Properties of Predictors for Autoregressive Time Series
研究了p阶自回归过程第(n+s)个观测值的预测，得到了平稳正态过程中预测误差均方的条件表达式，并证明了通常的回归方差公式及其推广能一致估计最小二乘预测的均方误差。
Abstract The prediction of the (n + s)th observation of the pth order autoregressive process is investigated. The mean square of the predictor error through terms of order n —1, conditional on Yn, Y n — 1, …, Y n — p + 1, is obtained for the stationary normal process. The mean squared error expression is similar to the usual regression formula for the variance of the predictor error. The usual regression formula for the estimated variance of a predictor error and its generalization to s-period prediction is shown to provide a consistent estimator of the mean squared error of the least squares predictor for both stationary and non-stationary processes.