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Assessing the Performance of Hierarchical Forecasting Methods on the Retail Sector

INESC Technology and Science, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
Faculty of Economics, University of Porto, Rua Dr. Roberto Frias, 4200-464 Porto, Portugal
School of Accounting and Administration of Porto, Polytechnic Institute of Porto, Rua Jaime Lopes Amorim, 4465-004 S. Mamede de Infesta, Portugal
Author to whom correspondence should be addressed.
Entropy 2019, 21(4), 436;
Received: 18 March 2019 / Revised: 16 April 2019 / Accepted: 22 April 2019 / Published: 24 April 2019
(This article belongs to the Special Issue Entropy Application for Forecasting)
PDF [982 KB, uploaded 26 April 2019]


Retailers need demand forecasts at different levels of aggregation in order to support a variety of decisions along the supply chain. To ensure aligned decision-making across the hierarchy, it is essential that forecasts at the most disaggregated level add up to forecasts at the aggregate levels above. It is not clear if these aggregate forecasts should be generated independently or by using an hierarchical forecasting method that ensures coherent decision-making at the different levels but does not guarantee, at least, the same accuracy. To give guidelines on this issue, our empirical study investigates the relative performance of independent and reconciled forecasting approaches, using real data from a Portuguese retailer. We consider two alternative forecasting model families for generating the base forecasts; namely, state space models and ARIMA. Appropriate models from both families are chosen for each time-series by minimising the bias-corrected Akaike information criteria. The results show significant improvements in forecast accuracy, providing valuable information to support management decisions. It is clear that reconciled forecasts using the Minimum Trace Shrinkage estimator (MinT-Shrink) generally improve on the accuracy of the ARIMA base forecasts for all levels and for the complete hierarchy, across all forecast horizons. The accuracy gains generally increase with the horizon, varying between 1.7% and 3.7% for the complete hierarchy. It is also evident that the gains in forecast accuracy are more substantial at the higher levels of aggregation, which means that the information about the individual dynamics of the series, which was lost due to aggregation, is brought back again from the lower levels of aggregation to the higher levels by the reconciliation process, substantially improving the forecast accuracy over the base forecasts. View Full-Text
Keywords: hierarchical forecasting; information criteria; entropy; model selection; ARIMA; state space models; retail hierarchical forecasting; information criteria; entropy; model selection; ARIMA; state space models; retail

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Oliveira, J.M.; Ramos, P. Assessing the Performance of Hierarchical Forecasting Methods on the Retail Sector. Entropy 2019, 21, 436.

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