ON THE TAIL BEHAVIORS OF A FAMILY OF GARCH PROCESSES

Ji-Chun Liu

Econometric Theory, 2006, vol. 22, issue 5, 852-862

Abstract: In this paper, some structural properties of a family of generalized autoregressive conditionally heteroskedastic (GARCH) processes are considered. First, a sufficient and necessary condition for the strict stationarity of this family of GARCH processes is given. Second, some simple conditions for the existence of the moments of the family of GARCH processes are also derived. Finally, we describe the tail of the marginal distribution of the family of GARCH processes.I am grateful to Bruce E. Hansen and an anonymous referee for helpful comments on the initial version.

Date: 2006
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