Optimal Combination of Survey Forecasts

We consider the problem of optimally combining individual forecasts of gross domestic product (GDP) and inflation from the Survey of Professional Forecasters (SPF) dataset for the Euro Area. Contrary to the common practice of using equal combination weights, we compute optimal weights which minimize the mean square forecast error (MSFE) in the case of point forecasts and maximize a logarithmic score in the case of density forecasts. We show that this is a viable strategy even when the number of forecasts to combine gets large, provided we constrain these weights to be positive and to sum to one. Indeed, this enforces a form of shrinkage on the weights which ensures good out-of-sample performance of the combined forecasts.