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Abstract:
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We develop bootstrap methods for testing, whether, in finite samples, competing out-of-sample forecasts from nested models are equally accurate. Most prior work focuses on a null hypothesis of equal accuracy in population---basically, whether coefficients on the extra variables in the larger, nesting model are zero. We instead use an asymptotic approximation that treats the coefficients as non-zero but small, such that, in a finite sample, forecasts from the small model are expected to be as accurate as forecasts from the large model. Under that approximation, we derive the limiting distributions of tests of equal mean square error, and develop bootstrap methods for estimating critical values. We do so for comparisons of both pairs of forecasts and multiple forecasts. We illustrate the procedures with applications to forecasting stock returns and inflation.
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