Probabilistic Time-Series Forecasting of Energy Demand Using ARIMA, Exponential Smoothing, and Prediction Interval Models
Abstract
Time-series forecasting is essential for operational planning, risk management, and resource allocation in electricity systems, where demand varies across hourly, weekly, and seasonal cycles. This study develops a statistical-probabilistic forecasting framework for estimating future energy demand while explicitly quantifying forecast uncertainty. The empirical analysis uses the Pennsylvania–New Jersey–Maryland (PJM) East hourly electricity consumption series, containing 145,366 hourly observations from 1 January 2002 to 3 August 2018. After removing duplicate timestamps and interpolating a limited number of missing hourly timestamps, the series was aggregated into 6,059 daily mean demand observations to support stable statistical modeling and interpretable medium-horizon evaluation. The proposed framework integrates time-series diagnostics, autocorrelation analysis, annual seasonal benchmarks, autoregressive integrated moving average (ARIMA) modeling, seasonal autoregressive integrated moving average (SARIMA) modeling, exponential smoothing, and dynamic harmonic regression with ARIMA errors, together with validation-calibrated prediction intervals. Model performance was evaluated using mean absolute error (MAE), root mean squared error (RMSE), mean absolute percentage error (MAPE), symmetric mean absolute percentage error (sMAPE), and mean absolute scaled error (MASE), while probabilistic reliability was assessed through empirical interval coverage and average interval width. The results show that the dynamic harmonic regression model with ARIMA errors achieved the strongest test-set performance, with an MAE of 2,446.264 megawatts (MW), an RMSE of 3,245.231 MW, a MAPE of 7.430%, and a MASE of 0.874, outperforming the annual seasonal naive benchmark. The calibrated 95% prediction interval achieved 94.419% empirical coverage, indicating reliable uncertainty quantification with practical interpretability. The study contributes a transparent, reproducible, and uncertainty-aware forecasting framework for energy-demand analysis. It demonstrates that combining classical statistical forecasting with probabilistic interval calibration provides richer decision support than point forecasts alone.