Density forecasting of daily electricity demand with ARMA-GARCH, CAViaR, and CARE econometric models

Can Bikcora, Lennart Verheijen, Siep Weiland

Research output: Contribution to journalArticleAcademicpeer-review

44 Citations (Scopus)


The emerging need for risk-aware operational decisions on power systems calls for the development of accurate probabilistic load forecasting methods. To serve this purpose, various celebrated modeling approaches are applied from the field of economics where uncertainty forecasting has been a longstanding fundamental area of research. In particular, this paper proposes the use of ARMA-GARCH conditional mean–variance model in day-ahead forecasting and evaluates the CAViaR quantile regression model and the CARE expectile regression model as alternatives, with all of them incorporating exogenous inputs. In addition to the conventional quasi-maximum likelihood estimation (QMLE) of the ARMA-GARCH model, a special emphasis is put on least-squares (LS) based iterative and nonlinear estimation schemes. Empirical results are generated based on low-voltage side currents collected from transformers in the Netherlands, with the forecasts being assessed probabilistically via the continuous ranked probability score. Performance comparisons demonstrated improved results with the ARMA-GARCH model in relation to the others. Moreover, its estimation by means of the proposed iterative LS estimation method achieved the best forecast performance in a short runtime, thereby proven to be attractive for practical deployment.

Original languageEnglish
Pages (from-to)148-156
Number of pages9
JournalSustainable Energy, Grids and Networks
Publication statusPublished - 1 Mar 2018


  • Conditional mean–variance models
  • Density forecasting
  • Expectile regression
  • Quantile regression
  • Short-term load forecasting


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