Pointwise forecast, confidence and prediction intervals in electricity demand and price

Resumen

Analysis of the electricity demand and price is presented, within the Spanish Electricity Market, applying statistical tools from the field of functional data. It begins with a descriptive analysis of the electrical data, studying its particular features. This kind of data conform a functional time series. Functional outlier detection methods are proposed to deal specifically with functional time series, taking dependence in this data structure into account. Then, a comparative study among different prediction techniques for next-day electricity demand and price is performed. It includes naïve procedures, time series ARIMA models and robust functional principal components analysis. The use of functional regression methods is proposed in this field. Specifically, the functional nonparametric regression model is used together with the semi-functional partial linear regression model, which allows incorporating external covariates as temperature and wind power production. Bootstrap procedures are proposed to build confidence intervals for the considered functional regression models. Validity of these bootstrap procedures is proved theoretically and they are applied to both a simulation study and the electricity demand and price data. Finally, bootstrap procedures are proposed to build prediction intervals and prediction density, which are also applied to the electrical data.