QUASI-MAXIMUM LIKELIHOOD ESTIMATION OF SEMI-STRONG GARCH MODELS

This note proves the consistency and asymptotic normality of the quasi-maximum likelihood estimator (QMLE) of the parameters of a generalized autoregressive conditional heteroskedastic (LARCH) model with martingale difference centered squared innovations. The results are obtained under mild conditions and generalize and improve those in Lee and Hansen (1994, Econometric Theory 10, 29-52) for the local QMLE in semistrong GARCH(1, 1) models. In particular, no restrictions on the conditional mean are imposed. Our proofs closely follow those in Francq and Zakoian (2004, Bernoulli 10, 605-637) for independent and identically distributed innovations.