Forecast Encompassing and Parameter Estimation

A desirable property of a forecast is that it encompasses competing predictions, in the sense that the accuracy of the preferred forecast cannot be improved through linear combination with a rival prediction. In this paper, we investigate the impact of the uncertainty associated with estimating model parameters in-sample on the encompassing properties of out-of-sample forecasts. Specifically, using examples of non-nested econometric models, we show that forecasts from the true (but estimated) data generating process (DGP) do "not" encompass forecasts from competing mis-specified models in general, particularly when the number of in-sample observations is small. Following this result, we also examine the scope for achieving gains in accuracy by combining the forecasts from the DGP and mis-specified models. Copyright 2005 Blackwell Publishing Ltd.