Econometrica: May, 1996, Volume 64, Issue 3

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

https://doi.org/0012-9682(199605)64:3<575:CAANOT>2.0.CO;2-C
p. 575-596

Robin L. Lumsdaine

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.