Forecasting and Prequential Validation for Time Varying Meta-Elliptical Distributions

Abstract

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

Identifiability and estimation of meta-elliptical copula generators

“…Thanks to Sklar's theorem, meta-elliptical copulas can be used as key components of many flexible multivariate models, far beyond elliptically-distributed random vectors. Moreover, the literature has considered parametric families of generators that include the popular Gaussian and/or Student copulas as particular cases, with practical applications in hydrology [13,37], risk management [6,12], econometrics [35], biology, etc.…”

Identifiability and estimation of meta-elliptical copula generators

“…Moreover, by considering a family of generators that contains g Gauss , these copulas can easily contain the very popular Gaussian and/or Student copulas. Therefore, practical applications of such distributions are numerous, particularly in hydrology [16,41], risk management [9,15], econometrics [39], biology, etc.…”