NM–QELE for ARMA–GARCH models with non-Gaussian innovations

Abstract

Although the quasi maximum likelihood estimator based on Gaussian density (Gaussian-QMLE) is widely used to estimate parameters in ARMA models with GARCH innovations (ARMA–GARCH models), it does not perform successfully when error distribution of ARMA–GARCH models is either skewed or leptokurtic. In order to circumvent such defects, Lee and Lee (submitted for publication) proposed the quasi maximum estimated-likelihood estimator using Gaussian mixture-based likelihood (NM–QELE) for GARCH models. In this paper, we adopt the NM–QELE method for estimating parameters in ARMA–GARCH models and demonstrate the validity of NM–QELE by verifying its consistency.