Econometrica: Nov 2015, Volume 83, Issue 6

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

https://doi.org/10.3982/ECTA10581
p. 2485-2505

Peter Reinhard Hansen, Allan Timmermann

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 X2‐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.



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