Estimating ARCH Models when the Coefficients are Allowed to be Equal to Zero

Christian Francq () and Jean-Michel Zakoïan
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Christian Francq: CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - GENES - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - GENES - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, IP Paris - Institut Polytechnique de Paris
Jean-Michel Zakoïan: CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - GENES - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - GENES - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique

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Abstract: In order to be consistent with volatility processes, the autoregressive conditional heteroscedastic (ARCH) models are constrained to have nonnegative coefficients. The estimators incorporating these constraints possess non standard asymptotic distributions when the true parameter has zero coefficients. This situation, where the parameter is on the boundary of the parameter space, must be considered to derive the critical values of tests that one or several ARCH coefficients are equal to zero. In this paper we compare the asymptotic theoretical properties, as well as the finite sample behavior, of the main estimation methods in this framework.

Date: 2016-04-03
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Published in Austrian Journal of Statistics, 2016, 37 (1), ⟨10.17713/ajs.v37i1.284⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05417906

DOI: 10.17713/ajs.v37i1.284

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