Horizon confidence sets

This paper introduces a new statistical procedure to discriminate between competing forecasting models at different forecast horizons. Unlike existing tests, which eliminate a model from all horizons if dominated according to some loss measure, our methodology identifies an ‘optimal’ set of models at each horizon, retaining a model that performs well at a given horizon even if dominated at others. While our method is especially useful in applications to long-term forecasting as well as short-term nowcasting, it can also be applied in wider settings like the comparison of forecasting models across countries. We conduct a small Monte Carlo study to investigate the finite sample properties and apply our procedure to nowcasting US real GDP growth and its subcomponents, comparing a factor-based nowcasting method to a naïve benchmark. Unlike existing methods, ours can formally detect the point in the quarter at which the factor method beats the benchmark or vice versa.