Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models.

This paper provides a proof of the consistency and asymptotic normality of the quasi-maximum likelihood estimator in GARCH(1,1) and IGARCH(1,1) models. In contrast to the case of a unit root in the conditional mean, the presence of a 'unit root' in the conditional variance does not affect the limiting distribution of the estimators; in both models, estimators are normally distributed. In addition, a consistent estimator of the covariance matrix is available, enabling the use of standard test statistics for inference. Copyright 1996 by The Econometric Society.