On the sign of the optimal combining weights under the error‐variance minimizing criterion

Abstract

Building on the well-known measure of the optimal combining weights under the error-variance minimizing criterion, this note has extended the sign-determination rule to the case of combining more than two competing forecasts. The algebraic rule derived provides a quick way to check the sign of each combining weight without directly comparing the correlation and variances of individual forecasting errors.

On the Distribution of the Inverted Linear Compound of Dependent F-Variates and its Application to the Combination of Forecasts

“…Among methods of combining forecasts (Liang, 1992), the formula (2) proposed by Reid (1969), Dickinson (1973) or Newbold & Granger (1974) is perhaps the single most extensively used measure of the optimal weights. Despite the popularity of this formula, very little is known about the sampling properties of its estimator.…”