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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	2256-2271
Number of pages	16
Journal	Annals of Applied Probability
Volume	16
Issue number	4
DOIs	https://doi.org/10.1214/105051606000000565
Publication status	Published - 1 Jan 2006
Externally published	Yes

Keywords

Ergodicity
GARCH-type models
Markov chains
Nonlinear time series
Threshold models
β-Mixing

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10.1214/105051606000000565

Cite this

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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 - Saïdi, Youssef

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

AN - SCOPUS:33846893175

SN - 1050-5164

VL - 16

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

Abstract

Keywords

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