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Inference in GARCH when some coefficients are equal to zero

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  • Christian Francq

    (GREMARS University Lille 3)

  • Jean-Michel Zakoïan

    (GREMARS University Lille 3 and CREST)

Abstract

The asymptotic distribution of the QML estimator for GARCH processes, with coefficients possibly equal to zero, is established. This distribution is the projection of a normal vector distribution onto a convex cone. The results are derived under mild conditions which, for important subclasses, coincide with those made in the recent literature when the coefficients are positive. The QML estimator is shown to converge to its asymptotic distribution locally uniformly. Using these results, we consider the problem of testing that one or several GARCH coefficients are null. The null distribution and the local asymptotic powers of the Wald, score and quasi-likelihood ratio tests are derived. Asymptotic optimality issues are addressed. A set of numerical experiments illustrates the practical relevance of our theoretical results

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Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2006 with number 64.

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Date of creation: 04 Jul 2006
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Handle: RePEc:sce:scecfa:64

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Cited by:
  1. Hafner, Christian M. & Preminger, Arie, 2009. "Asymptotic Theory For A Factor Garch Model," Econometric Theory, Cambridge University Press, vol. 25(02), pages 336-363, April.
  2. Hafner, Christian M. & Preminger, Arie, 2009. "On asymptotic theory for multivariate GARCH models," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2044-2054, October.

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