In a full rank normal regression model, the existence of an unbiased estimate of the distribution associated to any "future" observation is studied. A necessary and sufficient condition in terms of the point at which the "future" observation will be taken is given for such an estimate to exist. This criterion is introduced to consider the validity of extrapolation.
"On a Criterion for Extrapolation in Normal Regression." Ann. Statist. 3 (1) 219 - 222, January, 1975. https://doi.org/10.1214/aos/1176343010