A Predictability Test for a Small Number of Nested Models

Abstract

In this paper we introduce tests of Likelihood Ratio types for one sided multivariate hypothesis to evaluate the null that a parsimonious model performs equally well as a small number of models which nest the benchmark. We show that the limiting distributions of the test statistics are non standard. For critical values we consider two approaches: (i) boostrapping and (ii) simulations assuming normality of the mean square prediction error (MSPE) difference. The size and the power performance of the tests are compared via Monte Carlo experiments with two existing tests proposed in Hubrich and West (2010): a chi-squared test and the maximum of t-statistic test. We find that all tests are well sized for one step ahead forecasts; for multi-step forecasts the normal approximation delivers grossly oversized tests, while the bootstrap provides with smaller size distortions. The experiments on the power reveal that the chi-squared test performs last while the ranking between the likelihood-ratio type test and the max-t stat depends on the simulation settings. Last, we apply our test to draw conclusions about the predictive ability of a Phillips type curve for the US core inflation.

Keywords: Out-of sample, point-forecast evaluation, multi-model comparison, predictive ability, direct multi-step forecasts, fixed regressors bootstrap

JEL Classification: C12, C15, C52, C53