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.
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He et al. (1999) studied this question.
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