Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/92702
Authors: 
Ling, Shiqing
MacAleer, Michael
Year of Publication: 
2001
Series/Report no.: 
ISER Discussion Paper, Institute of Social and Economic Research, Osaka University 535
Abstract: 
This paper investigates some structural properties of a family of GARCH processes. A simple sufficient condition for the existence of the αδ-order stationary solution of the processes is derived, where α element of (0, 1] and δ > 0. The solution is strictly stationary and ergodic, and the causal expansion of the family of GARCH processes is also established. Furthermore, the necessary and sufficient condition for the existence of the moments is obtained. The technique used in this paper for the moment conditions is different to that used in He and Terasvirta (1999a), and avoids the assumption that the process started at some finite value infinitely many periods ago. Moreover, the conditions for the strict stationarity of the model and the existence of its moments are simple to check and should prove useful in practice.
Subjects: 
Ergodicity
Existence of moments
GARCH
Stationarity
JEL: 
C22
C51
Document Type: 
Working Paper

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