Journal of Energy Markets

Probabilistic forecasting of medium-term electricity demand: a comparison of time series models

Kevin Berk and Alfred Müller

  • We compare time series models for probabilistic forecasting of electricity demand.
  • Increasing the number of parameters does not necessarily improve the model performance.
  • Deviations of the yearly seasonalities from a trigonometric function are rather random than systematic.
  • Hyperbolic distributions provide a very good fit to the model innovations.


The uncertainty of customer demand and its relation to the fluctuation of electricity price is an important risk factor in electricity markets. Therefore, there is a need for the probabilistic forecasting of medium-term electricity demand from end customers. There already exists a comprehensive literature on various load forecasting techniques, but it typically considers the grid load or private households. Load forecasting models for companies seem to be rare so far. As the consumption patterns of companies vary significantly between different business sectors, model building and calibration that depends on the specific sector seems reasonable. In this paper, we introduce a whole class of time series models for modeling customer demand. The models vary in their number of parameters for seasonal patterns, whether or not a dependence on grid load is included and what kind of distribution is used for the residuals. We use the continuous ranked probability score (CRPS) to compare different time series models. We evaluate model performance using the historical load data of companies from different business sectors. The results reveal that for yearly seasonality the use of sine and cosine functions is typically better than using dummies for each month. Moreover, hyperbolic distributions often provide a very good fit to the model innovations of the log demand in the case of industry customers, whereas normal distributions may be better in the case of customers from the retail and service sectors.