Distributional Tests in Multivariate Dynamic Models with Normal and Student T Innovations
64 Pages Posted: 21 Dec 2009 Last revised: 30 Jul 2010
Date Written: December 21, 2009
We derive Lagrange Multiplier and Likelihood Ratio specifi cation tests for the null hypotheses of multivariate normal and Student t innovations using the Generalised Hyperbolic distribution as our alternative hypothesis. We decompose the corresponding Lagrange Multiplier-type tests into skewness and kurtosis components, from which we obtain more powerful one-sided Kuhn-Tucker versions that are equivalent to the Likelihood Ratio test, whose asymptotic distribution we provide. We conduct detailed Monte Carlo exercises to study our proposed tests in finite samples. Finally, we present an empirical application to ten US sectoral stock returns, which indicates that their conditional distribution is mildly asymmetric and strongly leptokurtic.
Keywords: Bootstrap, Inequality Constraints, Kurtosis, Normality Tests, Skewness, Supremum Test, Underidentifed parameters
JEL Classification: C12, C52, C32
Suggested Citation: Suggested Citation