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When Simplicity Offers a Benefit, Not a Cost: Closed-Form Estimation of the GARCH(1,1) Model that Enhances the Efficiency of Quasi-Maximum Likelihood
Simple, multi-step estimators are developed for the popular GARCH(1,1) model, where these estimators are either available entirely in closed form or dependent upon a preliminary estimate from, for example, quasi-maximum likelihood. Identification sources to asymmetry in the model's innovations, casting skewness as an instrument in a linear, two-stage least squares estimator. Properties of regular variation coupled with point process theory establish the distributional limits of these estimators as stable, though highly non-Gaussian, with slow convergence rates relative to the ??n-case. Moment ...