Forecast Combination and Encompassing

Abstract

Forecast combination is often found to improve forecast accuracy. This chapter considers different types of forecast combination and tests of forecast encompassing. The latter indicate when a combination is more accurate than an individual forecast ex post, in a range of circumstances: when the forecasts themselves are the objects of interest; when the forecasts are derived from models with unknown parameters; and when the forecast models are nested. We consider forecast encompassing tests which are framed in terms of the model's estimated parameters and recognize that parameter estimation uncertainty affects forecast accuracy, as well as conditonal tests of encompassing. We also look at the conditions under which forecast encompassing can be established irrespective of the form of the loss function.