Some Comments on the Combination of Forecasts

Abstract

This paper examines some of the theoretical implications of combining forecasts using a minimum variance criterion. In particular, the derivation of the exact expression for the minimum variance weight vector is provided, together with a proof that the error variance of the composite forecast is no greater than that of any of the component forecasts. A detailed examination is made of the probability distributions of the weight estimators, and an explanation is given for the occurrence of negative weights.