PREDICTION ERRORS IN NONSTATIONARY AUTOREGRESSIONS OF INFINITE ORDER
研究了无限阶非平稳自回归过程的预测问题，给出了最小二乘预测均方误差的渐近表达式，揭示了非平稳性、模型复杂度和模型误设的影响，为后续模型选择提供理论基础。
Assume that observations are generated from nonstationary autoregressive (AR) processes of infinite order. We adopt a finite-order approximation model to predict future observations and obtain an asymptotic expression for the mean-squared prediction error (MSPE) of the least squares predictor. This expression provides the first exact assessment of the impacts of nonstationarity, model complexity, and model misspecification on the corresponding MSPE. It not only provides a deeper understanding of the least squares predictors in nonstationary time series, but also forms the theoretical foundation for a companion paper by the same authors, which obtains asymptotically efficient order selection in nonstationary AR processes of possibly infinite order.