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    Rights statement: This is the author’s version of a work that was accepted for publication in International Journal of Production Economics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in International Journal of Production Economics, 240, 2021 DOI: 10.1016/j.ijpe.2021.108221

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    Embargo ends: 7/01/23

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Stochastic coherency in forecast reconciliation

Research output: Contribution to journalJournal articlepeer-review

Published
Article number108221
<mark>Journal publication date</mark>31/10/2021
<mark>Journal</mark>International Journal of Production Economics
Volume240
Number of pages14
Publication StatusPublished
Early online date7/07/21
<mark>Original language</mark>English

Abstract

Hierarchical forecasting has been receiving increasing attention in the literature. The notion of coherency is central to this, which implies that the hierarchical time series follows some linear aggregation constraints. This notion, however, does not take several modelling uncertainties into account. We propose to redefine coherency as stochastic. This allows to accommodate overlooked uncertainties in forecast reconciliation. We show analytically that there are two potential sources of uncertainty in forecast reconciliation. We use simulated data to demonstrate how these uncertainties propagate to the covariance matrix estimation, introducing uncertainty in the reconciliation weights matrix. This then increases the uncertainty of the reconciled forecasts. We apply our understanding to modelling accident and emergency admissions in a UK hospital. Our analysis confirms the insights from stochastic coherency in forecast reconciliation. It shows that we gain accuracy improvement from forecast reconciliation, on average, at the cost of the variability of the forecast error distribution. Users may opt to prefer less volatile error distributions to assist decision making.

Bibliographic note

This is the author’s version of a work that was accepted for publication in International Journal of Production Economics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in International Journal of Production Economics, 240, 2021 DOI: 10.1016/j.ijpe.2021.108221