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FOURTH MOMENT STRUCTURE OF THE GARCH(p,q) PROCESS

Published online by Cambridge University Press:  01 December 1999

Changli He  and
Timo Teräsvirta
Changli He
Affiliation:
Stockholm School of Economics
Timo Teräsvirta
Affiliation:
Stockholm School of Economics
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Abstract

In this paper, a necessary and sufficient condition for the existence of the unconditional fourth moment of the GARCH(p,q) process is given and also an expression for the moment itself. Furthermore, the autocorrelation function of the centered and squared observations of this process is derived. The statistical theory is further illustrated by a few special cases such as the GARCH(2,2) process and the ARCH(q) process.

Type
Research Article
Information
Econometric Theory , Volume 15 , Issue 6 , December 1999 , pp. 824 - 846
Copyright
© 1999 Cambridge University Press

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