# Hierarchical forecast reconciliation with machine learning

arXiv: https://arxiv.org/abs/2006.02043 · HTML: https://mlsanity.com/paper/2006.02043/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2020.

## Built on by (most cited first, 9 of 9)

- [Hierarchical learning, forecasting coherent spatio-temporal individual and aggregated building loads](https://mlsanity.com/paper/2301.12967/) (2023)
- [Cross-Temporal Forecast Reconciliation at Digital Platforms with Machine Learning](https://mlsanity.com/paper/2402.09033/) (2024)
- [Hierarchical forecasting for aggregated curves with an application to day-ahead electricity price auctions](https://mlsanity.com/paper/2305.16255/) (2023)
- [Improving the forecast accuracy of wind power by leveraging multiple hierarchical structure](https://mlsanity.com/paper/2308.03472/) (2023)
- [A Comprehensive Forecasting Framework based on Multi-Stage Hierarchical Forecasting Reconciliation and Adjustment](https://mlsanity.com/paper/2412.14718/) (2024)
- [Structural hierarchical learning for energy networks](https://mlsanity.com/paper/2302.03978/) (2023)
- [Nonlinear reconciliation: Error reduction theorems](https://mlsanity.com/paper/2507.22500/) (2025)
- [FoReco and FoRecoML: A Unified Toolbox for Forecast Reconciliation in R](https://mlsanity.com/paper/2604.27696/) (2026)
- [Hierarchical Forecast Reconciliation for Urban Rail Transit Demand Prediction under Operational Disruptions](https://mlsanity.com/paper/2606.07044/) (2026)

## Abstract (arXiv)

Hierarchical forecasting methods have been widely used to support aligned decision-making by providing coherent forecasts at different aggregation levels. Traditional hierarchical forecasting approaches, such as the bottom-up and top-down methods, focus on a particular aggregation level to anchor the forecasts. During the past decades, these have been replaced by a variety of linear combination approaches that exploit information from the complete hierarchy to produce more accurate forecasts. However, the performance of these combination methods depends on the particularities of the examined series and their relationships. This paper proposes a novel hierarchical forecasting approach based on machine learning that deals with these limitations in three important ways. First, the proposed method allows for a non-linear combination of the base forecasts, thus being more general than the linear approaches. Second, it structurally combines the objectives of improved post-sample empirical forecasting accuracy and coherence. Finally, due to its non-linear nature, our approach selectively combines the base forecasts in a direct and automated way without requiring that the complete information must be used for producing reconciled forecasts for each series and level. The proposed method is evaluated both in terms of accuracy and bias using two different data sets coming from the tourism and retail industries. Our results suggest that the proposed method gives superior point forecasts than existing approaches, especially when the series comprising the hierarchy are not characterized by the same patterns.