Testing the Nullity of GARCH Coefficients: Correction of the Standard Tests and Relative Efficiency Comparisons

Christian Francq and Jean-Michel Zakoian

No 2008-04, Working Papers from Center for Research in Economics and Statistics

Abstract: This article is concerned by testing the nullity of coefficients in GARCH models. The problem is nonstandard because the quasi-maximum likelihood estimator is subject to positivity constraints. The paperestablishes the asymptotic null and local alternative distributions of Wald, score, and quasi-likelihood ratiotests. Efficiency comparisons under fixed alternatives are also considered. Two cases of special interestare: (i) tests of the null hypothesis of one coefficient equal to zero and (ii) tests of the null hypothesisof no conditional heteroscedasticity. The results are illustrated by means of simulation experiments. Anempirical application to the Standard & Poor 500 and the CAC40 indexes is proposed.

Pages: 48
Date: 2008
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Related works:
Journal Article: Testing the Nullity of GARCH Coefficients: Correction of the Standard Tests and Relative Efficiency Comparisons (2009)
Working Paper: Testing the nullity of GARCH coefficients: correction of the standard tests and relative efficiency comparisons (2008)
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