An Asymptotic Expansion in the Garch(1,1) Model

We develop order T-1 asymptotic expansions for the quasi-maximum likelihood estimator (QMLE) and a two step approximate QMLE in the GARCH(1,1) model. We calculate the approximate mean and skewness and hence the Edgeworth-B distribution function. We suggest several methods of bias reduction based on these approximation.