Hierarchical forecasting for aggregated curves with an application to day-ahead electricity price auctions

Aggregated curves are common structures in economics and finance, and the most prominent examples are supply and demand curves. In this study, we exploit the fact that all aggregated curves have an intrinsic hierarchical structure, and thus hierarchical reconciliation methods can be used to improve the forecasting accuracy. We provide an in-depth theory of how aggregated curves can be constructed or deconstructed, and conclude that these methods are equivalent under weak assumptions. We consider multiple reconciliation methods for aggregated curves, including previously established bottom-up, top-down, and linear optimal reconciliation approaches. We also present a new benchmark reconciliation method called ‘aggregated-down’ with similar complexity to bottom-up and top-down approaches, but it tends to provide better accuracy in this setup. We conducted an empirical forecasting study based on the German day-ahead power auction market by predicting the demand and supply curves, where their equilibrium determines the electricity price for the next day. Our results demonstrate that hierarchical reconciliation methods can be used to improve the forecasting accuracy of aggregated curves.