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Electricity price forecasting

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  • Rafal Weron
  • Florian Ziel

Abstract

Electricity price forecasting (EPF) is a branch of energy forecasting on the interface between econometrics/statistics and engineering, which focuses on predicting the spot and forward prices in wholesale electricity markets. Its beginnings can be traced back to the early 1990s, when power sector deregulation led to the introduction of competitive markets in the UK and Scandinavia. The changes quickly spread throughout Europe and North America, and nowadays - in many countries worldwide - electricity is traded under market rules using spot and derivative contracts. Over the last 25 years, a variety of methods and ideas have been tried for EPF, with varying degrees of success. In this chapter we first briefly discuss the forecasting horizons and the types of forecasts, then review the forecasting tools and the evaluation techniques used in the EPF literature.

Suggested Citation

  • Rafal Weron & Florian Ziel, 2018. "Electricity price forecasting," HSC Research Reports HSC/18/08, Hugo Steinhaus Center, Wroclaw University of Technology.
    • Handle: RePEc:wuu:wpaper:hsc1808
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    1. Katarzyna Hubicka & Grzegorz Marcjasz & Rafal Weron, 2018. "A note on averaging day-ahead electricity price forecasts across calibration windows," HSC Research Reports HSC/18/03, Hugo Steinhaus Center, Wroclaw University of Technology.
    2. Ziel, Florian & Steinert, Rick & Husmann, Sven, 2015. "Efficient modeling and forecasting of electricity spot prices," Energy Economics, Elsevier, vol. 47(C), pages 98-111.
    3. Dudek, Grzegorz, 2016. "Multilayer perceptron for GEFCom2014 probabilistic electricity price forecasting," International Journal of Forecasting, Elsevier, vol. 32(3), pages 1057-1060.
    4. Koopman, Siem Jan & Ooms, Marius & Carnero, M. Angeles, 2007. "Periodic Seasonal Reg-ARFIMAGARCH Models for Daily Electricity Spot Prices," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 16-27, March.
    5. Raffaella Giacomini & Halbert White, 2006. "Tests of Conditional Predictive Ability," Econometrica, Econometric Society, vol. 74(6), pages 1545-1578, November.
    6. Bartosz Uniejewski & Jakub Nowotarski & Rafał Weron, 2016. "Automated Variable Selection and Shrinkage for Day-Ahead Electricity Price Forecasting," Energies, MDPI, vol. 9(8), pages 1-22, August.
    7. Angelica Gianfreda, Lucia Parisio and Matteo Pelagatti, 2016. "The Impact of RES in the Italian DayAhead and Balancing Markets," The Energy Journal, International Association for Energy Economics, vol. 0(Bollino-M).
    8. Benth, Fred Espen & Kiesel, Rüdiger & Nazarova, Anna, 2012. "A critical empirical study of three electricity spot price models," Energy Economics, Elsevier, vol. 34(5), pages 1589-1616.
    9. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-474, October.
    10. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    11. Misiorek Adam & Trueck Stefan & Weron Rafal, 2006. "Point and Interval Forecasting of Spot Electricity Prices: Linear vs. Non-Linear Time Series Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(3), pages 1-36, September.
    12. Florian Ziel & Rick Steinert, 2015. "Electricity Price Forecasting using Sale and Purchase Curves: The X-Model," Papers 1509.00372, arXiv.org, revised Aug 2016.
    13. Grzegorz Marcjasz & Bartosz Uniejewski & Rafal Weron, 2017. "Importance of the long-term seasonal component in day-ahead electricity price forecasting revisited: Neural network models," HSC Research Reports HSC/17/03, Hugo Steinhaus Center, Wroclaw University of Technology.
    14. Vehvilainen, Iivo & Pyykkonen, Tuomas, 2005. "Stochastic factor model for electricity spot price--the case of the Nordic market," Energy Economics, Elsevier, vol. 27(2), pages 351-367, March.
