PREDICTION ERRORS IN NONSTATIONARY AUTOREGRESSIONS OF INFINITE ORDER

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.