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

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.