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 normalit y 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 model s, estimators are normally distributed. In addition, a consistent esti mator of the covariance matrix is available, enabling the use of stand ard test statistics for inference.