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Comptes Rendus Mathématique
Volume 346, n° 3-4
pages 221-224 (février 2008)
Doi : 10.1016/j.crma.2007.11.023
Received : 12 June 2006 ;  accepted : 22 November 2007
On the ARCH model with random coefficients
Sur le modèle ARCH avec des coefficients aléatoires
 

Abdelouahab Bibi , Moussedek Bousseboua
Département de mathématiques, Université Mentouri Constantine, Algeria 

Abstract

In the usual ARCH model, the coefficients have a degenerate distribution, and it is thus constant over realizations. In this Note we introduce the ARCH model, involving coefficients that are independent random variables and may vary over realizations. Conditions for the existence of a stationary solution and conditions ensuring the existence of higher order moments are obtained. The covariance structures of such models are studied. To cite this article: A. Bibi, M. Bousseboua, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The full text of this article is available in PDF format.
Résumé

Contrairement aux modèles ARCH usuels, où les coefficients sont supposés constants, nous considérons dans cette Note, une classe de modèles ARCH à coefficients aléatoires. Les conditions assurant l’existence et l’unicité de solutions stationnaires ainsi que l’existence des moments d’ordre supérieur et la structure de covariance de cette classe de modèles sont étudiées. Pour citer cet article : A. Bibi, M. Bousseboua, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The full text of this article is available in PDF format.


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