Return interval, dependence structure, and multivariate normality

We focus on changes in the multivariate distribution of index returns stemming purely from varying the return interval, assuming daily to quarterly returns. Whereas long-tailedness is present in daily returns, we find that, in agreement with a well-established idea, univariate return distributions converge to normality as the return interval is lengthened. Such convergence does not occur, however, for multivariate distributions. Using a new method to parametrically model the dependence structure of stock index returns, we show that the persistence of a dependence structure implying negative asymptotic dependence in return series is the reason for the rejection of multivariate normality for low return frequencies.