# A machine learning approach for forecasting hierarchical time series

arXiv: https://arxiv.org/abs/2006.00630 · HTML: https://mlsanity.com/paper/2006.00630/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 May 2020.

## Built on by (most cited first, 29 of 29)

- [Unified Training of Universal Time Series Forecasting Transformers](https://mlsanity.com/paper/2402.02592/) (2024)
- [Time-MoE: Billion-Scale Time Series Foundation Models with Mixture of Experts](https://mlsanity.com/paper/2409.16040/) (2024)
- [Timer: Generative Pre-trained Transformers Are Large Time Series Models](https://mlsanity.com/paper/2402.02368/) (2024)
- [fev-bench: A Realistic Benchmark for Time Series Forecasting](https://mlsanity.com/paper/2509.26468/) (2025)
- [TSAQA: Time Series Analysis Question And Answering Benchmark](https://mlsanity.com/paper/2601.23204/) (2026)
- [Falcon-X: A Time Series Foundation Model for Heterogeneous Multivariate Modeling](https://mlsanity.com/paper/2605.27286/) (2026)
- [Synapse: Adaptive Arbitration of Complementary Expertise in Time Series Foundational Models](https://mlsanity.com/paper/2511.05460/) (2025)
- [Nexus : An Agentic Framework for Time Series Forecasting](https://mlsanity.com/paper/2605.14389/) (2026)
- [Zero-shot Forecasting by Simulation Alone](https://mlsanity.com/paper/2601.00970/) (2026)
- [Dirichlet Proportions Model for Hierarchically Coherent Probabilistic Forecasting](https://mlsanity.com/paper/2204.10414/) (2022)
- [Global Optimization for Cardinality-constrained Minimum Sum-of-Squares Clustering via Semidefinite Programming](https://mlsanity.com/paper/2209.08901/) (2022)
- [Hierarchical Proxy Modeling for Improved HPO in Time Series Forecasting](https://mlsanity.com/paper/2211.15092/) (2022)
- [Into the ORBIT for Time Series: Training Regimes for Foundation Models](https://mlsanity.com/paper/2608.13262/) (2026)
- [Hierarchical learning, forecasting coherent spatio-temporal individual and aggregated building loads](https://mlsanity.com/paper/2301.12967/) (2023)
- [Quantum Autoencoder for Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2504.17548/) (2025)
- [Green Energy Management for Sustainable Data Centers Using Deep Reinforcement Learning](https://mlsanity.com/paper/2507.21153/) (2025)
- [Super-Linear: A Lightweight Pretrained Mixture of Linear Experts for Time Series Forecasting](https://mlsanity.com/paper/2509.15105/) (2025)
- [Foundation Models and Fine-Tuning: Toward a New Generation of Models for Time Series Forecasting](https://mlsanity.com/paper/2607.23146/) (2026)
- [A Trainable Reconciliation Method for Hierarchical Time-Series](https://mlsanity.com/paper/2101.01329/) (2021)
- [Predicting municipalities in financial distress: a machine learning approach enhanced by domain expertise](https://mlsanity.com/paper/2302.05780/) (2023)
- [Multivariate Online Linear Regression for Hierarchical Forecasting](https://mlsanity.com/paper/2402.14578/) (2024)
- [A Comprehensive Forecasting Framework based on Multi-Stage Hierarchical Forecasting Reconciliation and Adjustment](https://mlsanity.com/paper/2412.14718/) (2024)
- [Optimizing accuracy and diversity: a multi-task approach to forecast combinations](https://mlsanity.com/paper/2310.20545/) (2023)
- [Hierarchical Time Series Forecasting with Robust Reconciliation](https://mlsanity.com/paper/2510.20383/) (2025)
- [Mod`eles de Fondation et Ajustement : Vers une Nouvelle G'en'eration de Mod`eles pour la Pr'evision des S'eries Temporelles](https://mlsanity.com/paper/2511.22674/) (2025)
- [Improving Day-Ahead Grid Carbon Intensity Forecasting by Joint Modeling of Local-Temporal and Cross-Variable Dependencies Across Different Frequencies](https://mlsanity.com/paper/2601.06530/) (2026)
- [Hierarchical Spatio-Temporal Transformer for Coherent Emergency Department Forecasting](https://mlsanity.com/paper/2607.27106/) (2026)
- [fable.intermittent: benchmarking probabilistic forecasting methods for intermittent time series](https://mlsanity.com/paper/2609.28607/) (2026)
- [Hierarchical Time Series Forecasting with Operator-Valued Kernels](https://mlsanity.com/paper/2610.18196/) (2026)

## Abstract (arXiv)

In this paper, we propose a machine learning approach for forecasting hierarchical time series. When dealing with hierarchical time series, apart from generating accurate forecasts, one needs to select a suitable method for producing reconciled forecasts. Forecast reconciliation is the process of adjusting forecasts to make them coherent across the hierarchy. In literature, coherence is often enforced by using a post-processing technique on the base forecasts produced by suitable time series forecasting methods. On the contrary, our idea is to use a deep neural network to directly produce accurate and reconciled forecasts. We exploit the ability of a deep neural network to extract information capturing the structure of the hierarchy. We impose the reconciliation at training time by minimizing a customized loss function. In many practical applications, besides time series data, hierarchical time series include explanatory variables that are beneficial for increasing the forecasting accuracy. Exploiting this further information, our approach links the relationship between time series features extracted at any level of the hierarchy and the explanatory variables into an end-to-end neural network providing accurate and reconciled point forecasts. The effectiveness of the approach is validated on three real-world datasets, where our method outperforms state-of-the-art competitors in hierarchical forecasting.