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Working Paper

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 contains 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 overlapping, 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 empirical application comparing the predictive content of credit spreads to growth in real stock prices for forecasting U.S. real GDP growth.

Working Papers of the Federal Reserve Bank of Cleveland are preliminary materials circulated to stimulate discussion and critical comment on research in progress. They may not have been subject to the formal editorial review accorded official Federal Reserve Bank of Cleveland publications. The views expressed in this paper are those of the authors and do not represent the views of the Federal Reserve Bank of Cleveland or the Federal Reserve System.

Suggested Citation

Clark, Todd E., and Michael W. McCracken. 2011. “Tests of Equal Forecast Accuracy for Overlapping Models.” Federal Reserve Bank of Cleveland, Working Paper No. 11-21.