A parsimonious diffusion equation for electricity demand

We present a parsimonious model for describing the stochastic dynamics of electricity demand in the nsw region of the National Electricity Market. We apply a moment matching approach to calibrate the parameters and perform in-sample and out-of-sample tests to demonstrate the model's capability and weaknesses. We show a solid improvement when the calibration uses the minimum and maximum daily temperatures in the regression. We clearly express the relationship between the drift term and the expected demand, which is a nontrivial connection and has not been made explicit in other publications. References An Introduction to Australia's National Electricity Market , July 2010, Australian Energy Market Operator Limited, Accessed from http://www.aemo. com.au/corporate/0000-0262.pdf March 2011. J. Alcock, J. Goard and T. Vassallo, Calibrating Mean Reverting Jump Diffusion Models: An Application to the nsw Electricity Market, in T. Marchant Ed. Proceedings of the 2007 Mathematics and Statistics in Industry Study Group , MISG, Wollongong, 57–81, 2007. http://www.uow. edu.au/content/groups/public/@web/@inf/@math/documents/doc/uow040974.pdf C. Blanco and D. Soronow, Mean Reverting Processes–-Energy Price Processes Used for Derivatives Pricing and Risk Management, Commodities Now , June, 68–72, 2001. http://www.fea. com/resources/a_mean_reverting_processes. pdf S. R. Brubacher and G. Tunnicliffe Wilson, Interpolating Time Series with Application to the Estimation of Holiday Effects on Electricity Demand, J. Royal Statistical Society Series C , 25:107–116, 1976. http://www.jstor. org/stable/2346678 N. R. Draper, and H. Smith, Applied Regression Analysis , Wiley Series in Probability and Statistics, 1998. R. F. Engle, C. Mustafa, J. Rice, Modelling peak electricity demand, Journal of Forecasting , 11:241–251, 1992. doi:10.1002/for.3980110306 E. Erdogdu, Electricity demand analysis using cointegration and ARIMA modelling: A case study of Turkey, Energy Policy , 35:1129–1146, 2007. doi:10.1016/j.enpol. 2006.02. 013 F. Li, Singular value decomposition expansion for electrical demand analysis, IMA Journal of Mathematics Applied in Business and Industry , 11:37–48, 2000. doi:10.1093/imaman/11.1. 37 H. Geman, Commodities and Commodity Derivatives , Wiley, Chichester, 2005. J. M. Gourd and N. Hansen, Comparison of the performance of a time-dependent short-interest rate model with time-dependent models, Applied Mathematical Finance , 11:147–164, 2004. doi:10.1080/13504860410001686034 S. Mirasgedis, Y. Sarafidis, E. Georgopoulou, D. P. Lalas, M. Moschovits, F. Karagiannis and D. Papakonstantinou, Models for mid-term electricity demand forecasting incorporating weather influences, Energy , 31:208–227, 2006. doi:10.1016/j.energy. 2005.02. 016 B. Oksendal, Stochastic Differential Equations: An Introduction with Applications , 4th ed., Springer-Verlag, New York, NY, 1995. B. R. Szkuta, L. A. Sanabria, T. S. Dillon, Electricity price short-term forecasting using artificial networks, IEEE Trans Power Systems , 14:851–857, 1999. doi:10.1109/59.780895 B. Petschel, Mean Reversion Models for Weather Derivatives , PhD Thesis, University of Queensland, 2005 J. W. Taylor, Short-term electricity demand forecasting using double seasonal exponential smoothing, Journal Operational Research Society , 54:799–805, 2003. doi:10.1057/palgrave.jors. 2601589 S. C. Tripathy, Demand Forecasting in a Power System, Energy Convers. Mgmt. 38:1475–1481, 1997. doi:10.1016/S0196-8904(96)00101-X R. Weron and A. Misiorek, Modeling and Forecasting Electricity Loads: A Comparison, in Proceedings of The European Electricity Market EEM-04 Lodz, Poland, 135–142, 2004. C. J. Ziser, Z. Y. Dong, T. Saha, Investigation of Weather Dependency and Load Diversity on Queensland Electricity Demand, in M. Negnevitsky Ed. Proceedings of Australasian Universities Power Engineering Conference 2005 , AUPEC, Hobart, 2:457–462, 2005.