# Reconciling Hierarchical Forecasts via Bayes' Rule

## TL;DR

This paper introduces a Bayesian approach for hierarchical forecast reconciliation, deriving closed-form solutions under Gaussian assumptions and comparing with existing methods like MinT and Kalman filter.

## Contribution

It proposes a novel Bayesian framework for hierarchical forecast reconciliation, providing new algorithms and theoretical insights.

## Key findings

- Closed-form Bayesian updating formulas under Gaussian assumptions
- Algorithms that differ based on independence assumptions
- Experimental comparison with MinT and Kalman filter methods

## Abstract

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.