An Application Of Extreme Value Theory In Modelling Electricity Production In Kenya

Abstract

Extreme Value Theory provides a well-established statistical model for the computation of extreme risk measure which includes, Value at Risk and Expected Shortfall. In this paper we apply Univariate Extreme Value Theory to model extreme production for the Kenyan Electricity. We demonstrate that Extreme value theory can successfully be applied in predicting future Value at Risk to the electricity production. This will provide solutions to the problems faced by producers and consumers in the electricity market. In this paper Value at Risk is estimated using a Peak Over Threshold method. This technique models the distribution of exceedances over a high threshold rather than the individual observations. It concentrates on observation that exceeds central limits, focusing on the tail of the distribution. Extreme value theory is also applied to compute the tail risk measures at given confidence interval.  An overview of the Extreme Value Theory and Peaks Over Threshold Method are also given. These methods are applied to electricity production in Kenya and the data exhibit some trend and modeled as a Gumbel distribution since the shape parameter is not significantly different from zero.

Keywords: Risk Modeling, Value at Risk, Extreme Value Theory.