Long Term Interval Forecasts of Demand using Data-Driven Dynamic Regression Models

Long-term electricity load forecasts are the main inputs of production planning and scheduling at different horizons and load forecasting plays an important role in balancing the electricity grid. Forecast (prediction) intervals provide the measure of uncertainty of the point forecasts (predictions). However, a data-driven innovation distribution approach is not available to calculate long-term prediction intervals when using deep learning neural networks dynamic regression (NNDR) models. In this paper, a feedforward NNDR model for long-term electricity demand forecasting is introduced and the corresponding datadriven prediction intervals (PIs) are obtained. The novelty of this paper is to use long-term point forecasts and model innovation residuals to obtain three classes of PIs by using data-driven innovation distribution, nonlinear adaptive trapezoidal fuzzy numbers and bootstrapping. It is shown that NNDR models and dynamic regression models with Seasonal Autoregressive Integrated Moving Average (SARIMA) errors (DRSARIMA) are capable of modelling seasonality as well as nonlinearity for demand and other features such as temperature and a day type indicator. NNDR models and DRSARIMA models are evaluated through numerical experiments and the results show that the proposed NNDR model outperforms the DRSARIMA model to forecast demand during the volatile period. It is also shown that innovation residuals from DRSARIMA and NNDR follow heavytailed t distributions. The data-driven probabilistic Student t PIs have higher coverage probabilities than either trapezoidal fuzzy PIs or the bootstrap PIs for both DRSARIMA and NNDR models.