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

TL;DR

This paper introduces a robust reconciliation method for hierarchical time series forecasting using M-estimation, improving resilience against irregularities and outliers while maintaining efficiency in normal cases, demonstrated through numerical experiments and real-data application.

Contribution

It develops a novel robust reconciliation approach for HTS forecasting using M-estimation and a modified Newton-Raphson algorithm, addressing outliers and irregular series effectively.

Findings

Effective handling of abnormal series with non-normal errors.

High efficiency in normal data scenarios.

Successful application to Australian domestic tourism data.

Abstract

Aggregation constraints, arising from geographical or sectoral division, frequently emerge in a large set of time series. Coherent forecasts of these constrained series are anticipated to conform to their hierarchical structure organized by the aggregation rules. To enhance its resilience against potential irregular series, we explore the robust reconciliation process for hierarchical time series (HTS) forecasting. We incorporate M-estimation to obtain the reconciled forecasts by minimizing a robust loss function of transforming a group of base forecasts subject to the aggregation constraints. The related minimization procedure is developed and implemented through a modified Newton-Raphson algorithm via local quadratic approximation. Extensive numerical experiments are carried out to evaluate the performance of the proposed method, and the results suggest its feasibility in handling numerous abnormal cases (for instance, series with non-normal errors). The proposed robust reconciliation also demonstrates excellent efficiency when no outliers exist in HTS. Finally, we showcase the practical application of the proposed method in a real-data study on Australian domestic tourism.