  The current literature in probabilistic forecasting is focused on quantifying
the uncertainty of each random variable individually. This leads to the failure
in informing about interdependence structure of uncertainty at different
locations and/or different lead times. When there is a positive or negative
association between a number of random variables, the prediction regions for
them should be reflected by multivariate or joint uncertainty sets. The
existing literature is very primitive in the area of multivariate uncertainty
sets modeling. In this paper, uncertainty regions are generated in the form of
multivariate prediction intervals. We will examine the performance of Gaussian
and R-Vine copulas in characterizing the correlated behavior of PV power
generations at successive lead-times. Copulas are compared based on
goodness-of-fit metrics as well as skill scores. A framework is elaborated to
generate multivariate prediction intervals out of the scenarios generated from
Gaussian and R-vine multivariate densities. The resultant multivariate
prediction intervals are evaluated based on their calibration and sharpness.
The approaches are tested on a real-world dataset including PV power
measurements and weather forecasts. This paper provides a series of useful
analyses and comparative results for multivariate uncertainty modeling of PV
power that can serve as a basis for future works in the area.
