Identifying spikes and seasonal components in electricity spot price data: A guide to robust modeling

Janczura, Joanna and Trueck, Stefan and Weron, Rafal and Wolff, Rodney (2012): Identifying spikes and seasonal components in electricity spot price data: A guide to robust modeling.

Abstract

An important issue in fitting stochastic models to electricity spot prices is the estimation of a component to deal with trends and seasonality in the data. Unfortunately, estimation routines for the long-term and short-term seasonal pattern are usually quite sensitive to extreme observations, known as electricity price spikes. Improved robustness of the model can be achieved by (a) filtering the data with some reasonable procedure for outlier detection, and then (b) using estimation and testing procedures on the filtered data. In this paper we examine the effects of different treatment of extreme observations on model estimation and on determining the number of spikes (outliers). In particular we compare results for the estimation of the seasonal and stochastic components of electricity spot prices using either the original or filtered data. We find significant evidence for a superior estimation of both the seasonal short-term and long-term components when the data have been treated carefully for outliers. Overall, our findings point out the substantial impact the treatment of extreme observations may have on these issues and, therefore, also on the pricing of electricity derivatives like futures and option contracts. An added value of our study is the ranking of different filtering techniques used in the energy economics literature, suggesting which methods could be and which should not be used for spike identification.

• Item Type: MPRA Paper
• Language: English
• Keywords: Electricity spot price; Outlier treatment; Price spike; Robust modeling; Seasonality
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection; Q - Agricultural and Natural Resource Economics ; Environmental and Ecological Economics > Q4 - Energy > Q47 - Energy Forecasting; C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs > C80 - General

References

Barlow, M. (2002) A diffusion model for electricity prices. Mathematical Finance 12, 287-298.

Becker, R., Hurn, S., Pavlov, V. (2007) Modelling Spikes in Electricity Prices. The Economic Record 83(263), 371-382.

Benth, F.E., Benth, J.S., Koekebakker, S. (2008) Stochastic Modeling of Electricity and Related Markets. World Scientific, Singapore.

Bhanot, K. (2000) Behavior of power prices: Implications for the valuation and hedging of financial contracts. The Journal of Risk 2, 43-62.

Bierbrauer,M.,Menn, C., Rachev, S.T., Tr¨uck, S. (2007) Spot and derivative pricing in the EEX power market. Journal of Banking and Finance 31, 3462-3485.

Bierbrauer, M., Tr¨uck, S., Weron, R. (2004) Modeling electricity prices with regime switching models. Lecture Notes in Computer Science 3039, 859-867.

Boogert, A., Dupont, D. (2008) When supply meets demand: The case of hourly spot electricity prices. IEEE Transactions on Power Systems 23(2), 389-398.

Borovkova, S., Permana, F.J. (2006) Modelling electricity prices by the potential jump-diffusion. In: A.N. Shiryaev et al. (eds.), Stochastic Finance – Proceedings of StochFin2004, Springer, 239-264.

Cappe, O., Moulines E., Ryden T. (2005). Inference in Hidden Markov Models. Springer.

Cartea, A., Figueroa, M. (2005) Pricing in electricity markets: A mean reverting jump diffusion model with seasonality. Applied Mathematical Finance 12(4), 313-335.

Clewlow, L., Strickland, C. (2000). Energy Derivatives – Pricing and Risk Management. Lacima Publications.

De Jong, C. (2006) The nature of power spikes: A regime-switch approach. Studies in Nonlinear Dynamics & Econometrics 10(3), Article 3.

Deng, S.-J. (1998) Stochastic models of energy commodity prices and their applications: Mean-reversion with jumps and spikes. PSerc Working Paper 98-28.

Erlwein, C., Benth, F.E., Mamon, R. (2010) HMM filtering and parameter estimation of an electricity spot price model. Energy Economics 32, 1034-1043.

Ethier, R., Mount, T. (1998) Estimating the volatility of spot prices in restructured electricity markets and the implications for option values. PSerc Working Paper 98-31.