    15. Nigar Hashimzade & Michael A. Thornton (ed.), 2013. "Handbook of Research Methods and Applications in Empirical Macroeconomics," Books, Edward Elgar Publishing, number 14327.
    16. De Jong Cyriel, 2006. "The Nature of Power Spikes: A Regime-Switch Approach," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(3), pages 1-28, September.
    17. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    18. Graham Elliott & Allan Timmermann, 2016. "Economic Forecasting," Economics Books, Princeton University Press, edition 1, number 10740.
    19. Holmberg, Pär & Newbery, David & Ralph, Daniel, 2013. "Supply function equilibria: Step functions and continuous representations," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1509-1551.
    20. Peter R. Hansen & Asger Lunde & James M. Nason, 2011. "The Model Confidence Set," Econometrica, Econometric Society, vol. 79(2), pages 453-497, March.
    21. Uniejewski, Bartosz & Marcjasz, Grzegorz & Weron, Rafał, 2019. "On the importance of the long-term seasonal component in day-ahead electricity price forecasting: Part II — Probabilistic forecasting," Energy Economics, Elsevier, vol. 79(C), pages 171-182.
    22. Francis X. Diebold, 2015. "Comparing Predictive Accuracy, Twenty Years Later: A Personal Perspective on the Use and Abuse of Diebold-Mariano Tests," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(1), pages 1-1, January.
    23. Helyette Geman & A. Roncoroni, 2006. "Understanding the Fine Structure of Electricity Prices," Post-Print halshs-00144198, HAL.
    24. Ventosa, Mariano & Baillo, Alvaro & Ramos, Andres & Rivier, Michel, 2005. "Electricity market modeling trends," Energy Policy, Elsevier, vol. 33(7), pages 897-913, May.
    25. Jeremy Berkowitz & Peter Christoffersen & Denis Pelletier, 2011. "Evaluating Value-at-Risk Models with Desk-Level Data," Management Science, INFORMS, vol. 57(12), pages 2213-2227, December.
    26. Mayer, Klaus & Trück, Stefan, 2018. "Electricity markets around the world," Journal of Commodity Markets, Elsevier, vol. 9(C), pages 77-100.
    27. Hyndman, Rob J. & Koehler, Anne B., 2006. "Another look at measures of forecast accuracy," International Journal of Forecasting, Elsevier, vol. 22(4), pages 679-688.
    28. 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, September.
    29. Nowotarski, Jakub & Weron, Rafał, 2018. "Recent advances in electricity price forecasting: A review of probabilistic forecasting," Renewable and Sustainable Energy Reviews, Elsevier, vol. 81(P1), pages 1548-1568.
    30. Florian Ziel, 2015. "Forecasting Electricity Spot Prices using Lasso: On Capturing the Autoregressive Intraday Structure," Papers 1509.01966, arXiv.org, revised Jan 2016.
    31. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    32. Alvaro Cartea & Marcelo Figueroa, 2005. "Pricing in Electricity Markets: A Mean Reverting Jump Diffusion Model with Seasonality," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(4), pages 313-335.
    33. Kiesel, Rüdiger & Paraschiv, Florentina, 2017. "Econometric analysis of 15-minute intraday electricity prices," Energy Economics, Elsevier, vol. 64(C), pages 77-90.
    34. Nowotarski, Jakub & Raviv, Eran & Trück, Stefan & Weron, Rafał, 2014. "An empirical comparison of alternative schemes for combining electricity spot price forecasts," Energy Economics, Elsevier, vol. 46(C), pages 395-412.
    35. Adam Misiorek & Rafal Weron, 2006. "Interval forecasting of spot electricity prices," HSC Research Reports HSC/06/05, Hugo Steinhaus Center, Wroclaw University of Technology.
    36. Kristiansen, Tarjei, 2012. "Forecasting Nord Pool day-ahead prices with an autoregressive model," Energy Policy, Elsevier, vol. 49(C), pages 328-332.
    37. Weron, Rafał, 2014. "Electricity price forecasting: A review of the state-of-the-art with a look into the future," International Journal of Forecasting, Elsevier, vol. 30(4), pages 1030-1081.
