Properties of Predictors in Overdifferenced Nearly Nonstationary Autoregression
分析了过度差分一个最大根接近1的平稳AR(p+1)过程的影响，发现近非平稳时过度差分模型ARIMA(p,1,0)的估计量是根T一致的，且因简约性其预测均方误差更小，但优势取决于剩余根、预测期和过程均值。
We analyze the effect of overdifferencing a stationary AR( p +1) process whose largest root is near unity. It is found that, if the process is nearly nonstationary, the estimators of the overdifferenced model ARIMA( p ,1,0) are root‐ T consistent. It is also found that this misspecified ARIMA( p ,1,0) has lower predictive mean squared error, to terms of small order, than the properly specified AR( p +1) model due to its parsimony. The advantage of the overdifferenced predictor depends on the remaining roots, the prediction horizon and the mean of the process.