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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
  • Zakoian, 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

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 16672.

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Date of creation: 2008
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Handle: RePEc:pra:mprapa:16672

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Keywords: Asymptotic efficiency of tests; Boundary; Chi-bar distribution; GARCH model; Quasi Maximum Likelihood Estimation; Local alternatives;

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  1. Donald W.K. Andrews, 1999. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1229, Cowles Foundation for Research in Economics, Yale University.
  2. Drost, F.C. & Klaassen, C.A.J., 1997. "Efficient estimation in semiparametric GARCH models," Open Access publications from Tilburg University urn:nbn:nl:ui:12-74146, Tilburg University.
  3. Wolak, Frank A., 1989. "Local and Global Testing of Linear and Nonlinear Inequality Constraints in Nonlinear Econometric Models," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 5(01), pages 1-35, April.
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  12. Francq, Christian & Zakoian, Jean-Michel, 2007. "Quasi-maximum likelihood estimation in GARCH processes when some coefficients are equal to zero," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 117(9), pages 1265-1284, September.
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  14. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 31(3), pages 307-327, April.
  15. Francq, Christian & Zako an, Jean-Michel, 2006. "Mixing Properties Of A General Class Of Garch(1,1) Models Without Moment Assumptions On The Observed Process," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 22(05), pages 815-834, October.
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  20. Claudia Kl�ppelberg & Ross A. Maller & Mark van de Vyver & Derick Wee, 2002. "Testing for reduction to random walk in autoregressive conditional heteroskedasticity models," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 5(2), pages 387-416, 06.
  21. Ling, Shiqing, 2007. "Self-weighted and local quasi-maximum likelihood estimators for ARMA-GARCH/IGARCH models," Journal of Econometrics, Elsevier, Elsevier, vol. 140(2), pages 849-873, October.
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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, Elsevier, vol. 56(2), pages 345-361.
  2. Francq, Christian & Zakoian, Jean-Michel, 2014. "Estimating multivariate GARCH and stochastic correlation models equation by equation," MPRA Paper 54250, University Library of Munich, Germany.
  3. Francq, Christian & Horvath, Lajos & Zakoian, Jean-Michel, 2014. "Variance targeting estimation of multivariate GARCH models," MPRA Paper 57794, University Library of Munich, Germany.

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