{
  "abstract": "A covariance matrix rarely distorts in a single direction: a shift can expand all variances simultaneously, shift variance along one or two principal directions, displace spectral mass without changing marginal means, or rotate the dependence structure. Default mean-shift detectors are blind to these effects, and no existing online procedure calibrates a family of spectral deviation tests with provable false alarm control across both time and tracking window selection; this paper fills that gap. We consider four spectral deviations: $D_{KL}(P_{1}\\|P_{0})$, $D_{KL}(P_{0}\\|P_{1})$, Jeffreys, and Bhattacharyya, each evaluated on the eigenvalues of the empirical relative covariance operator $\\widehatΣ_{0}^{-1/2}\\widehatΣ_{t}\\widehatΣ_{0}^{-1/2}$. Critical values come from a conditional parametric bootstrap that accounts for estimation uncertainty in both the past and tracking windows, an aspect asymptotic approaches typically overlook. The procedure controls the false alarm rate family-by-family over a predefined monitoring period and a range of candidate window sizes; when a single operational window is needed, a power-based criterion selects it. We prove consistency under constant alternatives via local spectral expansions with second-order sensitivity near the null. Simulations are conservative under the null and show detection power depends largely on spectral shape rather than magnitude: $D_{KL}(P_{1}\\|P_{0})$ excels under global inflation, while Jeffreys and Bhattacharyya cover a broader range of alternatives. We illustrate the approach on three financial applications: European stock indices, Fama-French sector portfolios, and large-cap technology stocks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14506",
  "author_total": 2,
  "authors": [
    {
      "name": "Mehmet Siddik Cadirci"
    },
    {
      "name": "Martin Singull"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/82r0hjn5mgj4r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14506",
  "fulltext_url": null,
  "id": "82r0hjn5mgj4r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14506",
  "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"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1804|Advanced Statistical Process Monitoring"
    ]
  ],
  "openalex": "W7213335629",
  "pdf_url": "https://arxiv.org/pdf/2609.14506",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/82r0hjn5mgj4r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14506",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14506"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Bootstrap-Calibrated Spectral Divergence Tests for Online Detection of Covariance Matrix Changes",
  "title_text": "Bootstrap-Calibrated Spectral Divergence Tests for Online Detection of Covariance Matrix Changes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:36Z",
  "url": "https://research.draconitic.com/paper/82r0hjn5mgj4r",
  "venue": "arXiv",
  "versions": []
}