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A GARCH (1,1) Estimator with (Almost) No Moment Conditions on the Error Term

A least squares estimation approach for the estimation of a GARCH (1,1) model is developed. The asymptotic properties of the estimator are studied given mild regularity conditions, which require only that the error term has a conditional moment of some order. We establish the consistency, asymptotic normality and the law of iterated logarithm for our estimate. The finite sample properties are assessed by means of an extensive simulation study.