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Some Statistical Investigations on the Nature and Dynamics of Electricity Prices

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  • Giulio Bottazzi
  • Sandro Sapio
  • Angelo Secchi

Abstract

It is widely accepted that in liberalized electricity markets log-returns display fat-tailed densities. Besides qualitative assessments, so far precise characterizations of the shape of the distribution have been seldom provided. In this work, we characterize the conditional and unconditional probability density functions of daily electricity log-returns, and of the underlying shocks from the NordPool market, for each of the 24 hours, through a very flexible and general family of distributions, namely the Subbotin family. Our study contributes with novel results in the field. First, we show that price fluctuations in electricity markets are additive in nature. We do this by exploiting a scaling relationship between price level and volatility, which is in turn a new result in the electricity markets literature. Second, in line with recent studies, we uncover the existence of multiple regimes in price dynamics, and we characterize the distributional shape for each of them. Interestingly, the shocks behind electricity price dynamics are approximately Laplace if one conditions on low price levels, and closer to a Gaussian in correspondence of high initial price levels. These results are at variance with the evidence from financial markets. The peculiar non-storable nature of electricity, and the varying strength of correlations between bidding behaviors at different load levels are suggested as possible key factors behind the specificities of electricity markets outcomes.

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Bibliographic Info

Paper provided by Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy in its series LEM Papers Series with number 2004/13.

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Date of creation: 01 Jul 2004
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Handle: RePEc:ssa:lemwps:2004/13

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Keywords: Electricity Markets; Subbotin Distribution; Laplace Distribution; Additive Process; Scaling;

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  1. Lucia, Julio J. & Schwartz, Eduardo, 2000. "Electricity prices and power derivatives: Evidence from the Nordic Power Exchange," University of California at Los Angeles, Anderson Graduate School of Management, Anderson Graduate School of Management, UCLA qt12w8v7jj, Anderson Graduate School of Management, UCLA.
  2. Haldrup, Niels & Nielsen, Morten Orregaard, 2006. "A regime switching long memory model for electricity prices," Journal of Econometrics, Elsevier, Elsevier, vol. 135(1-2), pages 349-376.
  3. Bystrom, Hans N. E., 2005. "Extreme value theory and extremely large electricity price changes," International Review of Economics & Finance, Elsevier, Elsevier, vol. 14(1), pages 41-55.
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  6. Sandro Sapio, 2004. "Markets Design, Bidding Rules, and Long Memory in Electricity Prices," Revue d'Économie Industrielle, Programme National Persée, vol. 107(1), pages 151-170.
  7. Alvaro Escribano & Juan Ignacio Peña & Pablo Villaplana, 2002. "Modeling Electricity Prices: International Evidence," Economics Working Papers we022708, Universidad Carlos III, Departamento de Economía.
  8. Knittel, Christopher R. & Roberts, Michael R., 2005. "An empirical examination of restructured electricity prices," Energy Economics, Elsevier, Elsevier, vol. 27(5), pages 791-817, September.
  9. Jeremy Berkowitz & Lutz Kilian, 2000. "Recent developments in bootstrapping time series," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 19(1), pages 1-48.
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  12. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, Elsevier, vol. 3(1-2), pages 125-144.
  13. Jeremy Berkowitz & Ionel Birgean & Lutz Kilian, 1999. "On the finite-sample accuracy of nonparametric resampling algorithms for economic time series," Finance and Economics Discussion Series, Board of Governors of the Federal Reserve System (U.S.) 1999-04, Board of Governors of the Federal Reserve System (U.S.).
  14. Von der Fehr, N.H.M. & Harbord, D., 1992. "Spot Market Competition in the UK Electricity Industry," Memorandum, Oslo University, Department of Economics 09/1992, Oslo University, Department of Economics.
  15. Rafal Weron & Michael Bierbrauer & Stefan Trück, 2003. "Modeling electricity prices: jump diffusion and regime switching," HSC Research Reports, Hugo Steinhaus Center, Wroclaw University of Technology HSC/03/01, Hugo Steinhaus Center, Wroclaw University of Technology.
  16. Bottazzi, Giulio & Secchi, Angelo, 2003. "Why are distributions of firm growth rates tent-shaped?," Economics Letters, Elsevier, Elsevier, vol. 80(3), pages 415-420, September.
  17. Joskow, Paul L, 1996. "Introducing Competition into Regulated Network Industries: From Hierarchies to Markets in Electricity," Industrial and Corporate Change, Oxford University Press, vol. 5(2), pages 341-82.
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Citations

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Cited by:
  1. Massimiliano Serati & Matteo Manera & Michele Plotegher, 2008. "Modelling electricity prices: from the state of the art to a draft of a new proposal," LIUC Papers in Economics, Cattaneo University (LIUC) 210, Cattaneo University (LIUC).
  2. Weron, Rafal, 2009. "Forecasting wholesale electricity prices: A review of time series models," MPRA Paper 21299, University Library of Munich, Germany.
  3. Joachim Kaldasch, 2011. "Evolutionary Model of Non-Durable Markets," Papers 1109.5791, arXiv.org.
  4. Joachim Kaldasch, 2012. "Evolutionäre Diffusion und der Produktlebenszyklus von Gebrauchsgütern," EconStor Preprints 59748, ZBW - German National Library of Economics.
  5. Joachim Kaldasch, 2013. "Evolutionary Model of a Anonymous Consumer Durable Market," Papers 1306.3395, arXiv.org.
  6. Kaldasch, Joachim, 2012. "Evolutionary model of the growth and size of firms," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 391(14), pages 3751-3769.
  7. Sandro Sapio, 2006. "An Empirically Based Model of the Supply Schedule in Day-Ahead Electricity Markets," LEM Papers Series, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy 2006/12, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  8. Tomasz Kozubowski & Saralees Nadarajah, 2010. "Multitude of Laplace distributions," Statistical Papers, Springer, Springer, vol. 51(1), pages 127-148, January.
  9. Weron, Rafal & Misiorek, Adam, 2007. "Heavy tails and electricity prices: Do time series models with non-Gaussian noise forecast better than their Gaussian counterparts?," MPRA Paper 2292, University Library of Munich, Germany, revised Oct 2007.
  10. Andrea Petrella & Sandro Sapio, 2010. "No PUN intended: A time series analysis of the Italian day-ahead electricity prices," RSCAS Working Papers, European University Institute 2010/03, European University Institute.
  11. Michel Culot & Valérie Goffin & Steve Lawford & Sébastien De Meten & Yves Smeers, 2013. "Practical stochastic modelling of electricity prices," Post-Print hal-01021603, HAL.

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