Point and interval forecasts of electricity demand with Reg-SARMA models

Abstract

This paper deals especially with a two-stage approach to forecasting hourly electricity demand by using a linear regression model with serially correlated residuals. Firstly, ordinary least squares are applied to estimate a linear regression model based on purely deterministic predictors (essentially, polynomials in time and calendar dummy variables). In the case wherein the regression residuals are not a white noise series, a SARMA (seasonal autoregressive moving average) process is applied to the estimated regression residuals. After examining a vast set of potential representations, the stationary and invertible process associated with the smaller Akaike information criterion and the smaller Ljung–Box statistic is selected. Secondly, two sets of instrumental predictors are added to the current model: the estimated residuals of the first regression model plus the estimated errors of the chosen SARMA process. The new regression model is estimated by again using ordinary least squares, but taking advantage of the fact that the new regressors eliminate serial correlation. Practical issues in points and interval forecasting are illustrated with reference to nine-day ahead prediction performance for short-term electric loads in Italy.