Annals of Applied Statistics

Modeling and forecasting electricity spot prices: A functional data perspective

Dominik Liebl

Full-text: Open access


Classical time series models have serious difficulties in modeling and forecasting the enormous fluctuations of electricity spot prices. Markov regime switch models belong to the most often used models in the electricity literature. These models try to capture the fluctuations of electricity spot prices by using different regimes, each with its own mean and covariance structure. Usually one regime is dedicated to moderate prices and another is dedicated to high prices. However, these models show poor performance and there is no theoretical justification for this kind of classification. The merit order model, the most important micro-economic pricing model for electricity spot prices, however, suggests a continuum of mean levels with a functional dependence on electricity demand.

We propose a new statistical perspective on modeling and forecasting electricity spot prices that accounts for the merit order model. In a first step, the functional relation between electricity spot prices and electricity demand is modeled by daily price-demand functions. In a second step, we parameterize the series of daily price-demand functions using a functional factor model. The power of this new perspective is demonstrated by a forecast study that compares our functional factor model with two established classical time series models as well as two alternative functional data models.

Article information

Ann. Appl. Stat., Volume 7, Number 3 (2013), 1562-1592.

First available in Project Euclid: 3 October 2013

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Functional factor model functional data analysis time series analysis fundamental market model merit order curve European Energy Exchange EEX


Liebl, Dominik. Modeling and forecasting electricity spot prices: A functional data perspective. Ann. Appl. Stat. 7 (2013), no. 3, 1562--1592. doi:10.1214/13-AOAS652.

