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

Author

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  • Christian Francq

    (Crest)

  • Jean-Michel Zakoïan

    (Crest)

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.

Suggested Citation

  • Christian Francq & Jean-Michel Zakoïan, 2008. "Testing the Nullity of GARCH Coefficients : Correction of the Standard Tests and Relative Efficiency Comparisons," Working Papers 2008-04, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2008-04
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    References listed on IDEAS

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    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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