{
  "abstract": "Quasi-periodic oscillations are characterized by fitting Lorentzian functions to a nonparametric estimate of the power spectral density, a two-step procedure that separates estimation from modeling and does not accommodate measurement error. We develop a parametric alternative based on autoregressive moving-average (ARMA) processes observed with measurement error. We derive an exact decomposition of the ARMA spectral density into real-valued components, one for each class of autoregressive roots under complex conjugation, plus a polynomial term when the moving-average order is at least the autoregressive order. Each component is a Wrapped Cauchy kernel, and for complex roots it is accompanied by a conjugate-Poisson term that makes the peak asymmetric and displaces its maximum from the frequency given by the argument of the root. We obtain closed-form expressions for the location, height, width, and asymmetry of each peak, and a matching variance decomposition. Parameters are estimated by maximum likelihood through the Kalman filter, and all descriptors follow by plug-in. Simulations show that the closed-form peak location is recovered without appreciable bias. An X-ray binary light curve illustrates the methodology.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14384",
  "author_total": 4,
  "authors": [
    {
      "name": "Darlin Soto-Vásquez"
    },
    {
      "name": "Francisco Cuevas-Pacheco"
    },
    {
      "name": "Giovanni Motta"
    },
    {
      "name": "Malgorzata Sobolewska"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0n9wsv4kb90bc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14384",
  "fulltext_url": null,
  "id": "0n9wsv4kb90bc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14384",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.AP"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "2604|Statistical and numerical algorithms"
    ]
  ],
  "openalex": "W7221829041",
  "pdf_url": "https://arxiv.org/pdf/2610.14384",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0n9wsv4kb90bc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:26Z",
      "native_id": "2610.14384",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14384"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.AP",
      "subfield": "statistics"
    }
  ],
  "title": "Decomposing the spectral density function of an ARMA process",
  "title_text": "Decomposing the spectral density function of an ARMA process",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:26Z",
  "url": "https://research.draconitic.com/paper/0n9wsv4kb90bc",
  "venue": "arXiv",
  "versions": []
}