On the ARCH model with random coefficients

Abdelouahab Bibi; Moussedek Bousseboua

doi:10.1016/j.crma.2007.11.023

Statistics/Probability Theory

On the ARCH model with random coefficients

Presented by: Paul Deheuvels

Abdelouahab Bibi ¹; Moussedek Bousseboua ¹

¹ Département de mathématiques, Université Mentouri Constantine, Algeria

Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 221-224.

Abstract
Résumé

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.

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.

Received: 2006-06-12
Accepted: 2007-11-22
Published online: 2008-02-01

DOI: 10.1016/j.crma.2007.11.023

Author's affiliations:

Abdelouahab Bibi ¹; Moussedek Bousseboua ¹

¹ Département de mathématiques, Université Mentouri Constantine, Algeria

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     title = {On the {ARCH} model with random coefficients},
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Abdelouahab Bibi; Moussedek Bousseboua. On the ARCH model with random coefficients. Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 221-224. doi : 10.1016/j.crma.2007.11.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.11.023/

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