arXiv math/07024192007-02-14math.PR

Stationarity and geometric ergodicity of a class of nonlinear ARCH models

Youssef Sa\"{ı}di, Jean-Michel Zako\"{ı}an

备注：: Published at http://dx.doi.org/10.1214/105051606000000565 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
发表信息：: Annals of Applied Probability 2006, Vol. 16, No. 4, 2256-2271
DOI：: 10.1214/105051606000000565

英文摘要：

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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