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

Quasi-maximum likelihood estimation of periodic GARCH processes