Flexible Multivariate GARCH Modeling for Heteroskedastic Asset Returns with an Asymmetric and Leptokurtic Distribution

Abstract

We propose the S(subscript U)-normal distribution for the estimation of multivariate GARCH models to describe the nonnormality features, such as asymmetry and fat tails, embedded in heteroskedastic asset returns. We show that the S(subscript U)-normal distribution consistently outperforms the normal, Student-t and skewed-t distributions for describing the conditional distribution and the extreme lower and upper tail shapes of daily returns of individual stocks, industry portfolios, and national equity indexes over the sample period of 1989:01 - 2009:12. The exceeding ratio (ER) test for VaR forecasts suggested by Kupiec (1995) shows that the S(subscript U)-normal consistently outperforms the normal, Student-t, skewed-t distributions in multivariate CCC- and DCC-GARCH models. The results indicate that (a) compared to the S(subscript U)-normal, both the normal and Student-t distributions tend to underestimate the tail-thickness around the lower and upper extreme tails, and (b) even with an improvement relative to the normal and Student-t, the skewed-t distribution is still problematic because it tends to overestimate the extreme tails.