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GARCH (1,1) Models with Exogenously-Driven Volatility: Structure and Estimation

Zakoïan, Jean-Michel; Regnard, Nazim (2008), GARCH (1,1) Models with Exogenously-Driven Volatility: Structure and Estimation. https://basepub.dauphine.fr/handle/123456789/2285

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Type
Document de travail / Working paper
Date
2008
Éditeur
Université Paris-Dauphine
Titre de la collection
Cahiers de la Chaire Finance et Développement Durable
Numéro dans la collection
13
Ville d’édition
Paris
Pages
35
Métadonnées
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Auteur(s)
Zakoïan, Jean-Michel
Regnard, Nazim
Résumé (EN)
This paper considers GARCH(1,1) models in which the time-varying coefficients are functions of the realizations of an exogenous stochastic process. Time series generated by this model are in general nonstationary. Necessary and sufficient conditions are given for the existence of non-explosive solutions, and for the existence of moments of these solutions. The asymptotic properties of the quasi-maximum likelihood estimator are derived under mild assumptions and its finite sample properties are investigated by simulations.
Mots-clés
Quasi-Maximum Likelihood Estimation; Strong Consistency; Time-Varying Models; Asymptotic Normality; Existence of Nonexplosive Solutions; GARCH; Nonstationary Processes
JEL
G13 - Contingent Pricing; Futures Pricing
C13 - Estimation: General
C73 - Stochastic and Dynamic Games; Evolutionary Games; Repeated Games