Nested forecast model comparisons: A new approach to testing equal accuracy

We develop methods for testing whether, in a finite sample, forecasts from nested models are equally accurate. Most prior work has focused on a null of equal accuracy in population — basically, whether the additional coefficients of the larger model are zero. Our asymptotic approximation instead treats the coefficients as non-zero but small, such that, in a finite sample, forecasts from the small and large models are expected to be equally accurate. We derive the limiting distributions of tests of equal mean square error, and develop a bootstrap for inference. Simulations show that our procedures have good size and power properties.