Robust Probabilistic Load Forecasting for a Single Household: A Comparative Study from SARIMA to Transformers on the REFIT Dataset

Probabilistic forecasting is essential for modern risk management, allowing decision-makers to quantify uncertainty in critical systems. This paper tackles this challenge using the volatile REFIT household dataset, which is complicated by a large structural data gap. We first address this by conducting a rigorous comparative experiment to select a Seasonal Imputation method, demonstrating its superiority over linear interpolation in preserving the data's underlying distribution. We then systematically evaluate a hierarchy of models, progressing from classical baselines (SARIMA, Prophet) to machine learning (XGBoost) and advanced deep learning architectures (LSTM). Our findings reveal that classical models fail to capture the data's non-linear, regime-switching behavior. While the LSTM provided the most well-calibrated probabilistic forecast, the Temporal Fusion Transformer (TFT) emerged as the superior all-round model, achieving the best point forecast accuracy (RMSE 481.94) and producing safer, more cautious prediction intervals that effectively capture extreme volatility.