  A crucial input into causal inference is the imputed counterfactual outcome.
Imputation error can arise because of sampling uncertainty from estimating the
prediction model using the untreated observations, or from out-of-sample
information not captured by the model. While the literature has focused on
sampling uncertainty, it vanishes with the sample size. Often overlooked is the
possibility that the out-of-sample error can be informative about the missing
counterfactual outcome if it is mutually or serially correlated. Motivated by
the best linear unbiased predictor (\blup) of \citet{goldberger:62} in a time
series setting, we propose an improved predictor of potential outcome when the
errors are correlated. The proposed \pup\; is practical as it is not restricted
to linear models, can be used with consistent estimators already developed, and
improves mean-squared error for a large class of strong mixing error processes.
Ignoring predictability in the errors can distort conditional inference.
However, the precise impact will depend on the choice of estimator as well as
the realized values of the residuals.
