Quasi-maximum likelihood estimation of GARCH with student distributed noise

Abstract

We establish the strong consistency and asymptotic normality of the quasi-maximum likelihood estimator (QMLE) for a GARCH process with Student marginal distribution. We first give a necessary and sufficient condition for the existence of a strictly stationary solution for the GARCH equation. Numerical simulations elaboreted the confirmation of the consistency of estimate.

Keywords:

• Asymptotic normality
• consistency
• GARCH process