{
  "abstract": "We develop a framework for simultaneous change-point inference of high-dimensional functional time series. The observations are modeled as temporally dependent vectors whose coordinates take values in possibly different separable Hilbert spaces, thereby covering a broad class of functional data. Heterogeneous mean changes may occur at coordinate-specific locations, and the contemporaneous dependence across coordinates is left unrestricted. Our procedure is based on coordinatewise cumulative-sum statistics and a residual block multiplier bootstrap that provides a common critical value for the global test and all coordinatewise decisions. We establish a nonasymptotic Gaussian approximation, quantitative nonasymptotic bounds for strong family-wise error control under arbitrary mixtures of changed and unchanged coordinates, covariance-adaptive detection guarantees, and simultaneous high-probability bounds for change-point localization. The bounds accommodate high-dimensional regimes in which the number of functional coordinates grows exponentially in a power of the sample size. We investigate finite-sample performance in simulations and illustrate the method using river discharge curves and high-frequency financial log returns.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05077",
  "author_total": 2,
  "authors": [
    {
      "name": "Axel Bücher"
    },
    {
      "name": "Colin Decker"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dkqt5gdbe8h77.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05077",
  "fulltext_url": null,
  "id": "dkqt5gdbe8h77",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05077",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1804|Advanced Statistical Process Monitoring"
    ]
  ],
  "openalex": "W7211912629",
  "pdf_url": "https://arxiv.org/pdf/2609.05077",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dkqt5gdbe8h77.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.05077",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05077"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Simultaneous Change-Point Inference for High-Dimensional Functional Time Series",
  "title_text": "Simultaneous Change-Point Inference for High-Dimensional Functional Time Series",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:25Z",
  "url": "https://research.draconitic.com/paper/dkqt5gdbe8h77",
  "venue": "arXiv",
  "versions": []
}