2020/02/21 by Alfred Müller, Müller, Alfred, Matthias Reuber +1
Computer Science · Economics, Econometrics and Finance · Energy · Mathematics · #Applications (stat.AP) #Computer science #Copula (linguistics) #Econometrics #Energy, Environment, and Transportation Policies #Extreme value theory #FOS: Computer and information sciences #Gaussian #Gumbel distribution #Market Dynamics and Volatility #Mathematics #Multivariate statistics #Physics #Probabilistic forecasting #Probabilistic logic #Solar Radiation and Photovoltaics #Statistics #Tail dependence #Vine copula #stat.AP
paper · pdf · doi:10.48550/arxiv.2002.09267
arxiv created 2020/02/21 · openalex publication_date 2020/02/21 · arxiv updated 2020/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The increasing importance of solar power for electricity generation leads to an increasing demand for probabilistic forecasting of local and aggregated PV yields. In this paper we use an indirect modeling approach for hourly medium to long term local PV yields based on publicly available irradiation data. We suggest a time series model for global horizontal irradiation for which it is easy to generate an arbitrary number of scenarios and thus allows for multivariate probabilistic forecasts for arbitrary time horizons. In contrast to many simplified models that have been considered in the literature so far it features several important stylized facts. Sharp time dependent lower and upper bounds of global horizontal irradiations are estimated that improve the often used physical bounds. The parameters of the beta distributed marginals of the transformed data are allowed to be time dependent. A copula-based time series model is introduced for the hourly and daily dependence structure based on a simple graphical structure known from the theory of vine copulas. Non-Gaussian copulas like Gumbel and BB1 copulas are used that allow for the important feature of so-called tail dependence. Evaluation methods like the continuous ranked probability score (CRPS), the energy score (ES) and the variogram score (VS) are used to compare the power of the model for multivariate probabilistic forecasting with other models used in the literature showing that our model outperforms other models in many respects.