{
  "abstract": "Fractional Gaussian noise and $\\FARIMA(0,d,0)$ have the same long-memory pole $|θ|^{-2d}$ and hence the same leading PACF law $α(n)\\sim d/n$. We show that this agreement breaks at the first non-universal order. For $0<d<1/2$, the pure fGn PACF satisfies $$ α_{\\fGn}(n)=\\frac d n+\\frac{C_{\\fGn}(d)}{n^2}+o(n^{-2}), \\qquad C_{\\fGn}(d)<d^2, $$ The proof uses the Bingham--Inoue--Kasahara representation, a phase-coefficient expansion for fGn, and a Hankel-operator perturbation argument. Thus the fGn spectral envelope is invisible at first order but visible in second-order finite prediction, explaining why short-memory order selection can differ when fGn data are fitted by FARIMA-type models.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.31416",
  "author_total": 1,
  "authors": [
    {
      "name": "Chunhao Cai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0wn9cn0y6tyeb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.31416",
  "fulltext_url": null,
  "id": "0wn9cn0y6tyeb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.31416",
  "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.PR"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2002|Complex Systems and Time Series Analysis"
    ]
  ],
  "openalex": "W7163054771",
  "pdf_url": "https://arxiv.org/pdf/2605.31416",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0wn9cn0y6tyeb.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2605.31416",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.31416"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Second-order PACF asymptotics and discrimination between fractional Gaussian noise and $\\FARIMA(0,d,0)$",
  "title_text": "Second-order PACF asymptotics and discrimination between fractional Gaussian noise and FARIMA(0,d,0)",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:50Z",
  "url": "https://research.draconitic.com/paper/0wn9cn0y6tyeb",
  "venue": "arXiv",
  "versions": []
}