Stationarity and geometric ergodicity of a class of nonlinear ARCH models

Youssef Saïdi; Jean Michel Zakoïan

doi:10.1214/105051606000000565

Stationarity and geometric ergodicity of a class of nonlinear ARCH models

Youssef Saïdi
, Jean Michel Zakoïan

Université Mohammed V
ENSAE

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

A class of nonlinear ARCH processes is introduced and studied. The existence of a strictly stationary and β-mixing solution is established under a mild assumption on the density of the underlying independent process. We give sufficient conditions for the existence of moments. The analysis relies on Markov chain theory. The model generalizes some important features of standard ARCH models and is amenable to further analysis.

langue originale	Anglais
Pages (de - à)	2256-2271
Nombre de pages	16
journal	Annals of Applied Probability
Volume	16
Numéro de publication	4
Les DOIs	https://doi.org/10.1214/105051606000000565
état	Publié - 1 janv. 2006
Modification externe	Oui

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10.1214/105051606000000565

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title = "Stationarity and geometric ergodicity of a class of nonlinear ARCH models",

abstract = "A class of nonlinear ARCH processes is introduced and studied. The existence of a strictly stationary and β-mixing solution is established under a mild assumption on the density of the underlying independent process. We give sufficient conditions for the existence of moments. The analysis relies on Markov chain theory. The model generalizes some important features of standard ARCH models and is amenable to further analysis.",

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AU - Zakoïan, Jean Michel

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N2 - A class of nonlinear ARCH processes is introduced and studied. The existence of a strictly stationary and β-mixing solution is established under a mild assumption on the density of the underlying independent process. We give sufficient conditions for the existence of moments. The analysis relies on Markov chain theory. The model generalizes some important features of standard ARCH models and is amenable to further analysis.

AB - A class of nonlinear ARCH processes is introduced and studied. The existence of a strictly stationary and β-mixing solution is established under a mild assumption on the density of the underlying independent process. We give sufficient conditions for the existence of moments. The analysis relies on Markov chain theory. The model generalizes some important features of standard ARCH models and is amenable to further analysis.

KW - Ergodicity

KW - GARCH-type models

KW - Markov chains

KW - Nonlinear time series

KW - Threshold models

KW - β-Mixing

U2 - 10.1214/105051606000000565

DO - 10.1214/105051606000000565

M3 - Article

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SN - 1050-5164

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SP - 2256

EP - 2271

JO - Annals of Applied Probability

JF - Annals of Applied Probability

IS - 4

ER -

Stationarity and geometric ergodicity of a class of nonlinear ARCH models

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