    38. Ziel, Florian & Steinert, Rick, 2018. "Probabilistic mid- and long-term electricity price forecasting," Renewable and Sustainable Energy Reviews, Elsevier, vol. 94(C), pages 251-266.
    39. Ziel, Florian & Weron, Rafał, 2018. "Day-ahead electricity price forecasting with high-dimensional structures: Univariate vs. multivariate modeling frameworks," Energy Economics, Elsevier, vol. 70(C), pages 396-420.
    40. Magdalena Borgosz-Koczwara & Aleksander Weron & Agnieszka Wyłomańska, 2009. "Stochastic models for bidding strategies on oligopoly electricity market," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(3), pages 579-592, July.
    41. Grzegorz Marcjasz & Tomasz Serafin & Rafał Weron, 2018. "Selection of Calibration Windows for Day-Ahead Electricity Price Forecasting," Energies, MDPI, vol. 11(9), pages 1-20, September.
    42. Dipeng Chen & Derek Bunn, 2014. "The Forecasting Performance of a Finite Mixture Regime‐Switching Model for Daily Electricity Prices," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 33(5), pages 364-375, August.
    43. Ziel, Florian & Steinert, Rick, 2016. "Electricity price forecasting using sale and purchase curves: The X-Model," Energy Economics, Elsevier, vol. 59(C), pages 435-454.
    44. Young, David & Poletti, Stephen & Browne, Oliver, 2014. "Can agent-based models forecast spot prices in electricity markets? Evidence from the New Zealand electricity market," Energy Economics, Elsevier, vol. 45(C), pages 419-434.
    45. Florian Ziel & Rick Steinert, 2017. "Probabilistic Mid- and Long-Term Electricity Price Forecasting," Papers 1703.10806, arXiv.org, revised May 2018.
    46. Paul L. Joskow, 2008. "Lessons Learned From Electricity Market Liberalization," The Energy Journal, , vol. 29(2_suppl), pages 9-42, December.
    47. N/A, 2016. "The World Economy: Forecast Summary," National Institute Economic Review, National Institute of Economic and Social Research, vol. 237(1), pages 2-2, August.
    48. Rick Steinert & Florian Ziel, 2018. "Short- to Mid-term Day-Ahead Electricity Price Forecasting Using Futures," Papers 1801.10583, arXiv.org.
    49. Weron, Rafał & Zator, Michał, 2014. "Revisiting the relationship between spot and futures prices in the Nord Pool electricity market," Energy Economics, Elsevier, vol. 44(C), pages 178-190.
    50. Maciejowska, Katarzyna & Nowotarski, Jakub & Weron, Rafał, 2016. "Probabilistic forecasting of electricity spot prices using Factor Quantile Regression Averaging," International Journal of Forecasting, Elsevier, vol. 32(3), pages 957-965.
    51. Harvey, David I & Leybourne, Stephen J & Newbold, Paul, 1998. "Tests for Forecast Encompassing," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 254-259, April.
    52. Hong, Tao & Pinson, Pierre & Fan, Shu & Zareipour, Hamidreza & Troccoli, Alberto & Hyndman, Rob J., 2016. "Probabilistic energy forecasting: Global Energy Forecasting Competition 2014 and beyond," International Journal of Forecasting, Elsevier, vol. 32(3), pages 896-913.
    53. Jakub Nowotarski & Rafał Weron, 2015. "Computing electricity spot price prediction intervals using quantile regression and forecast averaging," Computational Statistics, Springer, vol. 30(3), pages 791-803, September.
    54. Bordignon, Silvano & Bunn, Derek W. & Lisi, Francesco & Nan, Fany, 2013. "Combining day-ahead forecasts for British electricity prices," Energy Economics, Elsevier, vol. 35(C), pages 88-103.
    55. Bartosz Uniejewski & Rafal Weron & Florian Ziel, 2017. "Variance stabilizing transformations for electricity spot price forecasting," HSC Research Reports HSC/17/01, Hugo Steinhaus Center, Wroclaw University of Technology.
    56. Conejo, Antonio J. & Contreras, Javier & Espinola, Rosa & Plazas, Miguel A., 2005. "Forecasting electricity prices for a day-ahead pool-based electric energy market," International Journal of Forecasting, Elsevier, vol. 21(3), pages 435-462.
