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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