Shape-preserving minimum trace (SP-MinT): a regularized forecast reconciliation method for hierarchical time series
- 1Faculty of Engineering, Universidad Tecnológica de Bolívar
- 2Department of Industrial Engineering, Universidad del Norte
- 3Department of Electrical and Electronic Engineering, Universidad del Norte
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.
Related
- Translation as cultural dialogue: An explorative methodological approach to translation reconciliation of DLI-Est
- Improving the Use of Medicines Reconciliation Information in Inpatient Prescribing on an Elderly Care Ward: A Quality Improvement Project.
- Biologically informed network-regularized sparse consensus clustering (BioNet-SPACC) identifies a continuous plasma proteomic axis in major depressive disorder
- Performance of the Heatwave ED Forecast Tool in the Emergency Department Network of Ticino Canton, Switzerland
- Chronic intracranial neural dynamics forecast treatment response and therapeutic engagement during deep brain stimulation for OCD
BibTeX
@article{gonzalezsierra2026shapepreserving,
title = {{Shape-preserving minimum trace (SP-MinT): a regularized forecast reconciliation method for hierarchical time series}},
author = {Mauro Gonzalez-Sierra and Jorge I. Vélez and Adriana Arango-Manrique},
journal = {Scientific Reports},
year = {2026},
month = jul,
doi = {10.1038/s41598-026-61641-0},
url = {https://doi.org/10.1038/s41598-026-61641-0},
note = {CC BY},
}
RIS
TY - JOUR
TI - Shape-preserving minimum trace (SP-MinT): a regularized forecast reconciliation method for hierarchical time series
AU - Mauro Gonzalez-Sierra
AU - Jorge I. Vélez
AU - Adriana Arango-Manrique
PY - 2026
DA - 2026/07/01
JO - Scientific Reports
DO - 10.1038/s41598-026-61641-0
UR - https://doi.org/10.1038/s41598-026-61641-0
AB - 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.
SN - 2045-2322
ER -