TY - JOUR

T1 - Stochastic coherency in forecast reconciliation

AU - Pritularga, Kandrika

AU - Svetunkov, Ivan

AU - Kourentzes, Nikolaos

N1 - 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

PY - 2021/10/31

Y1 - 2021/10/31

N2 - 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.

AB - 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.

KW - Forecasting

KW - Coherency

KW - Model uncertainty

KW - Forecast combination

KW - Covariance estimation

U2 - 10.1016/j.ijpe.2021.108221

DO - 10.1016/j.ijpe.2021.108221

M3 - Journal article

VL - 240

JO - International Journal of Production Economics

JF - International Journal of Production Economics

SN - 0925-5273

M1 - 108221

ER -