Combining ranked mean value forecasts

A methodology is developed for combining mean value forecasts using not only all the important statistics related to the past performance and the dependence of the individual forecasts, but also a rank ordering of the individual forecasts representing the belief of a decision maker about the future performance of the forecasts. The maximum likelihood combination of the forecasts turns out to be a weighted linear combination of the individual forecasts, where the weights are a function of the rank order of the forecasts, correlation coefficients between the forecasts, and relative entropy information measures between the individual forecasts and the actual values. These weights are assessed once in the most general case and once in a special case where the forecasts are normally distributed. The sensitivity of the weights is also investigated. A sample application of this method for predicting US hog prices is also presented.