    57. Tilmann Gneiting & Fadoua Balabdaoui & Adrian E. Raftery, 2007. "Probabilistic forecasts, calibration and sharpness," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 243-268, April.
    58. Janczura, Joanna & Trück, Stefan & Weron, Rafał & Wolff, Rodney C., 2013. "Identifying spikes and seasonal components in electricity spot price data: A guide to robust modeling," Energy Economics, Elsevier, vol. 38(C), pages 96-110.
    59. Kanamura, Takashi & Ohashi, Kazuhiko, 2007. "A structural model for electricity prices with spikes: Measurement of spike risk and optimal policies for hydropower plant operation," Energy Economics, Elsevier, vol. 29(5), pages 1010-1032, September.
    60. Weron, Rafal & Misiorek, Adam, 2008. "Forecasting spot electricity prices: A comparison of parametric and semiparametric time series models," International Journal of Forecasting, Elsevier, vol. 24(4), pages 744-763.
    61. Weron, Rafal, 2008. "Market price of risk implied by Asian-style electricity options and futures," Energy Economics, Elsevier, vol. 30(3), pages 1098-1115, May.
    62. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    63. Gaillard, Pierre & Goude, Yannig & Nedellec, Raphaël, 2016. "Additive models and robust aggregation for GEFCom2014 probabilistic electric load and electricity price forecasting," International Journal of Forecasting, Elsevier, vol. 32(3), pages 1038-1050.
    64. Keles, Dogan & Scelle, Jonathan & Paraschiv, Florentina & Fichtner, Wolf, 2016. "Extended forecast methods for day-ahead electricity spot prices applying artificial neural networks," Applied Energy, Elsevier, vol. 162(C), pages 218-230.
    65. repec:dau:papers:123456789/1433 is not listed on IDEAS
    66. Janczura, Joanna & Weron, Rafal, 2010. "An empirical comparison of alternate regime-switching models for electricity spot prices," Energy Economics, Elsevier, vol. 32(5), pages 1059-1073, September.
    67. Hélyette Geman & Andrea Roncoroni, 2006. "Understanding the Fine Structure of Electricity Prices," The Journal of Business, University of Chicago Press, vol. 79(3), pages 1225-1262, May.
    68. Ries, Jan & Gaudard, Ludovic & Romerio, Franco, 2016. "Interconnecting an isolated electricity system to the European market: The case of Malta," Utilities Policy, Elsevier, vol. 40(C), pages 1-14.
    69. N/A, 2016. "The World Economy: Forecast Summary," National Institute Economic Review, National Institute of Economic and Social Research, vol. 238(1), pages 2-2, November.
    70. N/A, 2016. "The UK Economy: Forecast summary," National Institute Economic Review, National Institute of Economic and Social Research, vol. 237(1), pages 3-3, August.
    71. Rafal Weron, 2006. "Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0601, December.
    72. Huurman, Christian & Ravazzolo, Francesco & Zhou, Chen, 2012. "The power of weather," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3793-3807.
    73. Antonio Bello & Derek Bunn & Javier Reneses & Antonio Muñoz, 2016. "Parametric Density Recalibration of a Fundamental Market Model to Forecast Electricity Prices," Energies, MDPI, vol. 9(11), pages 1-15, November.
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    More about this item

    Keywords

    Electricity price forecasting; Probabilistic forecast; Ensemble forecast; Day-ahead market; Intraday market; Regression; Computational intelligence; Reduced-form model; Multi-agent simulation; Model evaluation; Predictive ability test;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • 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
    • C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • Q41 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Demand and Supply; Prices
    • Q47 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Energy Forecasting

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