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Bayesian estimation of stable CARMA spot models for electricity prices

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  • Müller, Gernot
  • Seibert, Armin

Abstract

We develop a Bayesian estimation procedure for the electricity spot price model in Benth et al. (2014). This model incorporates a trend and seasonality component, a stable CARMA process for the price spikes, and an additional Lévy process for mid-range price level changes. Our MCMC algorithm has two advantages over the existing stepwise estimation procedure presented in Benth et al. (2014): First, since our algorithm produces samples from the full posterior distribution over all parameters, we can estimate the parameters much more accurately, which is shown in simulation studies. Second, we can provide accuracy measures as credibility intervals in addition to the point estimates. The approach is quite general, so that it can be adapted also to other similar pricing models. For illustration, we analyse spot and future prices from the EEX using the new Bayesian method and provide estimates for the risk premium together with credibility regions.

Suggested Citation

  • Müller, Gernot & Seibert, Armin, 2019. "Bayesian estimation of stable CARMA spot models for electricity prices," Energy Economics, Elsevier, vol. 78(C), pages 267-277.
    • Handle: RePEc:eee:eneeco:v:78:y:2019:i:c:p:267-277
    DOI: 10.1016/j.eneco.2018.10.016
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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, August.
    2. P. Brockwell, 2001. "Lévy-Driven Carma Processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(1), pages 113-124, March.
    3. P. Brockwell, 2014. "Recent results in the theory and applications of CARMA processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(4), pages 647-685, August.
    4. Berk, K. & Hoffmann, A. & Müller, A., 2018. "Probabilistic forecasting of industrial electricity load with regime switching behavior," International Journal of Forecasting, Elsevier, vol. 34(2), pages 147-162.
    5. Benth, Fred Espen & Klüppelberg, Claudia & Müller, Gernot & Vos, Linda, 2014. "Futures pricing in electricity markets based on stable CARMA spot models," Energy Economics, Elsevier, vol. 44(C), pages 392-406.
    6. Borovkova, Svetlana & Schmeck, Maren Diane, 2017. "Electricity price modeling with stochastic time change," Energy Economics, Elsevier, vol. 63(C), pages 51-65.
    7. Fred Benth & Nils Detering, 2015. "Pricing and hedging Asian-style options on energy," Finance and Stochastics, Springer, vol. 19(4), pages 849-889, October.
    8. Rafal Weron, 2006. "Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach," HSC Books, Hugo Steinhaus Center, Wroclaw University of Science and Technology, number hsbook0601, December.
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    Cited by:

    1. Shao, Zhen & Zheng, Qingru & Yang, Shanlin & Gao, Fei & Cheng, Manli & Zhang, Qiang & Liu, Chen, 2020. "Modeling and forecasting the electricity clearing price: A novel BELM based pattern classification framework and a comparative analytic study on multi-layer BELM and LSTM," Energy Economics, Elsevier, vol. 86(C).
    2. Sabarathinam Srinivasan & Suresh Kumarasamy & Zacharias E. Andreadakis & Pedro G. Lind, 2023. "Artificial Intelligence and Mathematical Models of Power Grids Driven by Renewable Energy Sources: A Survey," Energies, MDPI, vol. 16(14), pages 1-56, July.
    3. Jürgen Kampf & Georgiy Shevchenko & Evgeny Spodarev, 2021. "Nonparametric estimation of the kernel function of symmetric stable moving average random functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(2), pages 337-367, April.
    4. Rowińska, Paulina A. & Veraart, Almut E.D. & Gruet, Pierre, 2021. "A multi-factor approach to modelling the impact of wind energy on electricity spot prices," Energy Economics, Elsevier, vol. 104(C).
    5. Sirin, Selahattin Murat & Camadan, Ercument & Erten, Ibrahim Etem & Zhang, Alex Hongliang, 2023. "Market failure or politics? Understanding the motives behind regulatory actions to address surging electricity prices," Energy Policy, Elsevier, vol. 180(C).
    6. Qiao, Weibiao & Yang, Zhe, 2020. "Forecast the electricity price of U.S. using a wavelet transform-based hybrid model," Energy, Elsevier, vol. 193(C).
    7. Donglan Liu & Xin Liu & Kun Guo & Qiang Ji & Yingxian Chang, 2023. "Spillover Effects among Electricity Prices, Traditional Energy Prices and Carbon Market under Climate Risk," IJERPH, MDPI, vol. 20(2), pages 1-18, January.
    8. Nikola Krečar & Andrej F. Gubina, 2020. "Risk mitigation in the electricity market driven by new renewable energy sources," Wiley Interdisciplinary Reviews: Energy and Environment, Wiley Blackwell, vol. 9(1), January.

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    More about this item

    Keywords

    α -Stable process; CARMA model; Electricity prices; Futures prices; Markov chain Monte Carlo; Seasonality; Stable density approximation;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • Q41 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Demand and Supply; Prices

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