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Quasi-maximum likelihood estimation of periodic GARCH processes

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arXiv
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Abstract

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.

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