Can Two Forecasts Have the Same Conditional Expected Accuracy?
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The method for testing equal predictive accuracy for pairs of forecasting models proposed by Giacomini and White (2006) has found widespread use in empirical work. The procedure assumes that the parameters of the underlying forecasting models are estimated using a rolling window of fixed width and incorporates the effect of parameter estimation in the null hypothesis that two forecasts have identical conditionally expected loss. We show that this null hypothesis cannot be valid under a rolling window estimation scheme and even fails in the absence of parameter estimation for many types of stochastic processes in common use. This means that the approach does not guarantee appropriate comparisons of predictive accuracy of forecasting models. We also show that the Giacomini-White approach can lead to substantial size distortions in tests of equal unconditional predictive accuracy and propose an alternative procedure with better properties.
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