Should fixed coefficients be reestimated every period for extrapolation?

This paper demonstrates that forecast accuracy is not necessarily improved when fixed coefficient models are sequentially reestimated, and used for prediction, after updating the database with the latest observation(s). This is at variance with the now popular method (see Meese and Rogoff (1983, 1985)) of sequentially reestimating fixed coefficient models for prediction as new data "rolls" in. It is argued that although "rolling" may minimize the variance of predictions for some classes of estimators, "rolling" does not necessarily yield accurate predictions (i.e., predictions that are close to actual data). Minimizing the mean squared prediction errors is a necessary condition for maximizing the probability that a given predictor is more accurate than other predictors. This minimization need not require, and may even exclude, the most recent data. A by-product of the demonstration is that for predictors based on the same sample size, a predictor with smaller variance need not be more accurate than another predictor with a larger variance.