A CLOSED-FORM ESTIMATOR FOR THE GARCH(1,1) MODEL
提出GARCH(1,1)模型的闭式估计量，无需数值优化，推导了渐近性质，并证明以它为起点的牛顿-拉夫森迭代可达到与QMLE相同的渐近分布。
We propose a closed-form estimator for the linear GARCH(1,1) model. The estimator has the advantage over the often used quasi-maximum likelihood estimator (QMLE) that it can be easily implemented and does not require the use of any numerical optimization procedures or the choice of initial values of the conditional variance process. We derive the asymptotic properties of the estimator, showing T(κ−1)/κ-consistency for some κ ∈ (1,2) when the fourth moment exists and -asymptotic normality when the eighth moment exists. We demonstrate that a finite number of Newton–Raphson iterations using our estimator as starting point will yield asymptotically the same distribution as the QMLE when the fourth moment exists. A simulation study confirms our theoretical results.The first author's research was supported by the Shoemaker Foundation. The second author's research was supported by the Economic and Social Science Research Council of the United Kingdom.