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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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.

Article information

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

Dates
First available in Project Euclid: 17 January 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1169065224

Digital Object Identifier
doi:10.1214/105051606000000565

Mathematical Reviews number (MathSciNet)
MR2288721

Zentralblatt MATH identifier
1121.60033

Subjects
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]

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

Citation

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. https://projecteuclid.org/euclid.aoap/1169065224


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