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...

Existing specification tests for conditional heteroskedasticity are derived under the assumption that the density of the innovation, or standardized error, is Gaussian, despite the fact that many recent empirical studies provide evidence that this density is not Gaussian. We obtain specification...