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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.
J. P. Dickinson (Tue,) studied this question.