{
  "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.",
  "abstract_shown": true,
  "affiliations": [
    "Faculty of Engineering, Universidad Tecnológica de Bolívar",
    "Department of Industrial Engineering, Universidad del Norte",
    "Department of Electrical and Electronic Engineering, Universidad del Norte"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Mauro Gonzalez-Sierra"
    },
    {
      "affs": [
        1
      ],
      "name": "Jorge I. Vélez"
    },
    {
      "affs": [
        2
      ],
      "name": "Adriana Arango-Manrique"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9a8t980031ady.bib",
  "cited_by": 0,
  "doi": "10.1038/s41598-026-61641-0",
  "fulltext_url": "https://doi.org/10.1038/s41598-026-61641-0",
  "id": "9a8t980031ady",
  "issns": [
    "2045-2322"
  ],
  "landing_url": "https://doi.org/10.1038/s41598-026-61641-0",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "lcc",
      "Q"
    ],
    [
      "lcc",
      "R"
    ],
    [
      "openalex",
      "2208|Energy Load and Power Forecasting"
    ]
  ],
  "openalex": "W7169722458",
  "pdf_url": "https://www.nature.com/articles/s41598-026-61641-0_reference.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-01",
  "publisher": "Nature Portfolio",
  "ris": "https://research.draconitic.com/paper/9a8t980031ady.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T13:45:41Z",
      "native_id": "01d8cea6c2fb4b4c90c493c18752ff41",
      "source": "doaj",
      "url": "https://doi.org/10.1038/s41598-026-61641-0"
    }
  ],
  "subjects": [
    {
      "field": "medicine",
      "origin": "lcc:R",
      "subfield": "general"
    }
  ],
  "title": "Shape-preserving minimum trace (SP-MinT): a regularized forecast reconciliation method for hierarchical time series",
  "title_text": "Shape-preserving minimum trace (SP-MinT): a regularized forecast reconciliation method for hierarchical time series",
  "type": "peer-reviewed",
  "updated_at": "2026-10-31T14:20:41Z",
  "url": "https://research.draconitic.com/paper/9a8t980031ady",
  "venue": "Scientific Reports",
  "versions": []
}