Probabilistic properties of the Béta-ARCH model

Jean Diebolt and Dominique Guegan (dominique.guegan@univ-paris1.fr)
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Jean Diebolt: UPMC - Université Pierre et Marie Curie - Paris 6
Dominique Guegan: CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique

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Abstract: In the present paper we consider the main probabilistic properties of the Markov chain Xt=aXt-1+[a0+(a1+(Xt-1)++a1-(Xt-1) -)2β]1/2εt , that we call the β-ARCH model. We examine the inevitability, irreducibility, Harris recurrence, ergodicity, geometric ergodicity, α-mixing, existence and nonexistence of finite moments and exponential moments of some order and sharp upper bounds for the tails of the stationary density of the process {Xt} in terms of the common density of the εt's.

Keywords: Markov chain; invertibility; ergodicity; mixing; tail of the stationary density; ARCH model; nonlinear time series; autoregressive.; autoregressive (search for similar items in EconPapers)
Date: 1994-01
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Citations: View citations in EconPapers (1)

Published in Statistica Sinica, 1994, 4 (1), pp.71-88

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-00199490

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