The maximum and minimum of primary forecasts

The purpose of this paper is to suggest that the maximum (or minimum) of a number of primary forecast may make a valuable addition to the forecasting accuracy of a combination of forecasts. Such forecasts are readily computable. Theoretical results are presented for two unbiased forecasts with correlated normally distributed errors, showing that the maximum (minimum) of two forecasts can have a smaller error variance than either of the primary forecasts and the forecast error can have low correlation with the primary errors. Empirical results are obtained for two different sets of forecasts available in the literature, and it is observed that a combination forecast including the maximum and/or minimum has attractive forecasting properties.