We propose notions of calibration for probabilistic forecasts of general
multivariate quantities. Probabilistic copula calibration is a natural analogue
of probabilistic calibration in the univariate setting. It can be assessed
empirically by checking for the uniformity of the copula probability integral
transform (CopPIT), which is invariant under coordinate permutations and
coordinatewise strictly monotone transformations of the predictive distribution
and the outcome. The CopPIT histogram can be interpreted as a generalization
and variant of the multivariate rank histogram, which has been used to check
the calibration of ensemble forecasts. Climatological copula calibration is an
analogue of marginal calibration in the univariate setting. Methods and tools
are illustrated in a simulation study and applied to compare raw numerical
model and statistically postprocessed ensemble forecasts of bivariate wind
vectors
