Evaluating Long-Horizon Forecasts

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Abstract
This paper examines the asymptotic and finite-sample properties of tests of equal forecast accuracy and encompassing applied to predictions from nested long-horizon regression models. We first derive the asymptotic distributions of a set of tests of equal forecast accuracy and encompassing, showing that the tests have non-standard distributions that depend on the parameters of the data-generating process. Using a simple parametric bootstrap for inference, we then conduct Monte Carlo simulations of a range of data-generating processes to examine the finite-sample size and power of the tests. In these simulations, the bootstrap yields tests with good finite-sample size and power properties, with the encompassing test proposed by Clark and McCracken (2001a) having superior power. The paper concludes with a reexamination of the predictive content of capacity utilization for core inflation.

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