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We introduce a novel approach for comparing out-of-sample multi-stepforecasts obtained from a pair of nested models that is based on the forecastencompassing principle. Our proposed approach relies on an alternative way oftesting the population moment restriction implied by the forecast encompassingprinciple and that links the forecast errors from the two competing models in aparticular way. Its key advantage is that it is able to bypass the variancedegeneracy problem afflicting model based forecast comparisons across nestedmodels. It results in a test statistic whose limiting distribution is standardnormal and which is particularly simple to construct and can accommodate bothsingle period and longer-horizon prediction comparisons. Inferences are alsoshown to be robust to different predictor types, including stationary,highly-persistent and purely deterministic processes. Finally, we illustratethe use of our proposed approach through an empirical application that exploresthe role of global inflation in enhancing individual country specific inflationforecasts.

Direct Multi-Step Forecast based Comparison of Nested Models via an Encompassing Test