{
  "abstract": "We propose an online testing framework for detecting distributional changes in serially dependent data with values in a separable metric space. Based on two-sample $U$-statistics, the framework encompasses sequential analogs of energy distance and maximum mean discrepancy (MMD) procedures while accommodating temporal dependence. We establish asymptotic theory for finite and open-ended monitoring horizons that characterizes the full asymptotic run-length distribution under $H_0$ and yields asymptotic false-alarm control. We further establish new spectral approximation results for kernel matrices formed from serially dependent observations, and use them to construct a feasible Monte Carlo calibration procedure. Our flexible window construction encompasses classical, Page-type, and full-scan historical-baseline monitoring and can achieve short detection delays for both early and late changepoints, without requiring sub-Gaussianity or high-order moments of the raw observations. Simulations show reliable false-alarm control across linear, nonlinear, high-dimensional, and functional time-series models and further demonstrate that, over a broad range of alternatives and changepoint locations, the proposed method can achieve substantially shorter delays than recent procedures designed specifically for rapid detection. Applications to foreign exchange rates, electricity-market curves, and daily air transportation networks illustrate the methodology across scalar, functional, and network-valued time series.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.26422",
  "author_total": 3,
  "authors": [
    {
      "name": "B. Cooper Boniece"
    },
    {
      "name": "Lajos Horváth"
    },
    {
      "name": "Lorenzo Trapani"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a18j5d7pzht17.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.26422",
  "fulltext_url": null,
  "id": "a18j5d7pzht17",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.26422",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "1804|Advanced Statistical Process Monitoring"
    ]
  ],
  "openalex": "W7204587607",
  "pdf_url": "https://arxiv.org/pdf/2608.26422",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a18j5d7pzht17.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:33:54Z",
      "native_id": "2608.26422",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.26422"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Online detection of distributional changes for time series in metric spaces",
  "title_text": "Online detection of distributional changes for time series in metric spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:54Z",
  "url": "https://research.draconitic.com/paper/a18j5d7pzht17",
  "venue": "arXiv",
  "versions": []
}