This paper evaluates six optimal and four ad hoc recursive combination methods on five actual data sets. The performance of all methods is compared to the mean and recursive least squares. A modification to one method is proposed and evaluated. The recursive methods were found to be very effective from start-up on two of the data sets. Where the optimal methods worked well so did the ad hoc ones, suggesting that often combination methods allowing 'local bias' adjustment may be preferable to the mean forecast and comparable to the optimal methods KEY WORDS Combining forecasts Linear recursive estimators Empirical evidence of the efficacy of a variety of combination methods, including the simple mean, has been demonstrated many times (e.g. Bates and Granger, 1969; Figlewski, 1983; Makridakis et a/., 1983). The evidence is sufficiently compelling to suggest that any decision maker should seek several forecasts o n a quantity of interest and at least average them, rather than simply taking the forecast of the 'best' model or expert. The demonstrated efficacy of the mean forecast has established it as a meaningful benchmark.
Granger and Ramanathan (1984) showed that, except under restrictive conditions, the use of a constant term and unrestricted weights results in combinations with lower mean squared error. This resulted in moving the combination problem directly into a linear model framework. Thus from a classical viewpoint, combinations using regression weights, constant over time, is, for the most part, the presently preferred method (e.g. Bopp, 1985; Mills and Stephenson, 1985). The disadvantages with the above are that:
A considerable history of data may be required to obtain estimated weights for situations involving several forecasters. This represents a significant loss of time when combination methods may benefit a user, but data-insufficiency problems may prevent the generation of combined forecasts.
Once obtained, the weights are constant and we would have t o refit the entire model t o obtain 'improved' estimates as new information becomes available.