Eydeland, A., Wolyniec, K. (2012) Energy and Power Risk Management (2nd ed.). Wiley, Hoboken, NJ.

Fanone, E., Gamba, A., Prokopczuk, M. (2012) The case of negative day-ahead electricity prices. Energy Economics, In press, doi:10.1016/j.eneco.2011.12.006.

Fleten, S.-E., Heggedal, A.M., Siddiqui, A. (2011) Transmission capacity between Norway and Germany: a real options analysis. Journal of Energy Markets 4(1), 121-147.

Garcia, R.C., Contreras, J., van Akkeren, M., Garcia, J.B. (2005) A GARCH forecasting model to predict day-ahead electricity prices. IEEE Transactions on Power Systems 20(2), 867-874.

Geman, H., Roncoroni, A. (2006) Understanding the fine structure of electricity prices. Journal of Business 79, 1225-1261.

Haldrup, N., Nielsen, F.S., Nielsen, M.Ø. (2010) A vector autoregressive model for electricity prices subject to long memory and regime switching. Energy Economics 32, 1044-1058.

Hambly, B., Howison, S., Kluge, T. (2009) Modelling spikes and pricing swing options in electricity markets. Quantitative Finance 9(8), 937-949.

Hamilton, J. (1990) Analysis of time series subject to changes in regime. Journal of Econometrics 45, 39-70.

Haerdle,W., Kerkyacharian, G., Picard, D., Tsybakov, A. (1998) Wavelets, Approximation and Statistical Applications. Lecture Notes in Statistics 129. Springer-Verlag, New York.

Higgs, H., Worthington, A. (2008) Stochastic price modeling of high volatility, mean-reverting, spike-prone commodities: The Australian wholesale spot electricity market. Energy Economics 30, 3172-3185.

Hirsch, G. (2009) Pricing of hourly exercisable electricity swing options using different price processes. Journal of Energy Markets 2(2), 3-46.

Hochberg, Y., Tamhane, A.C. (1987) Multiple Comparison Procedures. Wiley, Hoboken, NJ.

Hollander, M., Wolfe, D.A. (1999) Nonparametric Statistical Methods. Wiley, Hoboken, NJ.

Huisman, R. (2009) An Introduction to Models for the Energy Markets. Risk Books.

Huisman, R., de Jong, C. (2003) Option pricing for power prices with spikes. Energy Power Risk Management 7.11, 12-16.

Huisman, R., Mahieu, R. (2003) Regime jumps in electricity prices. Energy Economics 25, 425-434.

Jabłonska, M., Nampala, H., Kauranne, T. (2011) The multiple-mean-reversion jump-diffusion model for Nordic electricity spot prices. Journal of Energy Markets 4(2), 3-25.

Janczura, J., Weron, R. (2010). An empirical comparison of alternate regime-switching models for electricity spot prices. Energy Economics 32, 1059-1073.

Janczura, J., Weron, R. (2012) Efficient estimation of Markov regime-switching models: An application to electricity spot prices, AStA - Advances in Statistical Analysis, Online First DOI:10.1007/s10182-011-0181-2.

Kaminski, V. (2004) Managing Energy Price Risk: The New Challenges and Solutions, 3rd ed. Risk Books, London.

Kanamura, T., Ohashi, K. (2008) On transition probabilities of regime switching in electricity prices. Energy Economics 30, 1158-1172.

Karakatsani, N.V., Bunn, D.W. (2008) Intra-day and regime-switching dynamics in electricity price formation. Energy Economics 30, 1776-1797.

Keles, D., Hartel, R., Most, D., Fichtner, W. (2012) Compressed-air energy storage power plant investments under uncertain electricity prices: An evaluation of compressed-air energy storage plants in liberalized energy markets. Journal of Energy Markets 5(1), 53-84.

Kholodnyi, V.A. (2005). Modeling power forward prices for power with spikes: A non-Markovian approach. Nonlinear Analysis 63, 958-965.

Kim, C.-J. (1994) Dynamic linear models with Markov-switching. Journal of Econometrics 60, 1-22.

