Forecast combination when outcomes are difficult to predict

We show that when outcomes are difficult to forecast in the sense that forecast errors have a large common component that (a) optimal weights are not affected by this common component, and may well be far from equal to each other but (b) the relative mean square error loss from averaging over optimal combination can be small. Hence, researchers could well estimate combining weights that indicate that correlations could be exploited for better forecasts only to find that the difference in terms of loss is negligible. The results then provide an additional explanation for the commonly encountered practical situation of the averaging of forecasts being difficult to improve upon.

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