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Modeling electricity loads in California: ARMA models with hyperbolic noise

Author

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  • Joanna Nowicka-Zagrajek
  • Rafal Weron

Abstract

In this paper we address the issue of modeling and forecasting electricity loads. We apply a two-step procedure to a series of system-wide loads from the California power market. First, we remove the weekly and annual seasonalities. Then, after analyzing properties of the deseasonalized data we fit an autoregressive moving average model. The obtained residuals seem to be independent but with tails heavier than Gaussian. It turns out that the hyperbolic distribution provides an excellent fit. As a justification for our approach we supply out-of-sample forecasts. As it turns out, our method performs significantly better than the one used by the California System Operator.

Suggested Citation

  • Joanna Nowicka-Zagrajek & Rafal Weron, 2002. "Modeling electricity loads in California: ARMA models with hyperbolic noise," HSC Research Reports HSC/02/02, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    • Handle: RePEc:wuu:wpaper:hsc0202
    DOI: doi:10.1016/S0165-1684(02)00318-3
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    File URL: http://dx.doi.org/doi:10.1016/S0165-1684(02)00318-3
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    References listed on IDEAS

    as
    1. Ramanathan, Ramu & Engle, Robert & Granger, Clive W. J. & Vahid-Araghi, Farshid & Brace, Casey, 1997. "Shorte-run forecasts of electricity loads and peaks," International Journal of Forecasting, Elsevier, vol. 13(2), pages 161-174, June.
    2. Smith, Michael, 2000. "Modeling and Short-term Forecasting of New South Wales Electricity System Load," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(4), pages 465-478, October.
    3. Eberlein, Ernst & Keller, Ulrich & Prause, Karsten, 1998. "New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model," The Journal of Business, University of Chicago Press, vol. 71(3), pages 371-405, July.
    4. Weron, Rafal, 2000. "Energy price risk management," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 285(1), pages 127-134.
    5. Zhang, Guoqiang & Eddy Patuwo, B. & Y. Hu, Michael, 1998. "Forecasting with artificial neural networks:: The state of the art," International Journal of Forecasting, Elsevier, vol. 14(1), pages 35-62, March.
    6. Ludmila E. Ivancheva, 2001. "The non‐Gaussian nature of bibliometric and scientometric distributions: A new approach to interpretation," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 52(13), pages 1100-1105.
    7. Weron, R. & Kozłowska, B. & Nowicka-Zagrajek, J., 2001. "Modeling electricity loads in California: a continuous-time approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 344-350.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Electricity load; ARMA model; Heavy tails; Hyperbolic distribution; Forecast;
    All these keywords.

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • Q40 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - General

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