Some Exact Formulae for Autoregressive Moving Average Processes
给出了有限平稳自回归移动平均过程协方差矩阵的精确逆矩阵公式，并基于此得到近似结果，讨论了在计算算法和两步估计量分布中的应用，还提供了协方差矩阵的行列式公式，对精确最大似然估计有用。
This paper demonstrates that for a finite stationary autoregressive moving average process the inverse of the covariance matrix differs from the matrix of the covariances of the inverse process by a matrix of low rank. The formula for the exact inverse of the covariance matrix of the scalar or multivariate process is provided. We obtain approximations based on this formula and evaluate some of the approximate results in the existing literature. Applications to computational algorithms and to the distributions of two-step estimators are discussed. In addition the paper contains the formula for the determinant of the covariance matrix which is useful in exact maximum likelihood estimation; it also lists the expressions for the autocovariances of scalar autoregressive moving average processes.