Abstract :
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.
