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Probabilistic forecasts of renewable energy production provide users withvaluable information about the uncertainty associated with the expectedgeneration. Current state-of-the-art forecasts for solar irradiance havefocused on producing reliable \emph{point} forecasts. The additionalinformation included in probabilistic forecasts may be paramount for decisionmakers to efficiently make use of this uncertain and variable generation. Inthis paper, a stochastic differential equation (SDE) framework for modeling theuncertainty associated with the solar irradiance point forecast is proposed.This modeling approach allows for characterizing both the interdependencestructure of prediction errors of short-term solar irradiance and theirpredictive distribution. A series of different SDE models are fitted to atraining set and subsequently evaluated on a one-year test set. The final modelproposed is defined on a bounded and time-varying state space with zeroprobability almost surely of events outside this space.

Probabilistic Forecasts of Solar Irradiance by Stochastic Differential Equations