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

In this paper, a necessary and sufficient condition for the existence of the unconditional fourth inoipcnl of the GARCH(p,q ) process is given and also an expression for the moment itself. Furthermore , the autocorrclation 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.