Tests of Equal Forecast Accuracy for Overlapping Models
This paper examines the asymptotic and finite-sample properties of tests of equal forecast accuracy when the models being compared are overlapping in the sense of Vuong (1989). Two models are overlapping when the true model con- tains just a subset of variables common to the larger sets of variables included in the competing forecasting models. We consider an out-of-sample version of the two-step testing procedure recommended by Vuong but also show that an exact one-step procedure is sometimes applicable. When the models are over- lapping, we provide a simple-to-use fixed regressor wild bootstrap that can be used to conduct valid inference. Monte Carlo simulations generally support the theoretical results: the two-step procedure is conservative while the one-step procedure can be accurately sized when appropriate. We conclude with an em- pirical application comparing the predictive content of credit spreads to growth in real stock prices for forecasting U.S. real GDP growth.