Knittel, C.R., Roberts, M.R. (2005) An empirical examination of restructured electricity prices. Energy Economics 27, 791-817.

Koopman, S.J., Ooms,M., Carnero,M.A. (2007) Periodic seasonal reg-ARFIMA-GARCH models for daily electricity spot prices. Journal of the American Statistical Association 102(477), 16-27.

Lapuerta, C., Moselle, B. (2001) Recommendations for the Dutch electricity market. The Brattle Group Report, London.

Lucia, J.J., Schwartz, E.S. (2002) Electricity prices and power derivatives: Evidence fromthe Nordic Power Exchange. Review of Derivatives Research 5, 5-50.

Makridakis, S., Wheelwright, S.C., Hyndman, R.J. (1998) Forecasting – Methods and Applications, 3rd ed.. Wiley.

Mari, C. (2008) Random movements of power prices in competitive markets: A hybrid model approach. Journal of Energy Markets 1(2), 87-103.

Merton, R.C. (1976) Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics 3, 125-144.

Misiorek, A., Trueck, S.,Weron, R. (2006) Point and interval forecasting of spot electricity prices: Linear vs. non-linear time series models. Studies in Nonlinear Dynamics and Econometrics 10(3), Article 2.

Mount, T.D., Ning, Y., Cai, X. (2006) Predicting price spikes in electricity markets using a regime-switching model with time-varying parameters. Energy Economics 28: 62-80.

Nomikos, N.K., Soldatos, O.A. (2010) Analysis of model implied volatility for jump diffusion models: Empirical evidence from the Nordpool market. Energy Economics 32, 302-312.

Nowotarski, J., Tomczyk, J.,Weron, R. (2011)Wavelet-based modeling and forecasting of the seasonal component of spot electricity prices. The Energy Finance Christmas Workshop (EFC11), Wrocław, Dec. 19-20, 2011.

Pilipovic, D. (1998) Energy Risk: Valuing and Managing Energy Derivatives. McGraw-Hill, New York.

Percival, D.B., Walden, A.T. (2000) Wavelet Methods for Time Series Analysis. Cambridge University Press.

Seifert, J., Uhrig-Homburg, M. (2007) Modelling jumps in electricity prices: theory and empirical evidence. Review of Derivatives Research 10, 59-85.

Shahidehpour, M., Yamin, H., Li, Z. (2002) Market Operations in Electric Power Systems: Forecasting, Scheduling, and Risk Management. Wiley.

Simonsen, I. (2005) Volatility of power markets. Physica A 355, 10-20.

Stevenson, M. (2001) Filtering and forecasting spot electricity prices in the increasingly deregulated Australian electricity market. Research Paper No 63, Quantitative Finance Research Centre, University of Technology, Sydney.

Stevenson, M.J., Amaral, J.F.M., Peat, M. (2006) Risk management and the role of spot price predictions in the Australian retail electricity market. Studies in Nonlinear Dynamics and Econometrics 10(3), Article 4.

Trueck, S., Weron, R., Wolff, R. (2007) Outlier treatment and robust approaches for modeling electricity spot prices. Proceedings of the 56th Session of the ISI. Available at MPRA: http://mpra.ub.uni-muenchen.de/4711/.

Weron, R. (2006) Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach. Wiley, Chichester.

Weron, R. (2008) Market price of risk implied by Asian-style electricity options and futures. Energy Economics 30, 1098-1115.

Weron, R. (2009) Heavy-tails and regime-switching in electricity prices. Mathematical Methods of Operations Research 69(3), 457-473.

Weron, R., Bierbrauer, M., Trueck, S. (2004a) Modeling electricity prices: jump diffusion and regime switching. Physica A 336, 39-48.

Weron, R., Simonsen, I.,Wilman, P. (2004b) Modeling highly volatile and seasonal markets: Evidence from the Nord Pool electricity market. In: The Application of Econophysics, H. Takayasu (ed.), Springer, Tokyo, 182-191.