Assessing the Performance of Hierarchical Forecasting Methods on the Retail Sector

Abstract

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.

Forecasting: theory and practice

“…These are called hierarchical time series. On a retail business for example, individual sales of products at the bottom-level of the hierarchy can be grouped in categories and families of related products at increasing aggregation levels, with the total sales of the shop or distribution centre at the top level (Pennings and van Dalen, 2017;Oliveira and Ramos, 2019;Villegas and Pedregal, 2018). The forecasts of hierarchical time series produced independently of the hierarchical structure generally will not add up according to the aggregation constrains of the hierarchy, i.e., they are not coherent.…”

Forecasting Hierarchical Time Series in Power Generation

“…The optimal reconciliation approach proposed by [19] consists of an ordinary least squares problem based on the calculation of independent projections for all hierarchical levels, then applying a regression model to optimize the combination of these forecasts. According to [32], we can write the base prediction as:ŷ…”

Entropy Application for Forecasting

“…The contents cover a great diversity of topics, such as the aggregation and combination of individual forecasts [ 5 , 6 ], the comparison of forecasting performances [ 7 , 8 ], the analysis of forecasting uncertainty [ 9 ], robustness [ 10 ] and inconsistency [ 11 ], and the proposal of new forecasting approaches [ 12 , 13 , 14 ].…”

“…Furthermore, the empiric contents are also diverse including both simulated experiments and real-world applications. More specifically, the contributions provide empirical evidence that refer to the economic growth and gross domestic product (GDP) [ 5 , 9 ], the M4 competition dataset [ 8 ], the confidence and industrial trend surveys [ 9 ], and some stock exchange composite indices (Taiwan, Shanghai, Hong-Kong) [ 11 ], as well as other real data from a Portuguese retailer [ 7 ] and a Chinese grid company [ 12 ].…”