Tail Quantile Estimation of Heteroskedastic Intraday Increases in Peak Electricity Demand

Caston Sigauke, Andréhette Verster, Delson Chikobvu

Department of Mathematical Statistics and Actuarial Science University of the Free State, South Africa.
Department of Statistics and Operations Research, University of Limpopo South Africa.

DOI: 10.4236/ojs.2012.24054                

Abstract

Modelling of intraday increases in peak electricity demand using an autoregressive moving average-exponential generalized autoregressive conditional heteroskedastic-generalized single Pareto (ARMA-EGARCH-GSP) approach is discussed in this paper. The developed model is then used for extreme tail quantile estimation using daily peak electricity demand data from South Africa for the period, years 2000 to 2011. The advantage of this modelling approach lies in its ability to capture conditional heteroskedasticity in the data through the EGARCH framework, while at the same time estimating the extreme tail quantiles through the GSP modelling framework. Empirical results show that the ARMA-EGARCH-GSP model produces more accurate estimates of extreme tails than a pure ARMA-EGARCH model.

Keywords

Conditional Extreme Value Theory; Daily Electricity Peak Demand; Volatility; Tail Quantiles

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	J. Beirlant, Y. Goedgebeur, J. Segers and J. Teugels, “Statistics of Extremes Theory and Applications,” Wiley, London, 2004.
[2]	H. N. E. Bystrom, “Extreme Value Theory and Extremely Large Electricity Price Changes,” International Review of Economics and Finance, Vol. 14, No. 1, 2005, pp. 41-55. doi:10.1016/S1059-0560(03)00032-7
[3]	S. Coles, “An Introduction Statistical Modelling of Extreme Values,” Springer-Verlag, London, 2004.
[4]	A. J. McNeil and R. Frey, “Estimation of Tail-Related Risk Measures for Heteroscedastic Financial Time Series: An Extreme Value Approach,” Journal of Empirical Finance, Vol. 7, No. 3-4, 2000, pp. 271-300. doi:10.1016/S0927-5398(00)00012-8
[5]	R. Gencay and F. Selcuk. “Extreme Value Theory and Value-At-Risk: Relative Performance in Emerging Markets,” International Journal of Forecasting, Vol. 20, No. 2, 2004, pp. 287-303. doi:10.1016/j.ijforecast.2003.09.005
[6]	C. Hor, S. Watson, D. Infield and S. Majithia, “Assessing Load Forecast Uncertainty Using Extreme Value Theory,” 16th PSCC, Glasgow, 2008. http://www.pscc-central.org/uploads/tx_ethpublications/pscc2008_571.pdf
[7]	K. F. Chan and P. Gray, “Using Extreme Value Theory to Measure Value-At-Risk for Daily Electricity Spot Prices,” International Journal of Forecasting, Vol. 22, No. 2, 2006, pp. 283-300. doi:10.1016/j.ijforecast.2005.10.002
[8]	B. W. Silverman, “Density Estimation for Statistics and Data Analysis,” Chapman and Hall, London, 1986.
[9]	D. B. Nelson, “Conditional Heteroskedasticity in Asset Returns: A New Approach,” Econometrica, Vol. 59, No. 2, 1991, pp. 347-370.
[10]	K. Y. Ho and A. K. C. Tsui, “Analysis of Real GDP Growth Rates of Greater China: An Asymmetric Conditional Volatility Approach,” China Economic Review, Vol. 15, No. 4, 2004, pp. 424-442. doi:10.1016/j.chieco.2004.06.011
[11]	A. Verster and D. J. De Waal, “A Method for Choosing An Optimum Threshold If the Underlying Distribution Is Generalized Burr-Gamma,” South African Statistical Journal, Vol. 45, 2011, pp. 273-292.
[12]	E. K. Berndt, B. H. Hall, R. E. Hall and J. A. Hausman, “Estimation and Inference in Nonlinear Structural Models,” Annals of Economic and Social Measurement, Vol. 4, 1974, pp. 653-665.