Evaluating Long-Horizon Forecasts

This paper examines the asymptotic and Þnite-sample properties of tests of equal forecast accuracy and encompassing applied to predictions from nested long-horizon regression models. We Þrst 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 Þnite-sample size and power of the tests. In these simulations, the bootstrap yields tests with good Þnite—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 inßation.