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

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  • Francq, Christian
  • Zakoïan, Jean-Michel

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.

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Bibliographic Info

Article provided by American Statistical Association in its journal Journal of the American Statistical Association.

Volume (Year): 104 (2009)
Issue (Month): 485 ()
Pages: 313-324

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Handle: RePEc:bes:jnlasa:v:104:i:485:y:2009:p:313-324

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References

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Cited by:
  1. Boubacar Mainassara, Y. & Carbon, M. & Francq, C., 2012. "Computing and estimating information matrices of weak ARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 345-361.
  2. Francq, Christian & Horvath, Lajos & Zakoian, Jean-Michel, 2014. "Variance targeting estimation of multivariate GARCH models," MPRA Paper 57794, University Library of Munich, Germany.
  3. Francq, Christian & Zakoian, Jean-Michel, 2014. "Estimating multivariate GARCH and stochastic correlation models equation by equation," MPRA Paper 54250, University Library of Munich, Germany.

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