Nonlinear interval regression analysis with neural networks and grey prediction for energy demand forecasting

Predicting energy demand plays an important role in devising energy development plans for cities and countries. Available data on energy demand usually consist of a nonlinear real-valued sequence, but the samples are often derived from uncertain assessments without satisfying any statistical assumptions. This study thus establishes interval grey prediction models without statistical assumptions by using data intervals to represent uncertainty in energy demand forecasting. The proposed prediction models first apply nonlinear regression analysis using neural networks to determine the interval data. The models then employ grey prediction to derive the tendency of the upper and lower limits of energy demand. Finally, the best non-fuzzy performance value can be further obtained for each time point using the estimated upper and lower limits. The advantage of the proposed models is that hyper-parameter settings involving residual modification and machine learning are not a serious problem, and the construction is simple enough to implement as a computer program without any statistical assumptions. The forecasting accuracy of the proposed models was verified using actual energy demand data. The results showed that the proposed grey-prediction-based models using functional-link nets to modify residuals performed well compared to other interval grey prediction models.