On Combining Forecasts: Some Extensions and Results

This paper is about the motivation, methodology, and evaluation of combining the forecasts from two or more different models in a "combined" forecast. Granger and Newbold (Granger, C., P. Newbold. 1977. Forecasting Economic Time Series. Academic Press, New York.) have presented this method as one whereby an "optimal" forecast can be obtained. Makridakis and Winkler (1966) and Winkler and Makridakis (Winkler, R., S. Makridakis. 1983. The combination of forecasts: some empirical results. J. Roy. Statist. Soc., Ser. A 146 150--157.) have presented results to support this claim and Mahmoud (Mahmoud, Essam. 1984. Accuracy in forecasting: a survey. J. Forecasting 3 139--159.) has reviewed over 20 articles all claiming that combined forecasts out perform single model forecasts. This paper extends this topic in a number of directions. First a section on motivation provides additional reasons for combining forecasts. Combination problems are then discussed in §2, observations and evaluations of the problem presented are discussed in §3 and concluding remarks are contained in §4.