
Open Journal of Statistics, 2012, 2, 435-442
http://dx.doi.org/10.4236/ojs.2012.24054 Published Online October 2012 (http://www.SciRP.org/journal/ojs)
Tail Quantile Estimation of Heteroskedastic Intraday
Increases in Peak Electricity Demand
Caston Sigauke1*, Andréhette Verster2, Delson Chikobvu2
1Department of Statistics and Operations Research, University of Limpopo, Polokwane, South Africa
2Department of Mathematical Statistics and Actuarial Science, University of the Free State, Bloemfontein, South Africa
Email: *csigauke@gmail.com
Received August 9, 2012; revised September 12, 2012; accepted September 25, 2012
ABSTRACT
Modelling of intrad ay increases in peak electricity de mand using an autoregressive moving av erage-exponential gener-
alized autoregressive conditio nal heteroskedastic—generalized single Pareto ( ARMA-EGARCH-GSP) appro ach is dis-
cussed in this paper. The develop ed model is then used for extreme tail quantile estimation u sing 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 Quan tiles
1. Introduction
Peak electricity demand modelling is a policy concern
for countries throughout the world. Many countries are
investing heavily in the construction of new (reserve)
generating plants in order to increase electricity supply
during peak demand periods. Most countries including
those with emerging economies have embarked on use of
new and smart energy saving technologies and have put
in place integrated demand side management and energy
efficient strategies and policies in an effort to reduce
consumption. In this paper we discuss the distribution of
intraday changes in daily pe ak electricity d emand and the
modelling of extreme quantiles using an autoregressive
moving average-exponential generalized autoregressive
conditional heteroskedasticity-generalized single Pareto
(ARMA-EGARCH-GSP) approach. We define intraday
changes as daily increase/decrease in peak electricity
demand in daily peak demand (DPD) where DPD is the
maximum hourly demand in a 24-hour period. The paper
focuses on positive intraday changes. Modelling of un-
expected extreme po sitive intraday increases is i mportant
to load forecasters, systems operators and demand man-
agers in planning, load flow analysis and scheduling of
electricity.
The use of extreme value distribu tions requires that the
assumptions of independent and identical distributed
observations are met [1-4]. These assumptions provide
obstacles to the straightforward application of extreme
value to both financial market returns and electricity re-
turn series [2,4]. To overcome this problem, we adop t the
approach used by [4]. Using a two stage approach, [4]
estimate a GARCH model in stage one with a view to
filtering the return series to get nearly independent and
identical distributed residuals. In stage two, the extreme
value theory (EVT) framework is then applied to the
standardized residuals. The relative performance of val ue-
at-risk (VAR) models on daily stock market returns is
discussed in [5]. VAR is a measure of the risk of a port-
folio. An EVT approach is used to generate VAR esti-
mates and provide tail forecasts. Results from this study
indicate that EVT based VAR estimates are more accu-
rate at higher quantiles. The modelling approach dis-
cussed in this paper is important for assessing risk in
intraday increases in peak electricity demand forecasting.
This is supported by [6] who use the generalized extreme
value (GEV) theory and block maxima approach to esti-
mate the maximum load forecast errors in order to assess
risk in long-term electricity load forecasting. An applica-
tion of [4] modelling approach to electricity demand
forecasting is discussed in literature. Reference [2] ap-
plies a generalized Pareto distribution (GPD) to an auto-
regressive GARCH filtered price change series. Empiri-
cal results from this study show that a peaks-over-
threshold method provides accurate results in modelling
tails of hourly electricity price changes. Reference [7]
propose a model that accommodates autoregression and
*Corresponding a uthor.
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