Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator
研究了GARCH(1,1)模型拟极大似然估计量的抽样性质，允许扰动项非高斯、非独立，且过程可整合或轻微爆炸，证明了估计的一致性和渐近正态性。
This paper investigates the sampling behavior of the quasi-maximum likelihood estimator of the Gaussian GARCH(1,1) model. The rescaled variable (the ratio of the disturbance to the conditional standard deviation) is not required to be Gaussian nor independent over time, in contrast to the current literature. The GARCH process may be integrated (α + β = 1), or even mildly explosive (α + β > 1). A bounded conditional fourth moment of the rescaled variable is sufficient for the results. Consistent estimation and asymptotic normality are demonstrated, as well as consistent estimation of the asymptotic covariance matrix.