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A stochastic time-series model for solar irradiation

Author

Listed:
  • Larsson, Karl
  • Green, Rikard
  • Benth, Fred Espen

Abstract

We propose a novel stochastic time series model able to explain the stylized features of daily irradiation level data in 5 cities in Germany. The model is suitable for applications to risk management of photovoltaic power production in renewable energy markets. The suggested dynamics is a low-order autoregressive time series with seasonal level given by an atmospheric clear-sky model. Moreover, we detect a skewness property in the residuals which we explain by a winter–summer regime switch. The stochastic variance is modeled by a seasonally varying GARCH-dynamics. The winter and summer standardized residuals are proposed to be a Gaussian mixture model to capture the bimodal distributions. We estimate the model on the observed data, and perform a validation study. An application to energy markets studying the production at risk for a PV-producer is presented.

Suggested Citation

  • Larsson, Karl & Green, Rikard & Benth, Fred Espen, 2023. "A stochastic time-series model for solar irradiation," Energy Economics, Elsevier, vol. 117(C).
    • Handle: RePEc:eee:eneeco:v:117:y:2023:i:c:s0140988322005503
    DOI: 10.1016/j.eneco.2022.106421
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    References listed on IDEAS

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    1. Fred Espen Benth & Jūratė Šaltytė Benth & Steen Koekebakker, 2008. "Stochastic Modeling of Electricity and Related Markets," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6811, March.
    2. Laura Casula & Guglielmo D’Amico & Giovanni Masala & Filippo Petroni, 2020. "Performance estimation of photovoltaic energy production," Letters in Spatial and Resource Sciences, Springer, vol. 13(3), pages 267-285, December.
    3. Peter Alaton & Boualem Djehiche & David Stillberger, 2002. "On modelling and pricing weather derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(1), pages 1-20.
    4. Sean D. Campbell & Francis X. Diebold, 2005. "Weather Forecasting for Weather Derivatives," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 6-16, March.
    5. Kaldellis, John K. & Kapsali, Marina & Kavadias, Kosmas A., 2014. "Temperature and wind speed impact on the efficiency of PV installations. Experience obtained from outdoor measurements in Greece," Renewable Energy, Elsevier, vol. 66(C), pages 612-624.
    6. Wolfgang Karl Härdle & Brenda López Cabrera, 2012. "The Implied Market Price of Weather Risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(1), pages 59-95, February.
    7. Lingohr, Daniel & Müller, Gernot, 2019. "Stochastic modeling of intraday photovoltaic power generation," Energy Economics, Elsevier, vol. 81(C), pages 175-186.
    8. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-359, October.
    9. Fred E. Benth & Troels S. Christensen & Victor Rohde, 2021. "Multivariate continuous-time modeling of wind indexes and hedging of wind risk," Quantitative Finance, Taylor & Francis Journals, vol. 21(1), pages 165-183, January.
    10. Šaltytė Benth, Jūratė & Benth, Fred Espen, 2012. "A critical view on temperature modelling for application in weather derivatives markets," Energy Economics, Elsevier, vol. 34(2), pages 592-602.
    11. Cuppari, Rosa I. & Higgins, Chad W. & Characklis, Gregory W., 2021. "Agrivoltaics and weather risk: A diversification strategy for landowners," Applied Energy, Elsevier, vol. 291(C).
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    Cited by:

    1. Fabian A. Harang & Fred Espen Benth & Fride Straum, 2024. "Universal approximation on non-geometric rough paths and applications to financial derivatives pricing," Papers 2412.16009, arXiv.org, revised Dec 2025.
    2. Yoshioka, Hidekazu & Yoshioka, Yumi, 2024. "Generalized divergences for statistical evaluation of uncertainty in long-memory processes," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    3. Bufalo, Michele & Fanelli, Viviana, 2025. "A seasonal two-factor model for solar energy production: A climate extreme events analysis," Energy Economics, Elsevier, vol. 148(C).

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    JEL classification:

    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • Q4 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy

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