Forecasting and Prequential Validation for Time Varying Meta-Elliptical Distributions with a Study of Commodity Futures Prices

We consider forecasting and prequential (predictive sequential) validation of meta-elliptical distributions with time varying parameters. Using the weak prequential principle of Dawid, we conduct model validation avoiding nuisance parameters problems. Results rely on the structure of meta-elliptical distributions and we allow for discontinuities in the marginals and time varying parameters. We use our approach for the study of a large data set of 16 commodity prices.