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Article Dans Une Revue Statistica Sinica Année : 1994

Probabilistic properties of the Béta-ARCH model

Résumé

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.
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Dates et versions

halshs-00199490 , version 1 (19-12-2007)

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  • HAL Id : halshs-00199490 , version 1

Citer

Jean Diebolt, Dominique Guegan. Probabilistic properties of the Béta-ARCH model. Statistica Sinica, 1994, 4 (1), pp.71-88. ⟨halshs-00199490⟩
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