  This paper establishes the strong consistency and asymptotic normality of the
quasi-maximum likelihood estimator (QMLE) for a GARCH process with periodically
time-varying parameters. We first give a necessary and sufficient condition for
the existence of a strictly periodically stationary solution for the periodic
GARCH (P-GARCH) equation. As a result, it is shown that the moment of some
positive order of the P-GARCH solution is finite, under which we prove the
strong consistency and asymptotic normality (CAN) of the QMLE without any
condition on the moments of the underlying process.
