Probabilistic Reconciliation of Count Time Series

TL;DR

This paper introduces a new probabilistic reconciliation framework for count time series, generalizing Bayesian methods to improve forecast accuracy over existing Gaussian approaches.

Contribution

It proposes a formal definition of probabilistic reconciliation for count data and a novel Bayesian-based method applicable to both count and real-valued variables.

Findings

Major forecast improvement over Gaussian reconciliation

Reconciled probability mass functions for count variables

Applicable to both count and real-valued time series

Abstract

Forecast reconciliation is an important research topic. Yet, there is currently neither formal framework nor practical method for the probabilistic reconciliation of count time series. In this paper we propose a definition of coherency and reconciled probabilistic forecast which applies to both real-valued and count variables and a novel method for probabilistic reconciliation. It is based on a generalization of Bayes' rule and it can reconcile both real-value and count variables. When applied to count variables, it yields a reconciled probability mass function. Our experiments with the temporal reconciliation of count variables show a major forecast improvement compared to the probabilistic Gaussian reconciliation.