Infinite hidden Markov model for short-term solar irradiance forecasting

Abstract

Hidden state models are among the most widely used and efficient schemes for solar irradiance modeling in general and forecasting in particular. However, the complexity of such models – in terms of the number of states – is usually needed to be specified a priori. For solar irradiance data this assumption is very difficult to justify.In this paper, an infinite hidden Markov model (InfHMM) is introduced for short-term probabilistic forecasting of solar irradiance, where the assumption of fixed number of states a priori is relaxed and model complexity is determined during the model training. InfHMM is a non-parametric Bayesian model (NPB) indexed with an infinite dimensional parameter space which allows the automatic adaptation of the model to the “correct” complexity. This facilitates the automatic adaptation of the model to all weather conditions and locations. Posterior inference for InfHMM is performed using the Markov chain Monte Carlo algorithm, namely the beam sampler.Data from 13 different sources are used to validate the proposed model and subsequently it is compared to two well-established models in the literature: Markov-chain mixture distribution (MCM) and complete-history persistence ensemble (CH-PeEn) models. Important results are found, that cannot be derived from the existing finite models, such as the variation of the number of states within and across sites. The comparison of the models shows that the InfHMM is more consistent in term of the forecasting horizon.For reproducibility of the methodology presented in this paper, we have provided an R script for the InfHMM as supplementary material.