Signal Extraction Revision Variances as a Goodness-of-Fit Measure

We consider the topic of model misspecification with respect to unit roots. Although unit root misspecification may indeed be fairly common, the problem is difficult to appraise due to the inappropriateness of one-step ahead forecasting error methods. We propose an empirical revision variance measure for a model-based signal extraction estimate as a measure of model misspecification, based on the idea that high revision leads correspond to an implicit multi-step ahead forecasting error criterion. A hypothesis testing paradigm for the empirical revision measure is developed through theoretical calculations of the asymptotic distribution under the Null, and the method is assessed through real data studies as well as simulations