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Testing the nullity of GARCH coefficients: correction of the standard tests and relative efficiency comparisons

Christian Francq and Jean-Michel Zakoian

MPRA Paper from University Library of Munich, Germany

Abstract: This article is concerned by testing the nullity of coefficients in GARCH models. The problem is non standard because the quasi-maximum likelihood estimator is subject to positivity constraints. The paper establishes the asymptotic null and local alternative distributions of Wald, score, and quasi-likelihood ratio tests. Efficiency comparisons under fixed alternatives are also considered. Two cases of special interest are: (i) tests of the null hypothesis of one coefficient equal to zero and (ii) tests of the null hypothesis of no conditional heteroscedasticity. Finally, the proposed approach is used in the analysis of a set of financial data and leads to reconsider the preeminence of GARCH(1,1) among GARCH models.

Keywords: Asymptotic efficiency of tests; Boundary; Chi-bar distribution; GARCH model; Quasi Maximum Likelihood Estimation; Local alternatives (search for similar items in EconPapers)
JEL-codes: C01 C12 C22 (search for similar items in EconPapers)
Date: 2008
New Economics Papers: this item is included in nep-ecm and nep-ets
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Related works:
Journal Article: Testing the Nullity of GARCH Coefficients: Correction of the Standard Tests and Relative Efficiency Comparisons (2009) Downloads
Working Paper: Testing the Nullity of GARCH Coefficients: Correction of the Standard Tests and Relative Efficiency Comparisons (2008) Downloads
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