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MIXING PROPERTIES OF A GENERAL CLASS OF GARCH(1,1) MODELS WITHOUT MOMENT ASSUMPTIONS ON THE OBSERVED PROCESS

Published online by Cambridge University Press:  30 August 2006

Christian Francq  and
Jean-Michel Zakoïan
Christian Francq
Affiliation:
Université Lille 3, GREMARS
Jean-Michel Zakoïan
Affiliation:
Université Lille 3, GREMARS and CREST
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Abstract

We consider general, and possibly nonparametric, GARCH(1,1) processes. First we give conditions for the existence and the uniqueness of stationary ergodic solutions. Then we identify additional conditions for geometric ergodicity. These conditions consist of mild restrictions on the distribution of the latent independent process. No moment assumption is made on the generalized autoregressive conditionally heteroskedastic (GARCH) process. Applications to the asymptotic behavior of sample autocorrelations and to unit-root tests are proposed.This work was supported by INTAS (research project 03-51-3714). The authors gratefully acknowledge the quick and careful reading of the manuscript by Bruce Hansen and three referees. Their detailed comments led to a greatly improved presentation.

Type
Research Article
Information
Econometric Theory , Volume 22 , Issue 5 , October 2006 , pp. 815 - 834
Copyright
© 2006 Cambridge University Press

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