Probabilistic Reconciliation of Hierarchical Forecast via Bayes’ Rule

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