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Functional clustering and linear regression for peak load forecasting

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  • Goia, Aldo
  • May, Caterina
  • Fusai, Gianluca
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    Abstract

    In this paper we consider the problem of short-term peak load forecasting using past heating demand data in a district-heating system. Our data-set consists of four separate periods, with 198 days in each period and 24 hourly observations in each day. We can detect both an intra-daily seasonality and a seasonality effect within each period. We take advantage of the functional nature of the data-set and propose a forecasting methodology based on functional statistics. In particular, we use a functional clustering procedure to classify the daily load curves. Then, on the basis of the groups obtained, we define a family of functional linear regression models. To make forecasts we assign new load curves to clusters, applying a functional discriminant analysis. Finally, we evaluate the performance of the proposed approach in comparison with some classical models.

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    Bibliographic Info

    Article provided by Elsevier in its journal International Journal of Forecasting.

    Volume (Year): 26 (2010)
    Issue (Month): 4 (October)
    Pages: 700-711

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    Handle: RePEc:eee:intfor:v:26:y::i:4:p:700-711

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    Web page: http://www.elsevier.com/locate/ijforecast

    Related research

    Keywords: Short-term forecasting Out-of-sample Load curve Seasonality Functional regression Functional clustering Functional linear discriminant analysis;

    References

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    1. Hyndman, Rob J. & Shahid Ullah, Md., 2007. "Robust forecasting of mortality and fertility rates: A functional data approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4942-4956, June.
    2. Rob J Hyndman & Heather Booth, 2006. "Stochastic population forecasts using functional data models for mortality, fertility and migration," Monash Econometrics and Business Statistics Working Papers 14/06, Monash University, Department of Econometrics and Business Statistics.
    3. A. Onatski & V. Karguine, 2005. "Curve Forecasting by Functional Autoregression," Computing in Economics and Finance 2005 59, Society for Computational Economics.
    4. Ashish Sood & Gareth M. James & Gerard J. Tellis, 2009. "Functional Regression: A New Model for Predicting Market Penetration of New Products," Marketing Science, INFORMS, vol. 28(1), pages 36-51, 01-02.
    5. Cardot, Hervé & Ferraty, Frédéric & Sarda, Pascal, 1999. "Functional linear model," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 11-22, October.
    6. Gareth M. James & Trevor J. Hastie, 2001. "Functional linear discriminant analysis for irregularly sampled curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 533-550.
    7. Dordonnat, V. & Koopman, S.J. & Ooms, M. & Dessertaine, A. & Collet, J., 2008. "An hourly periodic state space model for modelling French national electricity load," International Journal of Forecasting, Elsevier, vol. 24(4), pages 566-587.
    8. Dotzauer, Erik, 2002. "Simple model for prediction of loads in district-heating systems," Applied Energy, Elsevier, vol. 73(3-4), pages 277-284, November.
    9. Alves da Silva, Alexandre P. & Ferreira, Vitor H. & Velasquez, Roberto M.G., 2008. "Input space to neural network based load forecasters," International Journal of Forecasting, Elsevier, vol. 24(4), pages 616-629.
    10. V. Dordonnat & S.J. Koopman & M. Ooms & A. Dessertaine & J. Collet, 2008. "An Hourly Periodic State Space Model for Modelling French National Electricity Load," Tinbergen Institute Discussion Papers 08-008/4, Tinbergen Institute.
    11. Rob J Hyndman & Shu Fan, 2008. "Density forecasting for long-term peak electricity demand," Monash Econometrics and Business Statistics Working Papers 6/08, Monash University, Department of Econometrics and Business Statistics.
    12. Rafal Weron, 2006. "Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0601.
    13. C. Abraham & P. A. Cornillon & E. Matzner-Løber & N. Molinari, 2003. "Unsupervised Curve Clustering using B-Splines," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 30(3), pages 581-595.
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    Cited by:
    1. Goia, Aldo, 2012. "A functional linear model for time series prediction with exogenous variables," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 1005-1011.
    2. Sigauke, C. & Chikobvu, D., 2011. "Prediction of daily peak electricity demand in South Africa using volatility forecasting models," Energy Economics, Elsevier, vol. 33(5), pages 882-888, September.
    3. Zhu, Suling & Wang, Jianzhou & Zhao, Weigang & Wang, Jujie, 2011. "A seasonal hybrid procedure for electricity demand forecasting in China," Applied Energy, Elsevier, vol. 88(11), pages 3807-3815.

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