Assessing the value of Hermite densities for predictive distributions

The empirical behaviour of two Hermitian densities—the Edgeworth asymptotic expansion, and the Gallant and Nychka ( 1987 ) squared transformation—are assessed and compared to Hansen's (1994) asymmetric Student t. The comparison focuses on VaR measurements and overall probability fits. In and out of sample, Berkowitz's ( 2001 ) extended procedures are also implemented. Results are moderately favourable to the Hermitians, supporting the semi‐nonparametric interpretation, and multivariate developments. Copyright © 2009 John Wiley & Sons, Ltd.