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Testing Normality : A GMM Approach

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Author Info
BONTEMPS, Christian
MEDDAHI, Nour
Abstract

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 rst class of moment conditions derived by Hansen and Scheinkman (1995) when the random variable of interest is a scalar di usion. 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.

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Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2002-14.

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Length: 49 pages
Date of creation: 2002
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Handle: RePEc:mtl:montde:2002-14

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Keywords: Normality Stein-Hansen-Scheinkman equation GMM Hermite lynomials rameter uncertainty HAC OPG regression

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  1. DUFOUR, Jean-Marie & KHALAF, Lynda & BEAULIEU, Marie-Claude, 2003. "Exact Skewness-Kurtosis Tests for Multivariate Normality and Goodness-of-Fit in Multivariate Regressions with Application to Asset Pricing Models," Cahiers de recherche 07-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ. [Downloadable!]
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