Stochastic coherency in forecast reconciliation

Hierarchical forecasting has been receiving increasing attention in the literature. The notion of coherency is central to this, which implies that hierarchical time series follows some linear aggregation constraints. This notion, however, does not take several modelling uncertainties into account. We propose redefine as stochastic. allows accommodate overlooked forecast reconciliation. show analytically there are two potential sources uncertainty use simulated data demonstrate how these propagate covariance matrix estimation, introducing reconciliation weights matrix. then increases reconciled forecasts. apply our understanding accident and emergency admissions a UK hospital. Our analysis confirms insights from stochastic It shows we gain accuracy improvement reconciliation, on average, at cost variability error distribution. Users may opt prefer less volatile distributions assist decision making.