Generalized Gaussian quasi-maximum likelihood estimation for most common time series

Yakoub Boularouk and Jean-Marc Bardet

Communications in Statistics - Theory and Methods, 2024, vol. 53, issue 4, 1459-1478

Abstract: We propose a consistent estimator for the parameter shape of the generalized gaussian noise in the class of causal time series including ARMA, AR(∞), GARCH, ARCH(∞), ARMA-GARCH, APARCH, ARMA-APARCH,…, processes. As well we prove the consistency and the asymptotic normality of the Generalized Gaussian Quasi-Maximum Likelihood Estimator (GGQMLE) for this class of causal time series with any fixed parameter shape, which over-performs the efficiency of the classical Gaussian QMLE. Monte Carlo experiments confirm that the accuracy of the proposed estimators.

Date: 2024
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DOI: 10.1080/03610926.2022.2103148

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