The Annals of Applied Probability

Stationarity and geometric ergodicity of a class of nonlinear ARCH models

Youssef Saïdi and Jean-Michel Zakoïan

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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.

Article information

Ann. Appl. Probab., Volume 16, Number 4 (2006), 2256-2271.

First available in Project Euclid: 17 January 2007

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Zentralblatt MATH identifier

Primary: 60G10: Stationary processes 60J05: Discrete-time Markov processes on general state spaces
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 91B84: Economic time series analysis [See also 62M10]

β-mixing ergodicity GARCH-type models Markov chains nonlinear time series threshold models


Saïdi, Youssef; Zakoïan, Jean-Michel. Stationarity and geometric ergodicity of a class of nonlinear ARCH models. Ann. Appl. Probab. 16 (2006), no. 4, 2256--2271. doi:10.1214/105051606000000565.

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