Modelling non-stationary time series using a peaks over threshold distribution with time varying covariates and threshold: An application to peak electricity demand

Long term peak electricity demand forecasting is a crucial step in the process of planning for power transmission and new generation capacity. This paper discusses an application of the Generalized Pareto Distribution to the modelling of daily peak electricity demand using South African data for the period 2000 to 2010. The main contribution of this paper is in the use of a cubic smoothing spline with a constant shift factor as a time varying threshold. An intervals estimator method is then used to decluster the observations above the threshold. We explore the influence of temperature by including it as a covariate in the Generalized Pareto Distribution parameters. A comparative analysis is done using the block maxima approach. The GPD model showed a better fit to the data compared to the GEVD model. Key findings from this study are that the Weibull class of distributions best fits the data which is bounded from above for both stationary and non-stationary models. Another key finding is that for different values of the temperature covariate the shape parameter is invariant and the scale parameter changes for different values of heating degree days.