Robust optimal reconciliation for hierarchical time series forecasting with M-estimation

Authors: Zhichao Wang, Shanshan Wang, Wei Cao, Fei Yang Date: 2026-02-26 Paper ID: openalex:2602.22694

Summary

This paper addresses the challenge of producing coherent forecasts for Hierarchical Time Series (HTS) that are robust to anomalous or irregular base forecasts. The authors introduce a robust reconciliation framework based on M-estimation, which minimizes a robust loss function subject to the necessary aggregation constraints. The core of the methodology involves an efficient minimization procedure implemented via a modified Newton-Raphson algorithm utilizing local quadratic approximation. Experimental results confirm that this robust approach effectively handles series with non-normal errors and maintains high efficiency in clean datasets, as validated on Australian domestic tourism data.

Key Contributions

• Proposes a robust reconciliation method for Hierarchical Time Series (HTS) forecasting by incorporating M-estimation to minimize a robust loss function.
• Develops a minimization procedure for the robust reconciliation problem using a modified Newton-Raphson algorithm based on local quadratic approximation.
• Demonstrates superior performance in handling abnormal time series cases (e.g., series with non-normal errors) compared to standard reconciliation methods.
• Shows that the robust method maintains excellent efficiency even when no outliers are present in the HTS structure.

Limitations

The paper focuses primarily on robustness against abnormal cases and does not detail comparisons against a wide range of statistical baselines (like ARIMA or Prophet) specifically within the context of M-estimation reconciliation.

Open Questions & Future Work

• compute-burden-cross-sectional-hts
• hts-non-stationary-components
• optimal-loss-function-selection
• probabilistic-reconciliation-uncertainty
• extending-rome-complex-hierarchies
• rome-general-reconciliation-framework
• covariance-design-robust-loss

Limitations

The paper focuses primarily on robustness against abnormal cases and does not detail comparisons against a wide range of statistical baselines (like ARIMA or Prophet) specifically within the context of M-estimation reconciliation.

Links

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