Probabilistic short-term load forecasting with conditional mean-variance and quantile regression models

C. Bikcora, L. Verheijen, S. Weiland

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

1 Citation (Scopus)
2 Downloads (Pure)


For the day-ahead density forecasting of electricity load, this paper proposes the combination of the autoregressive moving average (ARMA) model and the generalized autoregressive conditional heteroskedasticity (GARCH) model, with both of them admitting exogenous inputs. This composite structure on the conditional mean and variance is referred to as the ARMAX-GARCHX model. As an alternative to its estimation by means of log-likelihood maximization, approaches based on iterative least-squares (ILS) and nonlinear least-squares (NLS) are considered. Apart from the ARMAX-GARCHX model, quantile regression models (QRMs) are also tested in forecasting where a wide range of quantiles are separately modeled to approximate a density. Phase currents of several low voltage transformer cables from the Netherlands are forecasted to compare the performances, and as the probabilistic evaluation criterion, the continuous ranked probability score is used. As an outline of the results, the ARMAX-GARCHX model outperformed QRMs and among its estimation techniques, the likelihood-based approach had the best performance, though the differences in the errors are often minor. Thus, owing to its computational simplicity, the ILS solution can be a valuable option when processing large batches of data in practice.
Original languageEnglish
Title of host publicationProceedings of European Control Conference (ECC), Aalborg, Denmark, Jun. 2016
PublisherInstitute of Electrical and Electronics Engineers
Number of pages6
ISBN (Electronic)978-1-5090-2591-6
Publication statusPublished - Jun 2016
Event15th European Control Conference, ECC 2016 - Aalborg, Denmark
Duration: 29 Jun 20161 Jul 2016
Conference number: 15


Conference15th European Control Conference, ECC 2016
Abbreviated titleECC 2016
Internet address


Dive into the research topics of 'Probabilistic short-term load forecasting with conditional mean-variance and quantile regression models'. Together they form a unique fingerprint.

Cite this