Abstract:
Consumer behaviour towards different forms of utility varies over time. The
variation can be so large that the estimated relationship between the response
variable and its associated explanatory variables is seriously affected. In this
study, kernel smoothing based conditional quantile approach, a nonparametric
procedure is used to model volatile demand data. Nevertheless, quantile
regression procedures work well in non extreme parts of a given data but poorly
on extreme levels therefore we apply the threshold model of extreme value in
order to circumvent the lack of observation problem at the tail of the distribution.
It is shown that nonparametric estimation method has less bias relative to other
standard methods when the underlying distribution is not known. Various kernel
estimation methods and extreme value theory are discussed and the asymptotic
properties of the estimators given. The methods are applied to model extremes
in electricity demand and fuel price data. The underlying dynamics in the data
inform of volatility clustering is also estimated using a standard Generalised
Autoregressive Conditional Heteroscedastic (GARCH) model. A combination of
nonparametric approach and extreme value theory will be shown as a method
for estimation of value at risk. Value at risk is chosen in this work as it is
extensively used in practice. The results indicate that electricity demand
formation is influenced by time, behavioral variables and also by the forces of
the market mechanism. It is also found that fuel prices play a crucial role in
xviii
influencing electricity demand. From the extreme value methods it is found that
the goodness of fit depends on the estimated parameters that define the shape
and behavior of the fitted distribution function. This indicates that the extreme
value methods are case specific, which emphasizes the role of result validation.
From these methods, it is found that maximum possible information can be
extracted from the data and the threshold can be determined by calculation
instead of subjective judgment. It is also easy to implement these methods by a
complete program. With Generalized Pareto Distribution our estimates of value
at risk and the expected shortfall for negative rate of change of fuel prices
indicate that with probability 1% the daily rate of change of fuel prices could go
as low as -1.3818% and given this rate of change, the average rate of change
value will be 2.187%. Also with probability 5% the price daily rate of change
could drop to -0.624% and that when it does the average fall is 1.404%. These
results can be used to estimate risk measures in the energy related sectors as
well as providing insights to producers of energy and also as a reference for
actual or potential investors in the energy industry.
