Testing Normality : A GMM Approach

In this paper, we consider testing marginal normal distributional assumptions. More precisely, we propose tests based on moment conditions implied by normality. These moment conditions are known as the Stein (1972) equations. They coincide with the first class of moment conditions derived by Hansen and Scheinkman (1995) when the random variable of interest is a scalar diffusion. Among other examples, Stein equation implies that the mean of Hermite polynomials is zero. The GMM approach we adopted is well suited for two reasons. It allows us to study in detail the parameter uncertainty problem, i.e., when the tests depend on unknown parameters that have to be estimated. In particular, we characterize the moment conditions that are robust against parameter uncertainty and show that Hermite polynomials are special examples. This is the main contribution of the paper. The second reason for using GMM is that our tests are also valid for time series. In this case, we adopt a Heteroskedastic-Autocorrelation-Consistent approach to estimate the weighting matrix when the dependence of the data is unspecified. We also make a theoretical comparison of our tests with Jarque and Bera (1980) and OPG regression tests of Davidson and MacKinnon (1993). Finite sample properties of our tests are derived through a comprehensive Monte Carlo study. Finally, three applications to GARCH and realized volatility models are presented.

Statistiques 2004-2005 et 2005-2006 des bibliothèques universitaires et de recherche au Canada

Commentaire de M. Timothy Mark Executive Director / Directeur général Canadian Association of Research Libraries / Association des bibliothèques de recherche du Canada. Room / Pièce 239. 65 University Private / 65 université privé. Ottawa ON K1N 9A5 Tel / tél : 613.562.5385 Fax / téléc : 613.562.5195 www.carl-abrc.ca «J'ai lu avec beaucoup d'intêret et d'enthousiasme l'article Statistiques 2004-2005 et 2005 des bibliothèques universitaires et de recherche au Canada qui vient de paraître dans la revue Documentation et bibliothèques. Permettez-moi de vous féliciter, madame, sur un article qui démontre un haut niveau de recherche et d'analyse. A titre d'intérêt, l'article sera mentionné dans notre publication hebdomadaire "Cyberavis" demain. ( Prière de consulter le site web de l'ABRC). Recevez, madame, mes salutations less meilleures. Tim Mark. (Courriel daté du 14 février 2008) ==========================================