# Hierarchical Time Series Forecasting with Robust Reconciliation

arXiv: https://arxiv.org/abs/2510.20383 · HTML: https://mlsanity.com/paper/2510.20383/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 30 references that are in the map.
- First posted on arXiv 23 Oct 2025.

## Builds on (most cited first, 6 of 6)

- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [Data-Driven Robust Optimization](https://mlsanity.com/paper/1401.0212/) (2013)
- [A machine learning approach for forecasting hierarchical time series](https://mlsanity.com/paper/2006.00630/) (2020)
- [Hierarchical Demand Forecasting Benchmark for the Distribution Grid](https://mlsanity.com/paper/1910.03976/) (2019)
- [Prediction of hierarchical time series using structured regularization and its application to artificial neural networks](https://mlsanity.com/paper/2007.15159/) (2020)
- [Optimal Forecast Reconciliation with Uncertainty Quantification](https://mlsanity.com/paper/2402.06480/) (2024)

## Abstract (arXiv)

This paper focuses on forecasting hierarchical time-series data, where each higher-level observation equals the sum of its corresponding lower-level time series. In such contexts, the forecast values should be coherent, meaning that the forecast value of each parent series exactly matches the sum of the forecast values of its child series. Existing hierarchical forecasting methods typically generate base forecasts independently for each series and then apply a reconciliation procedure to adjust them so that the resulting forecast values are coherent across the hierarchy. These methods generally derive an optimal reconciliation, using a covariance matrix of the forecast error. In practice, however, the true covariance matrix is unknown and has to be estimated from finite samples in advance. This gap between the true and estimated covariance matrix may degrade forecast performance. To address this issue, we propose a robust optimization framework for hierarchical reconciliation that accounts for uncertainty in the estimated covariance matrix. We first introduce an uncertainty set for the estimated covariance matrix and formulate a reconciliation problem that minimizes the worst-case average of weighted squared residuals over this uncertainty set. We show that our problem can be cast as a semidefinite optimization problem. Numerical experiments demonstrate that the proposed robust reconciliation method achieved better forecast performance than existing hierarchical forecasting methods, which indicates the effectiveness of integrating uncertainty into the reconciliation process.