Testing the nullity of GARCH coefficients : correction of the standard tests and relative efficiency comparisons
AbstractThis 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.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 16672.
Date of creation: 2008
Date of revision:
Asymptotic efficiency of tests; Boundary; Chi-bar distribution; GARCH model; Quasi Maximum Likelihood Estimation; Local alternatives;
Other versions of this item:
- Francq, Christian & ZakoÃ¯an, Jean-Michel, 2009. "Testing the Nullity of GARCH Coefficients: Correction of the Standard Tests and Relative Efficiency Comparisons," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 313-324.
- 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, Centre de Recherche en Economie et Statistique.
- 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
- C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-08-16 (All new papers)
- NEP-ECM-2009-08-16 (Econometrics)
- NEP-ETS-2009-08-16 (Econometric Time Series)
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