Shape-preserving minimum trace (SP-MinT): a regularized forecast reconciliation method for hierarchical time series.

Authors

Mauro Gonzalez-Sierra, Jorge I Vélez, Adriana Arango-Manrique

Published in

Scientific reports. Jul 19, 2026. Epub Jul 19, 2026.

Abstract

Forecast reconciliation has become the standard for ensuring coherence in hierarchical time series. However, state-of-the-art methods like Minimum Trace (MinT) prioritize the minimization of error variance, often at the expense of distorting the temporal morphology of the forecast. This paper reframes forecast reconciliation as a multi-objective problem, showing that variance-optimal coherence is insufficient for operational decision-making, and proposing a shape-aware reconciler that explicitly encodes temporal structure. We introduce Shape-Preserving Minimum Trace (SP-MinT), a novel framework that regularizes the optimization process with domain-informed priors constructed from historical day-of-week profiles. We validate the method using a rigorous rolling cross-validation on real-world electricity demand data from Victoria, Australia. The results demonstrate that SP-MinT outperforms the standard MinT-WLS benchmark by reducing the Root Mean Squared Error (RMSE) by 31.94% and the Shape Error (Dynamic Time Warping) by 43.16%. By bridging the gap between statistical optimality and morphological fidelity, SP-MinT offers grid operators hierarchically coherent forecasts that respect physical ramping constraints.

PMID:
42472862
Bibliographic data and abstract were imported from PubMed on 20 Jul 2026.

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