Robin L. Lumsdaine, Consistency and Asymptotic Normality of the Quasi-Maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models, Econometrica, Vol. 64, No. 3 (May, 1996), pp. 575-596
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Robin L. Lumsdaine (1996) studied this question.
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