Quasi-maximum likelihood estimation of periodic GARCH and periodic ARMA-GARCH processes |
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Authors: | Abdelhakim Aknouche and Abdelouahab Bibi |
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Affiliation: | University of Sciences and Technology Houari Boumediene and University Mentouri |
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Abstract: | Abstract. This article establishes the strong consistency and asymptotic normality (CAN) of the quasi-maximum likelihood estimator (QMLE) for generalized autoregressive conditionally heteroscedastic (GARCH) and autoregressive moving-average (ARMA)-GARCH processes with periodically time-varying parameters. We first give a necessary and sufficient condition for the existence of a strictly periodically stationary solution of the periodic GARCH (PGARCH) equation. As a result, it is shown that the moment of some positive order of the PGARCH solution is finite, under which we prove the strong consistency and asymptotic normality of the QMLE for a PGARCH process without any condition on its moments and for a periodic ARMA-GARCH (PARMA-PGARCH) under mild conditions. |
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Keywords: | Periodic GARCH processes periodic ARMA-GARCH models strict periodic stationarity periodic ergodicity strong consistency asymptotic normality |
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