Stationarity and geometric ergodicity of a class of nonlinear ARCH models

Authors
Saïdi, Youssef Zakoïan, Jean-Michel
Citation
Saïdi, Youssef et Zakoïan, Jean-michel, Stationarity and geometric ergodicity of a class of nonlinear ARCH models, Annals of applied probability , 16(4), 2006, pp. 2256-2271
Journal title
Annals of applied probability → ACNP
ISSN journal
10505164
Volume
16
Issue
4
Year of publication
2006
Pages
2256 - 2271
Database
ACNP
SICI code
Abstract
A class of nonlinear ARCH processes is introduced and studied. The existence of a strictly stationary and .-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.