Forecast Pretesting and Correction

Sometimes it is suggested that end users can improve forecasts by some kind of corrections. At least implicitly, the idea is to use such corrections if the forecasts appear too inaccurate by some criteria. Alternative forecasts can be defined based on whether a preliminary test of forecast usefulness and a subsequent correction has been made. The mean squared errors as some such forecasts are studied using some recent results on inequality pretesting. Uncorrected forecasts are shown to perform reasonably well. The optimal minimax regret critical values for the preliminary tests are fairly high, implying that the hypothesis of forecast usefulness mostly should be accepted and uncorrected forecasts used.