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

Christian Francq () and Zako an, Jean-Michel
Authors registered in the RePEc Author Service: Jean-Michel Zakoian ()

Econometric Theory, 2006, vol. 22, issue 05, pages 815-834

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.

Date: 2006
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