Pseudo maximum likelihood estimation of the univariate GARCH (2,2) and asymptotic normality under dependent innovations

ABSTRACT

In this paper, we first consider the pseudo maximum likelihood estimation of the univariate GARCH (2,2) model and derive the underlying estimator. Then, we make use of the technique of martingales to establish the asymptotic normality of the pseudo-maximum likelihood estimator (PMLE) of the univariate GARCH (2,2) model. Contrary to previous approaches encountered in the statistical literature, the pseudo-likelihood function uses the general form of the density laws of the quadratic exponential family.

KEYWORDS:

• Asymptotic normality
• Pseudo-maximum likelihood estimator
• Quadratic exponential family
• Univariate GARCH (2,2) model.

AMS CLASSIFICATION CODE:

• 60G