On the Maximum Likelihood Estimation of the Parameters of a Gaussian Moving Average Process
本文推导了一种求解高斯移动平均过程参数最大似然估计的迭代方法，该方法包含协方差行列式，并与Godolphin的直接表示法在样本量较大时估计结果几乎相同，表明计算精确最大似然估计的额外努力难以证明其合理性。
Several authors have described methods for computing the exact maximum likelihood estimates for the parameters of a Gaussian moving average process. In this paper, an iterative procedure for solving the likelihood equations is derived which includes the covariance determinant. The procedure expresses the estimator of each parameter as a linear combination of a suitably large set of sample serial correlations which has many of the computational advantages of the direct representation of Godolphin (1977, 1978). It is also shown that the two procedures lead to virtually the same set of estimates for sample sizes likely to be encountered in practice. These results imply that the additional effort required to compute exact maximum likelihood estimates is hard to justify. Illustrations of all three procedures are given separately for the moving average model of order one: the iterative procedure for maximizing the exact likelihood function is less stable than the approximate procedures in certain cases.