IDEAS home Printed from https://ideas.repec.org/p/mse/cesdoc/b08013.html
   My bibliography  Save this paper

The k-factor Gegenbauer asymmetric Power GARCH approach for modelling electricity spot price dynamics

Author

Abstract

Electricity spot prices exhibit a number of typical features that are not found in most financial time series, such as complex seasonality patterns, persistence (hyperbolic decay of the autocorrelation function), mean reversion, spikes, asymmetric behavior and leptokurtosis. Efforts have been made worldwide to model the behaviour of the electricity's market price. In this paper, we propose a new approach dealing with the stationary k-factor Gegenbauer process with asymmetric Power GARCH noise under conditional Student-t distribution, which can take into account the previous features. We derive the stationary and invertible conditions as well as the ?th-order moment of this model that we called GGk-APARCH model. Then we focus on the estimation parameters and provide the analytical from of the likelihood which permits to obtain consitent estimates. In order to characterize the properties of these estimates we perform a Monte Carlo experiment. Finally the previous approach is used to the model electricity spot prices coming from the Leipzig Power Exchange (LPX) in Germany, Powernext in France, Operadora del Mercado Espagñol de Electricidad (OMEL) in Spain and the Pennsylvania-New Jersey-Maryland (PJM) interconnection in United States. In terms of forecasting criteria we obtain very good results comparing with models using hederoscedastic asymmetric errors

Suggested Citation

  • Abdou Kâ Diongue & Dominique Guegan, 2008. "The k-factor Gegenbauer asymmetric Power GARCH approach for modelling electricity spot price dynamics," Documents de travail du Centre d'Economie de la Sorbonne b08013, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:b08013
    as

