Abstract

This paper examines the asymptotic and finite-sample properties of bootstrap-based tests of equal forecast accuracy among many nested models. Although direct, multi-step forecasts are permitted, attention is restricted to an OLS-estimated linear framework. Our analytics allow both finite sample and asymptotic nesting. Our preferred, parametric bootstrap algorithm is comparable to that in Kilian (1999) but focuses on approximating the distribution of the ratio rather than the difference in MSEs. As in Hansen (2005), we find that judiciously chosen centering and rescaling constants, that vary with the hypothesis of interest, are necessary to achieve appropriately sized tests. Monte Carlo simulations find that out preferred bootstrap has better finite-sample size and power than other methods designed to manage the comparison of non-nested models. We conclude with an empirical application regarding the predictive content of various measures of macroeconomic slack for inflation.

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