Stationarity and geometric ergodicity of a class of nonlinear ARCH models

Details Stationarity and geometric ergodicity of a class of nonlinear ARCH models Stationarity and geometric ergodicity of a class of nonlinear ARCH models

2007-02-14

arxiv.org/abs/math/0702419v1

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.

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