Efficient estimation of Markov regime-switching models: An application to electricity wholesale market prices

Weron, Rafal and Janczura, Joanna (2010): Efficient estimation of Markov regime-switching models: An application to electricity wholesale market prices.

Abstract

In this paper we discuss the calibration issues of models built on mean-reverting processes combined with Markov switching. Due to the unobservable switching mechanism, estimation of Markov regime-switching (MRS) models requires inferring not only the model parameters but also the state process values at the same time. The situation becomes more complicated when the individual regimes are independent from each other and at least one of them exhibits temporal dependence (like mean reversion in electricity spot prices). Then the temporal latency of the dynamics in the regimes as to be taken into account. In this paper we propose a method that greatly reduces the computational burden induced by the introduction of independent regimes in MRS models. We perform a simulation study to test the efficiency of the proposed method and apply it to a sample series of wholesale electricity spot prices from the German EEX market. The proposed 3-regime MRS model fits this data well and also contains unique features that allow for useful interpretations of the price dynamics.

• Item Type: MPRA Paper
• Language: English
• Keywords: Markov regime-switching; heteroskedasticity; EM algorithm; independent regimes; electricity spot price
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; Q - Agricultural and Natural Resource Economics ; Environmental and Ecological Economics > Q4 - Energy > Q40 - General

References

Barz, G., Johnson, B. (1998). Modeling the prices of commodities that are costly to store: The case of electricity. Proceedings of the Chicago Risk Management Conference.

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

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

Christensen, T., Hurn, S., Lindsay, K. (2009). It never rains but it pours: modeling the persistence of spikes in electricity prices. The Energy Journal 30(1), 25-48.

Cox, J.C., Ingersoll, J.E., Ross, S.A. (1985). A theory of the term structure of interest rates. Econometrica 53, 385-407.

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

Dempster, A., Laird, N., Rubin, D.B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society 39, 1-38.

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

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.

Fink, G.A. (2008). Markov Models for Pattern Recognition: From Theory to Applications. Springer.

Franses, P.H., van Dijk, D. (2000). Nonlinear Time Series Models in Empirical Finance. Cambridge University Press.

Gray, S.F. (1996). Modeling the conditional distribution of interest rates as a regimeswitching process. Journal of Financial Economics 42, 27-62.

Hamilton, J. (1989). A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57, 357-384.

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

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

Huisman, R., de Jong, C. (2002). Option formulas for mean-reverting power prices with spikes. ERIM Report Series Reference No. ERS-2002-96-F&A.

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. (2010). Goodness-of-fit testing for regime-switching models. Working paper. Available at MPRA: http://mpra.ub.uni-muenchen.de/22871.

Kaminski, V. (1997). The challenge of pricing and risk managing electricity derivatives. In: The US Power Market. Risk Books.

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

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

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

Mamon, R.S., Elliott, R.J., eds. (2007). Hidden Markov Models in Finance. International Series in Operations Research & Management Science, Vol. 104, Springer.

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.

Scharpf, R.B., Parmigiani, G., Pevsner, J., Ruczinski, I. (2008) Hidden Markov models for the assessment of chromosomal alterations using high-throughput SNP arrays. The Annals of Applied Statistics 2(2), 687-713.

Shirley, K.E., Small, D.S., Lynch, K.G., Maisto, S.A., Oslin, D.W. (2010). Hidden Markov models for alcoholism treatment trial data. The Annals of Applied Statistics 4(1), 366-395.

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/.

Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics 5, 177-188.

Weron, R. (2006). Modeling and forecasting electricity loads and prices: A statistical approach. Wiley, Chichester.

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