Inference in multivariate dynamic models with elliptical innovations

Abstract

We obtain analytical expressions for the score of conditionally heteroskedastic dynamic regression models when the conditional distribution is elliptical. We pay special attention not only to the Student t and Kotz distributions, but also to flexible families such as discrete scale mixtures of normals and polynomial expansions. We derive score tests for multivariate normality versus those elliptical distributions. The alternative tests for multivariate normality present power properties that differ substantially under different alternative hypotheses. Finally, we illustrate the small sample performance of the alternative tests through Monte Carlo simulations.

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