Combining forecasts - forty years later

This article is dedicated to the memory of Clive Granger, a founding editor of this journal. Its title echoes the title of his invited review article in a special issue of the Journal of Forecasting in 1989. That issue marked the twentieth anniversary of the publication of his article with John Bates, which is widely regarded as the seminal article in the field of forecast combination. This article returns to two of the topics in 'Combining forecasts - twenty years later' that are of much current interest, namely the impact of forecasters' different information sets on the original point forecast combination result, and properties of different methods of combining density forecasts. A parallel result to his inefficiency-of-mean-forecasts result for point forecasts is seen to apply to density forecasts, where logarithmic combination is shown to have some advantage over linear combination.