Pseudo maximum-likelihood estimation of the univariate GARCH (1,1) and asymptotic properties

ABSTRACT

One provides in this paper the pseudo-likelihood estimator (PMLE) and asymptotic theory for the GARCH (1,1) process. Strong consistency of the pseudo-maximum-likelihood estimator (MLE) is established by appealing to conditions given in Jeantheau (1998) concerning the existence of a stationary and ergodic solution to the multivariate GARCH (p, q) process. One proves the asymptotic normality of the PMLE by appealing to martingales' techniques.

KEYWORDS:

• pseudo–maximum-likelihood
• estimation—strong consistency—GARCH (1,1)
• asymptotic normality
• Martingales' techniques

MATHEMATICS SUBJECT CLASSIFICATION:

• 60G