Combining Forecasts: Operational Adjustments to Theoretically Optimal Rules

Clemen and Winkler (1985) have described the theoretical effectiveness of Winkler's (1981) formula for optimally combining forecasts. The optimality of Winkler's formula is, however, contingent on actually knowing the forecasters' statistical properties, i.e., the variances and covariances of their forecasts. In realistic applications, of course, these properties have to be estimated, usually from a set of prior forecasts. In this case we show how the "operationally optimal" combining strategy differs from Winkler's "theoretically optimal" formula. Specifically, we provide figures indicating the operationally optimal strategy for combining two forecasts. We then propose a heuristic to choose the best set of parameter estimates in combining any number of forecasters and demonstrate its effectiveness via simulation.