{
  "abstract": "We propose a new $L_2$-type test for white noise which allows the dimension $p$ of the time series to either (i) be a fixed constant, or (ii) diverge with the sample size $n$. The proposed test statistic exhibits an interesting phase transition, following two different regimes of behavior: $p$ is fixed, and $p\\rightarrow\\infty$. Because identification of the operable regime is difficult, if not impossible in practice, we devise a novel adaptive bootstrap method to construct unified testing procedure across different phases. Numerical experiments confirm the good finite sample performance of the proposed adaptive $L_2$-type test in comparison to the existing methods in the literature. The proposed testing procedure has been implemented in R package HDTSA.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33418",
  "author_total": 4,
  "authors": [
    {
      "name": "Jinyuan Chang"
    },
    {
      "name": "Jing He"
    },
    {
      "name": "Weiming Li"
    },
    {
      "name": "Chen Lin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9xg19xjm6skbn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33418",
  "fulltext_url": null,
  "id": "9xg19xjm6skbn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33418",
  "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",
      "econ.EM"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7214795627",
  "pdf_url": "https://arxiv.org/pdf/2609.33418",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9xg19xjm6skbn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.33418",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33418"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "An adaptive $L_2$-type test for high-dimensional white noise",
  "title_text": "An adaptive L_2-type test for high-dimensional white noise",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:26Z",
  "url": "https://research.draconitic.com/paper/9xg19xjm6skbn",
  "venue": "arXiv",
  "versions": []
}