Properties of the Autocorrelation Function of Squared Observations for Second Order GARCH Processes under Two Sets of Parameter Constraints

Nonnegativety constraints on the parameters of the GARCH (p, Q) model may be relaxed without giving up the requirement of the conditional variance remaining non- negative with probability one. This paper looks into the consequences of adopting these less severe constraints in the GARCH (2,2) case and its two second-order special cases, GARCH (2,1) and GARCH (1,2). This is done by comparing the autocorrelation function of squared observations under these two sets of constraints. The less severe constraints allow more flexibility in the shape of the autocorrelation function than the constraints restricting the parameters to be nonnegative. The theory is illustrated by an empirical example.