This paper examines the effects of combining three econometric and three times-series forecasts of growth and inflation in the U.K. If forecasts are unbiased then a combination exploiting this fact will be more efficient than an unrestricted combination. Ex post econometric forecasts may be biased but ex ante they are unbiased. The results of the study are that a restricted linear combination of the econometric forecasts is superior to an unrestricted combination and also to the unweighted mean of the forecasts. However, it is not preferred to the best of the individual forecasts.
KEY WORDS Combining forecasts Econometric forecasts
Regression Linear constraints
In an innovative paper, Bates and Granger (1969) point out that when a number of different forecasts of the same event are available, each can generally be expected to embody useful information. This is because the forecasts may be based either on different information sets or on alternative assumptions about how the information should be processed. Bates and Granger suggest that if forecasts from different sources are combined in some way, the resulting forecasts may be more accurate than any of the individual components. They also consider a number of methods by which the weights on the different forccasts might be determined. These allow the weights on the forecasts to change in respQnse to past forecast errors. Makridakis and Hibon (1979) and Newbold and Granger (1974) report empirical results using these methods which suggest that combinations of forecasts are superior to individual forecasts. Granger and Ramanathan (1 984) show that if the forecast errors are stationary with a constant covariance matrix, then the optimal weights can be obtained by the unrestricted regression of the outcome series on a constant and the various forecasts. Clemen (1986) argues that forecasting efficiency may be improved if restrictions are imposed, even though they are invalid. However, in practice the assumption of stationary forecasts errors is unlikely to be correct to some degree for economic forecasts. For example, it is well known that forecasters analyse the * Paper presented at the Sixth International Symposium on Forecasting,