Nearest-Neighbor Based Non-Parametric Probabilistic Forecasting with Applications in Photovoltaic Systems

Time series forecasting (i.e. the prediction of unknown future time series values using known data) has found several applications in a number of fields, like, economics and electricity forecasting [15]. Most of the used forecasting models deliver a so-called point forecast [4], a value that according to the models’ criteria is most likely to occur. Nonetheless, such forecasts lack information regarding their uncertainty. A possibility of quantifying such uncertainty is by conducting probabilistic forecasts [6, 10], which can be delivered as prediction intervals (including the probability of the forecast being inside the interval) or complete conditional probability distributions of future time series values [12]. Such a quantification of the forecast uncertainty is of interest for several optimization problems, as e.g. model predictive control. Probabilistic forecasting is divided in parametric and non-parametric approaches. While the former assume that the forecast values follow a known distribution (e.g. Gaussian) and try to determine the parameters describing it, the latter make no assumptions, but instead attempt to approximate the underlying distribution via the training data. Non-parametric approaches have the advantage of not assuming that all values will follow the same probability distribution across all points in time [3, 21].