Forecasting Generalized Quantiles of Electricity Demand: A Functional Data Approach

Electricity load forecasts are an integral part of many decision-making pro- cesses in the electricity market. However, most literature on electricity load forecasting concentrates on deterministic forecasts, neglecting possibly impor- tant information about uncertainty. A more complete picture of future demand can be obtained by using distributional forecasts, allowing for a more efficient decision-making. A predictive density can be fully characterized by tail mea- sures such as quantiles and expectiles. Furthermore, interest often lies in the accurate estimation of tail events rather than in the mean or median. We pro- pose a new methodology to obtain probabilistic forecasts of electricity load, that is based on functional data analysis of generalized quantile curves. The core of the methodology is dimension reduction based on functional principal components of tail curves with dependence structure. The approach has sev- eral advantages, such as flexible inclusion of explanatory variables including meteorological forecasts and no distributional assumptions. The methodol- ogy is applied to load data from a transmission system operator (TSO) and a balancing unit in Germany. Our forecast method is evaluated against other models including the TSO forecast model. It outperforms them in terms of mean absolute percentage error (MAPE) and achieves a MAPE of 2.7% for the TSO.