Combining forecasts, encompassing and the properties of UK macroeconomic forecasts

The idea of combining forecasts is of great interest to forecasters and a linear combination of different forecasts can be more accurate than any individual forecast. For model builders, forecast encompassing is a way of checking whether any extra important information is contained in forecasts from rival models. Efficient forecasts have errors which are unrelated to any information available when they are formed. Combinations of forecasts, forecast encompassing and efficiency tests can all be achieved by a restricted or unrestricted regression of outcomes on the separate forecasts. This paper links these three approaches and examines the implications for recent UK annual forecasts.