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Periodically correlated models for short-term electricity load forecasting. (English) Zbl 1433.91110
Summary: During the last two decades, the model developed by J. R. Cancelo and A. Espasa [Forecasting daily demand for electricity with multiple-input nonlinear transfer function models: a case study. Tech. Rep. 91-21. Madrid: Carlos III University (1991), https://e-archivo.uc3m.es/bitstream/handle/10016/2808/we9121.pdf?sequence=1] has been used for predicting the Spanish electricity demand with good results. This paper proposes a new approach for estimating multiequation models that extends the previous work in different and important ways. Primarily, 24-h equations are assembled to form a periodic autoregressive-moving-average model, which significantly improves the short-term predictions. To reduce the computational problem, the full model is estimated in two steps, and a meticulous model of the nonlinear temperature effect is included using regression spline techniques. The method is currently being used by the Spanish Transmission System Operator (Red Eléctrica de España, REE) to make hourly forecasts of electricity demand from one to ten days ahead.
MSC:
91B84 Economic time series analysis
62G08 Nonparametric regression and quantile regression
62P30 Applications of statistics in engineering and industry; control charts
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
Software:
gamair
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References:
[1] Cancelo, J.; Espasa, A., Forecasting daily demand for electricity with multiple-input nonlinear transfer function models: a case study (1991), Carlos III University, Tech. rep
[2] Bunn, D.; Farmer, E., Comparative Models for Electrical Load Forecasting (1985), Wiley: Wiley New York
[3] Taylor, J. W.; de Menezes, L. M.; McSharry, P. E., A comparison of univariate methods for forecasting electricity demand up to a day ahead, Int. J. Forecast., 22, 1, 1-16 (2006)
[4] Taylor, J. W., Triple seasonal methods for short-term electricity demand forecasting, Eur. J. Oper. Res., 204, 1, 139-152 (2010) · Zbl 1178.91165
[5] Koopman, S. J.; Ooms, M.; Carnero, M. A., Periodic seasonal reg-ARFIMA-GARCH models for daily electricity spot prices, J. Am. Stat. Assoc., 102, 477, 16-27 (2007) · Zbl 1284.62786
[6] Clements, A.; Hurn, A.; Li, Z., Forecasting day-ahead electricity load using a multiple equation time series approach, Eur. J. Oper. Res., 251, 2, 522-530 (2016) · Zbl 1346.62159
[7] Ramanathan, R.; Engle, R.; Granger, C. W.; Vahid-Araghi, F.; Brace, C., Short-run forecasts of electricity loads and peaks, Int. J. Forecast., 13, 2, 161-174 (1997)
[8] Cottet, R.; Smith, M., Bayesian modeling and forecasting of intraday electricity load, J. Am. Stat. Assoc., 98, 464, 839-849 (2003)
[9] Cancelo, J. R.; Espasa, A.; Grafe, R., Forecasting the electricity load from one day to one week ahead for the Spanish system operator, Int. J. Forecast., 24, 4, 588-602 (2008)
[10] Dordonnat, V.; Koopman, S.; Ooms, M.; Dessertaine, A.; Collet, J., An hourly periodic state space model for modelling French national electricity load, Int. J. Forecast., 24, 4, 566-587 (2008)
[11] Engle, R. F.; Granger, C. W.J.; Rice, J., A. weiss, semiparametric estimates of the relation between weather and electricity sales, J. Am. Stat. Assoc., 81, 310-320 (1986)
[12] Charlton, N.; Singleton, C., A refined parametric model for short term load forecasting, Int. J. Forecast., 30, 2, 364-368 (2014)
[13] Pierrot, A.; Goude, Y., Short-term electricity load forecasting with generalized additive models, Proceedings of ISAP power, 410-416 (2011)
[14] Fan, S.; Hyndman, R. J., Short-term load forecasting based on a semi-parametric additive model, IEEE Trans. Power Syst., 27, 134-141 (2012)
[15] Gaillard, P.; Goude, Y.; Nedellec, R., Additive models and robust aggregation for GEFCom2014 probabilistic electric load and electricity price forecasting, Int. J. Forecast., 32, 3, 1038-1050 (2016)
[16] Ziel, F., Modeling public holidays in load forecasting: a german case study, J. Modern Power Syst. Clean Energy, 6, 2, 191-207 (2018)
[17] Nowicka-Zagrajek, J.; Weron, R., Modeling electricity loads in California: ARMA models with hyperbolic noise, Signal Process., 82, 1903-1915 (2002) · Zbl 1023.91040
[18] Smith, M., Modeling and short-term forecasting of New South Wales electricity system load, J. Busin. Econ. Stat., 18, 4, 465-478 (2000)
[19] López, M.; Valero, S.; Rodriguez, A.; Veiras, I.; Senabre, C., New online load forecasting system for the Spanish transport system operator, Electric Power Syst. Res., 154, 401-412 (2018)
[20] Azadeh, A.; Ghaderi, S.; Sohrabkhani, S., Forecasting electrical consumption by integration of neural network, time series and ANOVA, Appl. Math. Comput., 186, 2, 1753-1761 (2007) · Zbl 1222.78030
[21] Azadeh, A.; Ghaderi, S.; Tarverdian, S.; Saberi, M., Integration of artificial neural networks and genetic algorithm to predict electrical energy consumption, Appl. Math. Comput., 186, 2, 1731-1741 (2007) · Zbl 1222.78031
[22] Darbellay, G. A.; Slama, M., Forecasting the short-term demand for electricity: do neural networks stand a better chance?, Int. J. Forecast., 16, 1, 71-83 (2000)
[23] Hahn, H.; Meyer-Nieberg, S.; Pickl, S., Electric load forecasting methods: Tools for decision making, Eur. J. Oper. Res., 199, 3, 902-907 (2009) · Zbl 1176.90291
[24] Gladyshev, E. G., Periodically correlated random sequences, Sov. Math., 385-388 (1961) · Zbl 0212.21401
[25] Pagano, M., On periodic and multiple autoregressions, The Annals of Statistics, 6, 6, 1310-1317 (1978) · Zbl 0392.62073
[26] Tiao, G. C.; Grupe, M. R., Hidden periodic autoregressive-moving average models in time series data, Biometrika, 67, 2, 365-373 (1980) · Zbl 0436.62076
[27] Hastie, T.; Tibshirani, R., Generalized Additive Models (1990), Chapman and Hall/CRC · Zbl 0747.62061
[28] Wahba, G., Spline models for observational data (1990), SIAM: Society for Industrial and Applied Mathematics · Zbl 0813.62001
[29] Wood, S. N., Generalized Additive Models: An Introduction with R (2006), Chapman and Hall/CRC · Zbl 1087.62082
[30] Box, G.; Jenkins, G., Time Series Analysis: Forecasting and Control (1970), Holden-Day: Holden-Day San Francisco · Zbl 0249.62009
[31] Akaike, H., Information theory and an extension of the maximum likelihood principle, (Petrov, B. N.; Csaki, F., Proceedings of the Second International Symposium on Information Theory (1973)), 267-281 · Zbl 0283.62006
[32] Schwarz, G., Estimating the dimension of a model, Ann. Stat., 6, 461-464 (1978) · Zbl 0379.62005
[33] Franses, P. H., A note on the mean absolute scaled error, Int. J. Forecast., 32, 1, 20-22 (2016)
[34] Ziel, F.; Liu, B., Lasso estimation for GEFCom2014 probabilistic electric load forecasting, Int. J. Forecast., 32, 3, 1029-1037 (2016)
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