ASYMPTOTIC THEORY FOR THE GARCH(1,1) QUASI-MAXIMUM LIKELIHOOD ESTIMATOR

This Paper investigates the sampling behavior of the quasi-maximum lik elihood estimator of the Gaussian GARCH(1,1) model. The rescaled varia ble (the ratio of the disturbance to the conditional standard deviatio n) is not required to be Gaussian nor independent over time, in contra st to the current literature. The GARCH process may be integrated (alp ha + beta = 1), or even mildly explosive (alpha + beta > 1). A bounded conditional fourth moment of the rescaled variable is sufficient for the results. Consistent estimation and asymptotic normality are demons trated, as well as consistent estimation of the asymptotic covariance matrix.