Equivalence Between Out-of-Sample Forecast Comparisons and Wald Statistics

We establish the equivalence between a commonly used out-of-sample test of equal predictive accuracy and the difference between two Wald statistics. This equivalence greatly simplifies the computational burden of calculating recursive out-of-sample tests and evaluating their critical values. Our results shed new light on many aspects of the test and establishes certain weaknesses associated with using out-of-sample forecast comparison tests to conduct inference about nested regression models.