Modeling electricity demand and fuel prices using nonparametric methods and extreme value theory

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.