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Continuous invertibility and stable QML estimation of the EGARCH(1,1) model

dc.contributor.authorWintenberger, Olivier
dc.date.accessioned2013-01-12T10:22:02Z
dc.date.available2013-01-12T10:22:02Z
dc.date.issued2013
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/10825
dc.language.isoenen
dc.subjectstochastic recurrence equationen
dc.subjectexponential GARCHen
dc.subjectasymptotic normalityen
dc.subjectstrong consistencyen
dc.subjectquasi maximum likelihooden
dc.subjectvolatility modelsen
dc.subjectInvertible modelsen
dc.subject.ddc519en
dc.titleContinuous invertibility and stable QML estimation of the EGARCH(1,1) modelen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherLaboratoire de Finance Assurance (LFA) http://www.crest.fr/content/view/41/100/ Centre de Recherche en Économie et STatistique (CREST);France
dc.description.abstractenWe introduce the notion of continuous invertibility on a compact set for volatility models driven by a Stochastic Recurrence Equation (SRE). We prove the strong consistency of the Quasi Maximum Likelihood Estimator (QMLE) when the optimization procedure is done on a continuously invertible domain. This approach gives for the first time the strong consistency of the QMLE used by Nelson in \cite{nelson:1991} for the EGARCH(1,1) model under explicit but non observable conditions. In practice, we propose to stabilize the QMLE by constraining the optimization procedure to an empirical continuously invertible domain. The new method, called Stable QMLE (SQMLE), is strongly consistent when the observations follow an invertible EGARCH(1,1) model. We also give the asymptotic normality of the SQMLE under additional minimal assumptions.en
dc.relation.isversionofjnlnameScandinavian Journal of Statistics
dc.relation.isversionofjnlvol40
dc.relation.isversionofjnlissue4
dc.relation.isversionofjnldate2013
dc.relation.isversionofjnlpages846-867
dc.relation.isversionofdoihttp://dx.doi.org/10.1111/sjos.12038
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00751706en
dc.relation.isversionofjnlpublisherWiley
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.submittednonen


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