  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
forecast accuracy. We provide an in-depth theory on 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 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.