Export citation


  • Antoch, J., Prchal, L., De Rosa, M. R. and Sarda, P. (2010). Electricity consumption prediction with functional linear regression using spline estimators. J. Appl. Stat. 37 2027–2041.
  • Benedetti, J. K. (1977). On the nonparametric estimation of regression functions. J. R. Stat. Soc. Ser. B Stat. Methodol. 39 248–253.
  • Benko, M., Härdle, W. and Kneip, A. (2009). Common functional principal components. Ann. Statist. 37 1–34.
  • Borak, S. and Weron, R. (2008). A semiparametric factor model for electricity forward curve dynamics. Journal of Energy Markets 1 3–16.
  • Bosco, B., Parisio, L., Pelagatti, M. and Baldi, F. (2010). Long-run relations in European electricity prices. J. Appl. Econometrics 25 805–832.
  • Brockwell, P. J. and Davis, R. A. (1991). Time Series: Theory and Methods, 2nd ed. Springer, New York.
  • Burger, M., Graeber, B. and Schindlmayr, G. (2008). Managing Energy Risk: An Integrated View on Power and Other Energy Markets. Wiley, New York.
  • Christensen, T., Hurn, S. and Lindsay, K. (2009). It never rains but it pours: Modeling the persistence of spikes in electricity prices. The Energy Journal 30 25–48.
  • de Boor, C. (2001). A Practical Guide to Splines, revised ed. Applied Mathematical Sciences 27. Springer, New York.
  • Fan, J. and Gijbels, I. (1996). Local Polynomial Modelling and Its Applications. Monographs on Statistics and Applied Probability 66. Chapman & Hall, London.
  • Febrero-Bande, M. and Oviedo de la Fuente, M. (2012). Statistical computing in functional data analysis: The R package fda.usc. Journal of Statistical Software 51 1–28.
  • Ferraty, F. and Vieu, P. (2006). Nonparametric Functional Data Analysis: Theory and Practice. Springer, New York.
  • Gervini, D. (2008). Robust functional estimation using the median and spherical principal components. Biometrika 95 587–600.
  • Gneiting, T. and Raftery, A. E. (2007). Strictly proper scoring rules, prediction, and estimation. J. Amer. Statist. Assoc. 102 359–378.
  • Granger, C. W. J. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37 424–438.
  • Grimm, V., Ockenfels, A. and Zoettl, G. (2008). Strommarktdesign: Zur Ausgestaltung der Auktionsregeln an der EEX. Zeitschrift für Energiewirtschaft 32 147–161.
  • Hall, P., Müller, H.-G. and Wang, J.-L. (2006). Properties of principal component methods for functional and longitudinal data analysis. Ann. Statist. 34 1493–1517.
  • Härdle, W. K. and Trück, S. (2010). The dynamics of hourly electricity prices. SFB 649 Discussion Papers 2010-013.
  • Hays, S., Shen, H. and Huang, J. Z. (2012). Functional dynamic factor models with application to yield curve forecasting. Ann. Appl. Stat. 6 870–894.
  • Huisman, R. andDe Jong, C. (2003). Option pricing for power prices with spikes. Energy Power Risk Management 7 12–16.
  • Huisman, R., Huurman, C. and Mahieu, R. (2007). Hourly electricity prices in day-ahead markets. Energy Economics 29 240–248.
  • Karakatsani, N. and Bunn, D. (2008). Forecasting electricity prices: The impact of fundamentals and time-varying coefficients. International Journal of Forecasting 24 764–785.
  • Knittel, C. R. and Roberts, M. R. (2005). An empirical examination of restructured electricity prices. Energy Economics 27 791–817.
  • Koopman, S. J., Ooms, M. and Carnero, M. A. (2007). Periodic seasonal Reg-ARFIMA-GARCH models for daily electricity spot prices. J. Amer. Statist. Assoc. 102 16–27.
  • Kosater, P. and Mosler, K. (2006). Can Markov regime-switching models improve power-price forecasts? Evidence from German daily power prices. Applied Energy 83 943–958.
  • Lau, A. and McSharry, P. (2010). Approaches for multi-step density forecasts with application to aggregated wind power. Ann. Appl. Stat. 4 1311–1341.
  • Li, Y. and Hsing, T. (2010). Uniform convergence rates for nonparametric regression and principal component analysis in functional/longitudinal data. Ann. Statist. 38 3321–3351.
  • Liebl, D. (2013). Supplement to “Modeling and forecasting electricity spot prices: A functional data perspective.” DOI:10.1214/13-AOAS652SUPP.
  • Liu, C., Ray, S., Hooker, G. and Friedl, M. (2012). Functional factor analysis for periodic remote sensing data. Ann. Appl. Stat. 6 601–624.
  • Locantore, N., Marron, J. S., Simpson, D. G., Tripoli, N., Zhang, J. T. and Cohen, K. L. (1999). Robust principal component analysis for functional data. Test 8 1–73. With discussion and a rejoinder by the authors.
  • Park, B. U., Mammen, E., Härdle, W. and Borak, S. (2009). Time series modelling with semiparametric factor dynamics. J. Amer. Statist. Assoc. 104 284–298.
  • Ramsay, J. O. and Silverman, B. W. (2005). Functional Data Analysis, 2nd ed. Springer, New York.
  • Rice, J. A. and Silverman, B. W. (1991). Estimating the mean and covariance structure nonparametrically when the data are curves. J. R. Stat. Soc. Ser. B Stat. Methodol. 53 233–243.
  • Staniswalis, J. G. and Lee, J. J. (1998). Nonparametric regression analysis of longitudinal data. J. Amer. Statist. Assoc. 93 1403–1418.
  • Vilar, J. M., Cao, R. and Aneiros, G. (2012). Forecasting next-day electricity demand and price using nonparametric functional methods. International Journal of Electrical Power & Energy Systems 39 48–55.
  • Weron, R., Bierbrauer, M. and Trück, S. (2004). Modeling electricity prices: Jump diffusion and regime switching. Physica A: Statistical and Theoretical Physics 336 39–48.
  • Yao, F., Müller, H.-G. and Wang, J.-L. (2005). Functional data analysis for sparse longitudinal data. J. Amer. Statist. Assoc. 100 577–590.

Supplemental materials

  • Supplementary material: R-codes and data set. In this supplement we provide a zip file containing the R-Codes and the data set used to model and forecast electricity spot prices by the functional factor model as described in this paper.