Conditional Predictive Density Evaluation in the Presence of Instabilities

• Authors: Barbara Rossi.
• BSE Working Paper: 110171 | September 15
• Keywords: structural change , instability , predictive density , dynamic mis-specification , forecast evaluation
• JEL codes: C22, C52, C53
• structural change
• instability
• predictive density
• dynamic mis-specification
• forecast evaluation

We propose new methods for evaluating predictive densities. The methods include Kolmogorov-Smirnov and Cramer-von Mises-type tests for the correct specification of predictive densities robust to dynamic mis-specification. The novelty is that the tests can detect mis-specification in the predictive densities even if it appears only over a fraction of the sample, due to the presence of instabilities. Our results indicate that our tests are well sized and have good power in detecting mis-specification in predictive densities, even when it is time-varying. An application to density forecasts of the Survey of Professional Forecasters demonstrates the usefulness of the proposed methodologies.