Pseudo maximum likelihood estimation and asymptotic results of the GARCH (1, 2) Model under dependent innovations

Abstract

This paper deals with the pseudo maximum likelihood estimation of a GARCH (1,2) model under two reasonably weak, realistic and tractable assumptions: the innovations are dependent albeit conditionally independent, and belong to the quadratic exponential family, which contains several standard distributions. More specifically, the paper derives the consistency and asymptotic normality of the pseudo maximum likelihood estimator (PLME hereafter) under some regularity conditions by means of martingale techniques. Finally, extensive Monte Carlo experiments are conducted to examine the finite sample performance of the proposed PMLE.

KEYWORDS:

• Asymptotic normality
• Consistency
• Dependent innovations
• GARCH model
• Monte Carlo results
• Pseudo-maximum likelihood
• Quadratic exponential families

AMS classification codes:

• 60G