  Probabilistic forecasts of renewable energy production provide users with
valuable information about the uncertainty associated with the expected
generation. Current state-of-the-art forecasts for solar irradiance have
focused on producing reliable \emph{point} forecasts. The additional
information included in probabilistic forecasts may be paramount for decision
makers to efficiently make use of this uncertain and variable generation. In
this paper, a stochastic differential equation (SDE) framework for modeling the
uncertainty associated with the solar irradiance point forecast is proposed.
This modeling approach allows for characterizing both the interdependence
structure of prediction errors of short-term solar irradiance and their
predictive distribution. A series of different SDE models are fitted to a
training set and subsequently evaluated on a one-year test set. The final model
proposed is defined on a bounded and time-varying state space with zero
probability almost surely of events outside this space.
