Probabilistic Reconciliation of Hierarchical Forecast via Bayes' Rule

We present a novel approach for reconciling hierarchical forecasts, based on Bayes' rule. We define a prior distribution for the bottom time series of the hierarchy, based on the bottom base forecasts. Then we update their distribution via Bayes' rule, based on the base forecasts for the upper time series. Under the Gaussian assumption, we derive the updating in closed-form. We derive two algorithms, which differ as for the assumed independencies. We discuss their relation with the MinT reconciliation algorithm and with the Kalman filter, and we compare them experimentally.