dependence and tail dependence between random variables. We prove that when two random variables are characterized by asymmetric dependence (of any direction), the magnitude of asymmetry in their dependence structure decreases monotonically and approaches zero (i.e., symmetry) as the time interval increases. Also, when two random variables exhibit tail dependence, their tail dependence decreases monotonically and approaches zero (i.e., tail independence) as the time interval increases. Our results hold regardless of whether the variables are both additive, both multiplicative, or one is additive and the other is multiplicative.