Marginal Weibull Diffusion Model for Wind Speed Modeling and Short-Term Forecasting

  • Alain Bensoussan
  • Alexandre Brouste
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 254)


We propose a dynamical model for the wind speed which is a Markov diffusion process with Weibull marginal distribution. It presents several advantages, namely nice modeling features both in terms of marginal probability density function and temporal correlation. The characteristics can be interpreted in terms of shape and scale parameters of a Weibull law which is convenient for practitioners to analyze the results. We calibrate the parameters with the maximum quasi-likelihood method and use the model to generate and forecast the wind speed. We have tested the model on wind-speed datasets provided by the National Renewable Energy Laboratory. The model fits well the data and we obtain a very good performance in point and probabilistic forecasting in the short-term in comparison to the benchmark.


Statistical modeling Ergodic diffusions Wind speed forecasts 



We would like to thank the anonymous referees for their comments that improves our original work. This research has been supported by a grant from EREN Groupe and partially by NSF grant DMS-1612880, Research Grants Council of HKSAR 11303316 and ANR project CAESARS (ANR-15-CE05-0024).


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Authors and Affiliations

  1. 1.International Center for Risk and Decision Analysis, Jindal School of ManagementThe University of TexasDallasUSA
  2. 2.Department SEEMCity University of Hong KongHong KongPeople’s Republic of China
  3. 3.Institut du Risque et de l’Assurance du Mans, Laboratoire Manceau de MathématiquesLe Mans UniversitéLe MansFrance

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