    Download full text from publisher

    File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2008/B08013.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Koopman, Siem Jan & Ooms, Marius & Carnero, M. Angeles, 2007. "Periodic Seasonal Reg-ARFIMAGARCH Models for Daily Electricity Spot Prices," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 16-27, March.
    2. Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
    3. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    4. Knittel, Christopher R. & Roberts, Michael R., 2005. "An empirical examination of restructured electricity prices," Energy Economics, Elsevier, vol. 27(5), pages 791-817, September.
    5. Abdou Kâ Diongue & Dominique Guegan, 2004. "Estimating parameters for a k-GIGARCH process," Post-Print halshs-00188531, HAL.
    6. Andrew A. Weiss, 1984. "Arma Models With Arch Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 5(2), pages 129-143, March.
    7. Ling, Shiqing & McAleer, Michael, 2002. "NECESSARY AND SUFFICIENT MOMENT CONDITIONS FOR THE GARCH(r,s) AND ASYMMETRIC POWER GARCH(r,s) MODELS," Econometric Theory, Cambridge University Press, vol. 18(3), pages 722-729, June.
    8. Pagan, Adrian R. & Schwert, G. William, 1990. "Alternative models for conditional stock volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 267-290.
    9. Hylleberg, S. & Engle, R. F. & Granger, C. W. J. & Yoo, B. S., 1990. "Seasonal integration and cointegration," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 215-238.
    10. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
    11. Yi-Ting Chen, 2002. "On the Robustness of Ljung-Box and McLeod-Li Q Tests: A Simulation Study," Economics Bulletin, AccessEcon, vol. 3(17), pages 1-10.
    12. Bruno Bosco & Lucia Parisio & Matteo Pelagatti, 2007. "Deregulated Wholesale Electricity Prices in Italy: An Empirical Analysis," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 13(4), pages 415-432, November.
    13. Dominique Guegan & Abdou Kâ Diongue & Bertrand Vignal, 2004. "A k- factor GIGARCH process : estimation and application to electricity market spot prices," Post-Print halshs-00188533, HAL.
    14. Schwert, G William, 1990. "Stock Volatility and the Crash of '87," The Review of Financial Studies, Society for Financial Studies, vol. 3(1), pages 77-102.
    15. Soares, Lacir Jorge & Souza, Leonardo Rocha, 2006. "Forecasting electricity demand using generalized long memory," International Journal of Forecasting, Elsevier, vol. 22(1), pages 17-28.
    16. Rafal Weron & Ingve Simonsen & Piotr Wilman, 2003. "Modeling highly volatile and seasonal markets: evidence from the Nord Pool electricity market," Econometrics 0303007, University Library of Munich, Germany.
    17. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    18. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    19. repec:kap:iaecre:v:13:y:2007:i:4:p:415-432 is not listed on IDEAS
    20. Lester Hadsell, Achla Marathe and Hany A. Shawky, 2004. "Estimating the Volatility of Wholesale Electricity Spot Prices in the US," The Energy Journal, International Association for Energy Economics, vol. 0(Number 4), pages 23-40.
    21. Chung, Ching-Fan & Baillie, Richard T, 1993. "Small Sample Bias in Conditional Sum-of-Squares Estimators of Fractionally Integrated ARMA Models," Empirical Economics, Springer, vol. 18(4), pages 791-806.
    22. Helen Higgs & Andrew C. Worthington, 2005. "Systematic Features of High-Frequency Volatility in Australian Electricity Markets: Intraday Patterns, Information Arrival and Calendar Effects," The Energy Journal, International Association for Energy Economics, vol. 0(Number 4), pages 23-42.
    23. repec:ebl:ecbull:v:3:y:2002:i:17:p:1-10 is not listed on IDEAS
    24. Rafal Weron, 2006. "Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0601, December.
    25. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    26. Wilson, Jack W & Jones, Charles P & Lundstrum, Leonard L, 2001. "Stochastic Properties of Time-Averaged Financial Data: Explanation and Empirical Demonstration Using Monthly Stock Prices," The Financial Review, Eastern Finance Association, vol. 36(3), pages 175-190, August.
    27. Y. K. Tse, 1998. "The conditional heteroscedasticity of the yen-dollar exchange rate," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(1), pages 49-55.
    28. Hassler, Uwe & Wolters, Jurgen, 1994. "On the power of unit root tests against fractional alternatives," Economics Letters, Elsevier, vol. 45(1), pages 1-5, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Diongue, Abdou Kâ & Guégan, Dominique & Vignal, Bertrand, 2009. "Forecasting electricity spot market prices with a k-factor GIGARCH process," Applied Energy, Elsevier, vol. 86(4), pages 505-510, April.
    2. Montero, José M. & García-Centeno, Maria C. & Fernández-Avilés, Gema, 2011. "Modelling the Volatility of the Spanish Wholesale Electricity Spot Market. Asymmetric GARCH Models vs. Threshold ARSV model/Modelización de la volatilidad en el mercado eléctrico español. Modelos GARC," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 29, pages 597-616, Agosto.
    3. Faheem Jan & Ismail Shah & Sajid Ali, 2022. "Short-Term Electricity Prices Forecasting Using Functional Time Series Analysis," Energies, MDPI, vol. 15(9), pages 1-15, May.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Degiannakis, Stavros & Xekalaki, Evdokia, 2004. "Autoregressive Conditional Heteroskedasticity (ARCH) Models: A Review," MPRA Paper 80487, University Library of Munich, Germany.
    2. Diongue, Abdou Kâ & Guégan, Dominique, 2007. "The stationary seasonal hyperbolic asymmetric power ARCH model," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1158-1164, June.
    3. Per B. Solibakke, 2022. "Step‐ahead spot price densities using daily synchronously reported prices and wind forecasts," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(1), pages 17-42, January.
    4. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521779654, September.
    5. Geoffrey F. Loudon & Wing H. Watt & Pradeep K. Yadav, 2000. "An empirical analysis of alternative parametric ARCH models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(2), pages 117-136.
    6. Kian Teng Kwek & Kuan Nee Koay, 2006. "Exchange rate volatility and volatility asymmetries: an application to finding a natural dollar currency," Applied Economics, Taylor & Francis Journals, vol. 38(3), pages 307-323.
    7. Amélie Charles & Olivier Darné, 2019. "The accuracy of asymmetric GARCH model estimation," International Economics, CEPII research center, issue 157, pages 179-202.
    8. Eskandar A. Tooma, 2003. "Modeling and Forecasting Egyptian Stock Market Volatility Before and After Price Limits," Working Papers 0310, Economic Research Forum, revised Apr 2003.
    9. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038, Elsevier.
    10. Tak Siu & John Lau & Hailiang Yang, 2007. "On Valuing Participating Life Insurance Contracts with Conditional Heteroscedasticity," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 14(3), pages 255-275, September.
    11. Hentschel, Ludger, 1995. "All in the family Nesting symmetric and asymmetric GARCH models," Journal of Financial Economics, Elsevier, vol. 39(1), pages 71-104, September.
    12. S. M. Abdullah & Salina Siddiqua & Muhammad Shahadat Hossain Siddiquee & Nazmul Hossain, 2017. "Modeling and forecasting exchange rate volatility in Bangladesh using GARCH models: a comparison based on normal and Student’s t-error distribution," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 3(1), pages 1-19, December.
    13. Giot, Pierre & Laurent, Sebastien, 2004. "Modelling daily Value-at-Risk using realized volatility and ARCH type models," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 379-398, June.
    14. Bucevska Vesna, 2013. "An Empirical Evaluation of GARCH Models in Value-at-Risk Estimation: Evidence from the Macedonian Stock Exchange," Business Systems Research, Sciendo, vol. 4(1), pages 49-64, March.
    15. van Mierlo, J.G.A., 2001. "Over de verhouding tussen overheid, marktwerking en privatisering. Een economische meta-analyse," Research Memorandum 014, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    16. Xekalaki, Evdokia & Degiannakis, Stavros, 2005. "Evaluating volatility forecasts in option pricing in the context of a simulated options market," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 611-629, April.
    17. repec:awi:wpaper:0472 is not listed on IDEAS
    18. Kim, Dongcheol & Kon, Stanley J., 1999. "Structural change and time dependence in models of stock returns," Journal of Empirical Finance, Elsevier, vol. 6(3), pages 283-308, September.
    19. LeBaron, Blake, 2003. "Non-Linear Time Series Models in Empirical Finance,: Philip Hans Franses and Dick van Dijk, Cambridge University Press, Cambridge, 2000, 296 pp., Paperback, ISBN 0-521-77965-0, $33, [UK pound]22.95, [," International Journal of Forecasting, Elsevier, vol. 19(4), pages 751-752.
    20. Segnon Mawuli & Lau Chi Keung & Wilfling Bernd & Gupta Rangan, 2022. "Are multifractal processes suited to forecasting electricity price volatility? Evidence from Australian intraday data," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 26(1), pages 73-98, February.
    21. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.

    More about this item

    Keywords

    Asymmetric distribution function; electricity spot prices; Leptokurtosis; persistence; seasonality; GARMA; A-PARCH;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mse:cesdoc:b08013. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Lucie Label (email available below). General contact details of provider: https://edirc.repec.org/data/cenp1fr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.