e-Values for Real-Time Residential Electricity Demand Forecast Model Selection

Abstract: 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. Given the dynamic nature of energy forecasting, it is highly advantageous to assess the superiority of forecasting models not only retrospectively but continuously in real-time as new data and evidence becomes available, while simultaneously providing strong probabilistic guarantees for these decisions. In this work, we show that this can be achieved through the mathematical concept of e-values, which has recently gained massive attention in the field of statistics. It allows for unified construction principles for powerful tests and accurate statistical decisions, which can be evaluated at any chosen time points while maintaining an overall probabilistic error control. We extend the use of e-values 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 electricity demand forecasts based on different artificial intelligence based models. Our results indicate that e-values are able to improve the accuracy and reliability of forecasts in a dynamic environment, offering a valuable tool for real-time decision-making in the energy sector.