e-values based continuous-time model selection for residential electricity demand forecasts

With the growing number of forecasting techniques and the increasing significance of forecast-based operation, particularly in the rapidly evolving energy sector, selecting the most effective forecasting model has become a critical task. In this context, the superiority of a forecasting model over its alternatives will, in general, hold—if at all—only on average (over time or across scenarios), and model selection typically results in a single static decision. Instead, enabling real-time decision making in the energy and building context, we introduce the concept of $e$-values-based decisions, which has recently gained massive attention in the field of statistics. We obtain continuous-time, method-blind, data-dependent decision rules, which take and revise their decisions along with the incoming information of forecast errors. Nevertheless, they still provide statistical guarantees, including a fixed decision risk over the whole period of time. We extend the use of $e$-values for times where no procedure is significantly superior to its competitor by developing a simple persistence approach that dynamically combines input forecasts to generate new fused predictions. To demonstrate the performance of our method, we apply it to building electricity demand forecasts based on different artificial intelligence-based models. Our $e$-selection procedure enhances our forecast accuracy by 16.3 % compared to the deviation of a single forecast to an all-knowing forecaster. Additionally, it improves the reliability of the forecast in a dynamic environment, offering a valuable tool for real-time decision-making in the energy sector.