A note on mean squared prediction error under the unit root model with deterministic trend

Assume that observations are generated from the first-order autoregressive (AR) model with linear time trend and the unknown model coefficients are estimated by least squares. This article develops an asymptotic expression for the mean squared prediction error (MSPE) of the least squares predictor in the presence of a unit root. As a by-product, we also obtain a connection between the MSPE and the growth rate of the Fisher information. The key technical tool used to derive these results is the negative moment bound for the minimum eigenvalue of the normalized Fisher information matrix.