Time series analysis for prediction intervals of electricity demand with weather variables

Annual electricity demand is steadily increasing and the importance of forecasting the electricity demand is emerging since the dependence on domestic electricity is also increasing. The purpose of this study is analysis of the electricity demand considering seasonality and weather variables, for which we study time series modelling and forecasting analysis. ARIMA, SARIMA, ARIMAX, SARIMAX models are handled with optimally selected orders. Out-of-sample forecasting analysis is carried out to evaluate predicted values and their errors such as RMSE, MAE, MAPE and MSLE. The errors by four models are compared. As the optimal model, SARIMAX(2,1,1) (2,1,2,12) model with CDD, HDD and insolation has been chosen. For strict statistical analysis of prediction intervals, normal distribution, laplace distribution and bootstrap method are adopted to construct 80%, 95% prediction intervals. Coverage probability (CP), average length (AL) and mean interval score (MIS) of the prediction intervals by three approximations are evaluated. This study contributes with novelty in that it provides three approaches of prediction intervals along with their comparison. The results of this study are expected to be of practical help in the efficient operation of electricity supply system.