A preference-based method for forecast combination

Determing the best combination of competing forecasts is a problem that has been approached primarily from a statistical viewpoint. An alternative method is presented which is based on two behavioral considerations. First, the major consumers of forecasts, decision makers and managers exhibit a form of risk/regret whereby they assign different costs to different types of forecast error and prefer forecasts that are biased in favour of avoiding ‘high-cost’ errors. Second, the models from which forecasts are obtained are more often employed in a multi-step prediction mode even though their parameters have been chosen to minimize only one-step prediction error variance. The first consideration leads us to a finite state representation of error-type propagation. Then this is used in concert with the second consideration to formulate a quadratic program whose solution yields the error-type distribution most preferred by the decision maker. Finally, this vital information permits us to determine the optimal forecast combination. We illustrate the resulting methodology using several time series from the compilation of 1001 series used in Makridakis et al. (1982) and from the NBER forecast databank compiled by Zarnowitz (1984).