Improved methods of combining forecasts

TLDR

Linear combinations of forecasts can outperform individual forecasts, yet the usual practice restricts weights to sum to one. The study evaluates three alternative methods for forming linear forecast combinations. The methods were tested on quarterly hog price forecasts, using both in‑sample and out‑of‑sample data. Adding a constant term and relaxing the unity‑weight constraint yields the best performance, outperforming the conventional weighted‑average approach.

Abstract

Abstract It is well known that a linear combination of forecasts can outperform individual forecasts. The common practice, however, is to obtain a weighted average of forecasts, with the weights adding up to unity. This paper considers three alternative approaches to obtaining linear combinations. It is shown that the best method is to add a constant term and not to constrain the weights to add to unity. These methods are tested with data on forecasts of quarterly hog prices, both within and out of sample. It is demonstrated that the optimum method proposed here is superior to the common practice of letting the weights add up to one.