Stationarity and geometric ergodicity of a class of nonlinear ARCH models

Youssef Saidi and Jean-Michel Zakoian

MPRA Paper from University Library of Munich, Germany

Abstract: 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.

Keywords: β-mixing; ergodicity; GARCH-type models; Markov chains; nonlinear time series; threshold models. (search for similar items in EconPapers)
JEL-codes: C1 C22 C5 G1 (search for similar items in EconPapers)
Date: 2006, Revised 2006
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Citations: View citations in EconPapers (3)

Published in The Annals of Applied Probability 16.4(2006): pp. 2256-2271

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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:61988

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