Authors: Matthias Anderer and Feng Li

Abstract: Hierarchical forecasting with intermittent time series is a challenge in both research and empirical studies. Extensive research focuses on improving the accuracy of each hierarchy, especially the intermittent time series at bottom levels. Then hierarchical reconciliation could be used to improve the overall performance further. In this paper, we present a hierarchical-forecasting-with-alignment approach that treats the bottom level forecasts as mutable to ensure higher forecasting accuracy on the upper levels of the hierarchy. We employ a pure deep learning forecasting approach N-BEATS for continuous time series at the top levels and a widely used tree-based algorithm LightGBM for the intermittent time series at the bottom level. The hierarchical-forecasting-with-alignment approach is a simple yet effective variant of the bottom-up method, accounting for biases that are difficult to observe at the bottom level. It allows suboptimal forecasts at the lower level to retain a higher overall performance. The approach in this empirical study was developed by the first author during the M5 Forecasting Accuracy competition, ranking second place. The method is also business orientated and could benefit for business strategic planning.

This paper proposes a hierarchical-forecasting-with-alignment approach that focuses on improving the point forecast accuracy for upper levels by aligning the high accuracy top level forecasts with the aggregated bottom level forecasts in a hierarchical time series setting. The proposed top-down alignment approach ensures low forecasting errors on the upper levels of the hierarchy and improves the overall forecasting performance for an equally weighted metric like WRMSSE. Our research sheds light on an orthogonal direction for forecasting reconciliation, as suggested in e.g., Wickramasuriya (2019), allowing some suboptimal forecasts at the lower level while retaining the accuracy on upper levels.

The hierarchical forecasting with alignment approach is straightforward to implement in practice. Improving overall forecasting performance requires accurate forecasting on the top level of the hierarchy. We employ the state-of-the-art deep learning forecasting approach N-BEATS for continuous time series at the top levels and a widely used tree-based algorithm LightGBM with non-time series features for the bottom level intermittent time series. Both methods are easy to use and effortless to scale up with massive time series. It is worth mentioning that the presented framework is general, and one could easily replace N-BEATS and LightGBM with other appropriate forecasting algorithms.

One notable difference compared to other approaches in the M5 competition is that the approach focuses on improving the forecasting accuracy on the continuous upper levels. We do not directly take the forecasting accuracy from bottom level intermittent time-series as our central attention, and the bottom level forecasts are treated as mutable to ensure the hierarchical alignment. However, special combination techniques could improve the accuracy of intermittent time series forecasting.

Although we focus on the point forecast in this paper, the probabilistic forecast with the presented scheme should be straightforward to implement with a corresponding probabilistic loss function. Another direction for future research is finding the best combination of top-level and bottom-level models. At the moment, the forecasting for the upper levels and the bottom level is done independently. To utilize the information across hierarchical levels, we could consider a joint modeling scheme together with the alignment approach, or alignment with multiple levels in the future study. Combining the top-down alignment with other reconciliation methods is also possible but needs further investigation.

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