Mathematics – Probability
Scientific paper
2007-02-14
Annals of Applied Probability 2006, Vol. 16, No. 4, 2256-2271
Mathematics
Probability
Published at http://dx.doi.org/10.1214/105051606000000565 in the Annals of Applied Probability (http://www.imstat.org/aap/) by
Scientific paper
10.1214/105051606000000565
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.
Sa\"{ı}di Youssef
Zako\"{ı}an Jean-Michel
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