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A Larch Vector Valued Process

Paul Doukhan, Gilles Teyssière and Pablo Winant
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Paul Doukhan: Crest
Gilles Teyssière: Crest

No 2005-49, Working Papers from Centre de Recherche en Economie et Statistique

Abstract: We introduce a vector version of the LARCH(1) equation yielding asimple approach to various models like bilinear or GARCH models. To this aim weprovide an explicit chaotic expansion of a solution for this ARCH(1) equation, andshow the uniqueness of this solution under reasonable conditions. Independent orN-Markov approximations of this process allow to simulate a trajectory or to derivebounds for their weak dependence coefficients as defined by Doukhan and Louhichi(1999). We finally consider a long range dependent version of this model; in thiscase we provide an existence and uniqueness result.

Date: 2005
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