{
  "abstract": "Many real-world high-dimensional time series exhibit long-memory, but Gaussian graphical model testing in this regime remains understudied. We develop a direct, data-adaptive test statistic for assessing conditional independence in the graph structure of stationary Gaussian time series. We establish a finite-sample, Berry--Esseen type Gaussian approximation bound for the statistic, which applies to both short-memory and long-memory time series. The testing procedure is fully data-adaptive using block bootstrap method, on which we provide a finite-sample validity result including in the ultra-high-dimensional scenario, and can be extended to comparing graphical structures in two-sample tests. We also develop a consistency-empowered correction to the statistic and show that such tests attain asymptotic consistency in both size and power. Our proposed method is applied to a real-world fMRI data to understand functional connectivities within brain in different periods.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30565",
  "author_total": 3,
  "authors": [
    {
      "name": "Percy S. Zhai"
    },
    {
      "name": "Ping-Shou Zhong"
    },
    {
      "name": "Wei Biao Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d98gehvphbfpx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30565",
  "fulltext_url": null,
  "id": "d98gehvphbfpx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30565",
  "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",
      "math.ST"
    ],
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      "arxiv",
      "stat.ME"
    ],
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      "arxiv",
      "stat.ML"
    ],
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      "arxiv",
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    ],
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      "openalex",
      "2613|Statistical Methods and Inference"
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  "openalex": "W7214573673",
  "pdf_url": "https://arxiv.org/pdf/2609.30565",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d98gehvphbfpx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30565",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30565"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "High-dimensional Gaussian Graphical Model Testing for Long-Memory Time Series",
  "title_text": "High-dimensional Gaussian Graphical Model Testing for Long-Memory Time Series",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:03Z",
  "url": "https://research.draconitic.com/paper/d98gehvphbfpx",
  "venue": "arXiv",
  "versions": []
}