no. 21-22
Statistics
A conditional least squares approach to PGARCH and PARMA–PGARCH time series estimation
[L'estimateur des moindres carrés conditionnels dans les modèles PGARCH et PARMA–PGARCH]

Présenté par : Paul Deheuvels

Bibi, Abdelouahab1 ; Lescheb, Ines1
1 Département de Mathématiques, Université Mentouri Constantine, Algeria
Comptes Rendus. Mathématique, Tome 348 (2010) no. 21-22, pp. 1211-1216.

Dans cette Note, on étudie l'estimateur des moindres carrés conditionnels (CLS) dans les modèles GARCH périodiques (PGARCH) dont le carré centré des innovations est une différence de martingale. Cette approche est étendue aux modèles PARMA–PGARCH. La consistance forte et la normalité asymptotique ont été établies.

In this Note, a conditional least squares (CLS) estimates for periodic GARCH (PGARCH) models with martingale difference centered squared innovations is developed. The approach is extended to the PARMA–PGARCH models. We establish the strong consistency and the asymptotic normality for our estimate.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.10.019
Bibi, Abdelouahab 1 ; Lescheb, Ines 1

1 Département de Mathématiques, Université Mentouri Constantine, Algeria 
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Bibi, Abdelouahab; Lescheb, Ines. A conditional least squares approach to PGARCH and PARMA–PGARCH time series estimation. Comptes Rendus. Mathématique, Tome 348 (2010) no. 21-22, pp. 1211-1216. doi : 10.1016/j.crma.2010.10.019. http://www.numdam.org/articles/10.1016/j.crma.2010.10.019/

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[3] Bibi, A.; Lescheb, I. Strong consistency and asymptotic normality of least squares estimators for PGARCH and PARMA–PGARCH, Statist. Probab. Lett., Volume 80 (2010), pp. 1532-1542

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