Equivalence Between Out-of-Sample Forecast Comparisons and Wald Statistics - Hansen, Peter Reinhard; Timmermann, Allan (Econometrica, 2015)
We demonstrate the asymptotic equivalence between commonly used test statistics for out-of-sample forecasting performance and conventional Wald statistics. This equivalence greatly simplifies the computational burden of calculating recursive out-of-sample test statistics and their critical values. For the case with nested models, we show that the limit distribution, which has previously been expressed through stochastic integrals, has a simple representation in terms of -distributed random variables and we derive its density. We also generalize the limit theory to cover local alternatives and characterize the power properties of the test.