Robust Optimal Reconciliation for Hierarchical Time Series Forecasting With M‐Estimation

Abstract

ABSTRACT Aggregation constraints, arising from geographical or sectoral division, frequently occur in large collections of time series. Coherent forecasts for such constrained series are expected to adhere to the hierarchical structure defined by these aggregation rules. To enhance robustness against potential irregular series, we investigate a robust reconciliation approach for hierarchical time series (HTS) forecasting. Specifically, we incorporate M‐estimation to obtain reconciled forecasts by minimizing a robust loss function of transforming a group of base forecasts subject to the aggregation constraints. The associated optimization procedure is developed and implemented through a modified Newton–Raphson algorithm via local quadratic approximation. Extensive numerical experiments are conducted to evaluate the performance of the proposed method, and the results demonstrate its effectiveness in handling various abnormal scenarios (e.g., series with non‐normal errors). The proposed robust reconciliation approach also exhibits strong efficiency in the absence of outliers. Finally, we illustrate the practical applicability of the method through a real‐data study on Australian domestic tourism.

The authors' abstract, as published at the source. Journal of Forecasting, 2026 · DOI ↗