Modeling and Forecasting Electricity Spot Prices: A Functional Data Perspective

Liebl, Dominik (2013): Modeling and Forecasting Electricity Spot Prices: A Functional Data Perspective. Published in: The Annals of Applied Statistics , Vol. 7, No. 3 (September 2013): pp. 1562-1592.

Abstract

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 electric- ity 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 or- der 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 parameter- ize 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 se- ries models as well as two alternative functional data models.

• Item Type: MPRA Paper
• Language: English
• Keywords: Functional factor model, functional data analysis, time series analysis, fundamental market model, merit order curve, European Energy Exchange, EEX
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling

References

ANTOCH, J., P RCHAL, L., D E ROSA, M. R. and SARDA , P. (2010). Electricity consumption pre- diction with functional linear regression using spline estimators. J. Appl. Stat. 37 2027–2041. MR2740138

BENEDETTI, J. K. (1977). On the nonparametric estimation of regression functions. J. R. Stat. Soc. Ser. B Stat. Methodol. 39 248–253. MR0494656 B ENKO, M., HÄRDLE, W. and K NEIP , A. (2009). Common functional principal components. Ann. Statist. 37 1–34. MR2488343

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., P ELAGATTI, M. and BALDI, F. (2010). Long-run relations in European electricity prices. J. Appl. Econometrics 25 805–832. MR2756987 B ROCKWELL , P. J. and DAVIS, R. A. (1991). Time Series: Theory and Methods, 2nd ed. Springer, New York. MR1093459

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., H URN, S. and L INDSAY, 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. MR1900298

FAN, J. and G IJBELS , I. (1996). Local Polynomial Modelling and Its Applications. Monographs on Statistics and Applied Probability 66. Chapman & Hall, London. MR1383587

FEBRERO-BANDE, M. and OVIEDO DE LA F UENTE , 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. MR2229687

GERVINI, D. (2008). Robust functional estimation using the median and spherical principal compo- nents. Biometrika 95 587–600. MR2443177

GNEITING, T. and RAFTERY , A. E. (2007). Strictly proper scoring rules, prediction, and estimation. J. Amer. Statist. Assoc. 102 359–378. MR2345548

GRANGER, C. W. J. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37 424–438.

GRIMM , V., O CKENFELS, A. and ZOETTL, G. (2008). Strommarktdesign: Zur Ausgestaltung der Auktionsregeln an der EEX. Zeitschrift für Energiewirtschaft 32 147–161.

HALL, P., M ÜLLER , H.-G. and WANG, J.-L. (2006). Properties of principal component methods for functional and longitudinal data analysis. Ann. Statist. 34 1493–1517. MR2278365

HÄRDLE, W. K. and TRÜCK , S. (2010). The dynamics of hourly electricity prices. SFB 649 Dis- cussion 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. MR3012513

HUISMAN, R. and DE JONG, C. (2003). Option pricing for power prices with spikes. Energy Power Risk Management 7 12–16.

HUISMAN, R., HUURMAN , C. and M AHIEU, R. (2007). Hourly electricity prices in day-ahead mar- kets. Energy Economics 29 240–248.

KARAKATSANI, N. and BUNN , D. (2008). Forecasting electricity prices: The impact of fundamen- tals 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 C ARNERO, M. A. (2007). Periodic seasonal Reg-ARFIMA- GARCH models for daily electricity spot prices. J. Amer. Statist. Assoc. 102 16–27. MR2345529

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 M CSHARRY , P. (2010). Approaches for multi-step density forecasts with application to aggregated wind power. Ann. Appl. Stat. 4 1311–1341. MR2758330

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. MR2766854

LIU , C., R AY , S., H OOKER , G. and FRIEDL , M. (2012). Functional factor analysis for periodic remote sensing data. Ann. Appl. Stat. 6 601–624. MR2976484

LOCANTORE , N., MARRON, J. S., S IMPSON, D. G., T RIPOLI, 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. MR1707596

PARK , B. U., M AMMEN, E., HÄRDLE, W. and BORAK, S. (2009). Time series modelling with semiparametric factor dynamics. J. Amer. Statist. Assoc. 104 284–298. MR2504378

RAMSAY , J. O. and S ILVERMAN, B. W. (2005). Functional Data Analysis, 2nd ed. Springer, New York. MR2168993

RICE , J. A. and S ILVERMAN, B. W. (1991). Estimating the mean and covariance structure non- parametrically when the data are curves. J. R. Stat. Soc. Ser. B Stat. Methodol. 53 233–243. MR1094283

STANISWALIS , J. G. and L EE, J. J. (1998). Nonparametric regression analysis of longitudinal data. J. Amer. Statist. Assoc. 93 1403–1418. MR1666636

VILAR, J. M., C AO , 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 T RÜCK , 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 W ANG , J.-L. (2005). Functional data analysis for sparse longitudinal data. J. Amer. Statist. Assoc. 100 577–590. MR2160561