1993b). In any case, selecting the model with the minimum MSFE is an inadequate strategy since the model need not have constant parameters, nor encompass the forecast errors of competing models.
There appears to be a relatively short forecast horizon over which econometric models can yield marked gains relative to unconditional forecasts. This problem is exacerbated by the potential non-monotonicity of forecast variances as the horizon increases. We reconsidered the benefits of pooling complementary sources of forecast information, as against the weaknesses inherent in pooling forecasts based on competing models, which are implicit encompassing tests. We evaluated the role of intercept corrections, drawing on a recent taxonomy to demonstrate that specific forms of such corrections can make forecasts more robust to model misspecification and to structural change. This finding is consistent with the empirical evidence that intercept corrections improve model-based forecasts.
A comprehensive list of sources of forecast error was developed, and a positive aspect of our paper was to reveal where econometrics could contribute value added to the forecasting process in a world where models are mimics rather than facsimiles of the data generation process, where that process is not constant over time, and where investigators disagree about model choice.
We use three approximations to obtain a more tractable expression following Schmidt ( 1977), Baillie ( 1979b) and Chong and
Hendry ( 1986). Let:
ψ + ̂ = ψ + δ (101) where δ is Op(1/√T) so that powers of δ are asymptotically negligible, then:
ψ + ̂h= (ψ + δ)h ≅ ψh + hδψh-1 = ψh + hψh-1(ψ + ̂ - ψ). (102) Consequently:
V[ψ + ̂h - ψh] ≅ V[hψh-1(ψ + ̂ - ψ)] = h2ψ2(h-1)V[ψ + ̂]. (103) This result also follows from the usual formula for a nonlinear estimation function: