On the Bias in Estimates of Forecast Mean Squared Error
研究了有限观测序列（非季节或季节自回归移动平均过程）的预测问题，识别并分析了预测均方误差通常估计量的四种偏误来源，发现该估计量向下偏误，尤其在平稳或可逆区域边界附近严重，并针对最大似然估计提出了一个减少偏误的替代估计量。
Abstract We examine the forecasting problem for a finite series of observations from either a nonseasonal or a seasonal autoregressive-moving average process. Four sources of bias in the usual estimator of forecast mean squared error are identified and analyzed for particular models using maximum likelihood and least squares parameter estimates. The usual estimator is found to be biased downwards, especially near the boundary of a stationary or invertible region, and the bias is severe for least squares estimators. An alternative estimator is proposed for the maximum likelihood case, which is shown generally to have reduced bias. Key Words: Autoregressive-moving average modelsForecast mean squared errorMaximum likelihood estimation