Testing Normality: A GMM Approach

Christian Bontemps and Nour Meddahi

Cahiers de recherche from Universite de Montreal, Departement de sciences economiques

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.

Keywords: Normality; Stein-Hansen-Scheinkman equation; GMM; Hermite lynomials; rameter uncertainty; HAC; OPG regression (search for similar items in EconPapers)
Pages: 49 pages
Date: 2002
New Economics Papers: this item is included in nep-ecm and nep-ets
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Citations: View citations in EconPapers (5)

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http://hdl.handle.net/1866/485 (application/pdf)

Related works:
Journal Article: Testing normality: a GMM approach (2005)
Working Paper: Testing normality: a GMM approach (2005)
Working Paper: Testing Normality: A GMM Approach (2002)
Working Paper: TESTING NORMALITY: A GMM APPROACH (2002)
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Persistent link: https://EconPapers.repec.org/RePEc:mtl:montde:2002-14

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