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Non-nested model selection in unstable environments

We consider non-nested model selection tests in the presence of possible data and parameter instabilities. The novelty of our approach is that we allow the models’ relative performance to be varying over time, whereas existing model selection techniques look for an overall best model. We argue that the time path of the models’ relative performance may contain useful information that is lost when seeking a model that performs best “on average”. We consider two competing nonnested nonlinear and possibly misspecified dynamic models and provide statistical and graphical methods to: (1) analyze the evolution of the models’ relative performance over historical samples; and (2) monitor the models’ relative performance in real time, as new data becomes available. Our methods are valid under general data assumptions and can be applied to multivariate models that are estimated by a variety of techniques including ML, GMM and Bayesian methods. An empirical application provides insights into the time variation in the performance of Smets and Wouters’ (2003) DSGE model of the European economy relative to that of Bayesian VARs.