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DOI: 10.1080/02331880601107064

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Statistics A Journal of Theoretical and Applied Statistics 41, 1 (2007) 31-45

ARCH type bilinear weakly dependent models

Paul Doukhan 1, 2, 3, Hélène Madré 1, Mathieu Rosenbaum 1, 4

(2007-02)

Giraitis and Surgailis (2002) introduced $ARCH$-type bilinear models for their specific long range dependence properties. We rather consider weak dependence properties of these models. The computation of mixing coefficients for such models does not look as an accessible objective. So, we resort to the notion of weak dependence introduced by Doukhan and Louhichi (1999), whose use seems more relevant here. The decay rate of the weak dependence coefficients sequence is established under different specifications of the model coefficients. This implies various limit theorems and asymptotics for statistical procedures. We also derive bounds for the joint densities of this model in the case of regular inputs.

1:	Centre de Recherche en Économie et Statistique (CREST)
	INSEE – École Nationale de la Statistique et de l'Administration Économique
2:	Centre d'économie de la Sorbonne (CES)
	CNRS : UMR8174 – Université Paris I - Panthéon-Sorbonne
3:	Statistique Appliquée et MOdélisation Stochastique (SAMOS)
	Université Paris I - Panthéon-Sorbonne
4:	Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA)
	Université Paris-Est Marne-la-Vallée (UPEMLV) – Université Paris-Est Créteil Val-de-Marne (UPEC) – CNRS : UMR8050 – Fédération de Recherche Bézout

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Mathematics/Statistics

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From: Paul Doukhan <>

Submitted on: Thursday, 3 May 2007 11:23:40

Updated on: Thursday, 27 September 2007 18:03:59