Stationarity and geometric ergodicity of a class of nonlinear arch models

• 成果类型: Article
• 署名作者: Saidi, Youssef; Zakoian, Jean-Michel
• 署名单位: Mohammed V University in Rabat; Institut Polytechnique de Paris; ENSAE Paris; Universite de Lille
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051606000000565
• 发表日期: 2006
• 页码: 2256-2271
• 关键词: garch processes; time-series; conditional heteroskedasticity

摘要

A class of nonlinear ARCH processes is introduced and studied. The existence of a strictly stationary and beta-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.