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 Ka...

We obtain a limit of a hierarchical Bayes estimator of a finite population mean when the sample size is large. The limit is in the sense of ordinary calculus, where the sample observations are treated as fixed quantities. Our result suggests a simple way to correct the hierarchical Bayes estimator to achieve design-consistency, a well-known property in the traditional randomization approach to ...

This paper builds on a simple unified representation of shrinkage Bayes estimators based on hierarchical Normal-Gamma priors. Various popular penalized least squares estimators for shrinkage and selection in regression models can be recovered using this single hierarchical Bayes formulation. Using 129 U.S. macroeconomic quarterly variables for the period 1959 – 2010 I exhaustively evaluate the ...