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

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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
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    File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2008/B08013.pdf
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    1. Shintani, Mototsugu & Linton, Oliver, 2004. "Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos," Journal of Econometrics, Elsevier, pages 1-33.
    2. Dominique Guegan & L. Mercier, 1998. "Stochastic or chaotic dynamics in high frequency financial data," Post-Print halshs-00199167, HAL.
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    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, pages 505-510.
    2. Diongue, Abdou Kâ & Guégan, Dominique & Vignal, Bertrand, 2009. "Forecasting electricity spot market prices with a k-factor GIGARCH process," Applied Energy, Elsevier, pages 505-510.
    3. 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 Economía Aplicada, Estudios de Economía Aplicada, vol. 29, pages 597-616, Agosto.

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    Keywords

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

    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

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