  In this article asymptotic expressions for the final prediction error (FPE)
and the accumulated prediction error (APE) of the least squares predictor are
obtained in regression models with nonstationary regressors. It is shown that
the term of order $1/n$ in FPE and the term of order $\log n$ in APE share the
same constant, where $n$ is the sample size. Since the model includes the
random walk model as a special case, these asymptotic expressions extend some
of the results in Wei (1987) and Ing (2001). In addition, we also show that
while the FPE of the least squares predictor is not affected by the
contemporary correlation between the innovations in input and output variables,
the mean squared error of the least squares estimate does vary with this
correlation.
