{
  "abstract": "A score-driven filter multiplies its scaled log-likelihood score by a scale parameter. We call this coefficient the gain and learn it online. Given the current state and realised scaled score, each admissible gain selects a reachable next state and predictive density. A scalar gain moves along a line; diagonal gains control coordinatewise transmission and may change direction. We evaluate gain selection using a one-step predictive Kullback-Leibler objective. In the scalar unscaled case, the negative consecutive-score product is a stochastic gradient; the positive product used in accelerated recursions is a descent direction. Positive scalar score scaling changes only the effective learning rate. Strictly increasing, continuously differentiable gain links with positive derivative induce mirror-descent geometry, while persistence adds a Bregman pull towards a reference gain. Under convexity, compactness, integrability, and schedule conditions, projected and discounted mirror updates satisfy dynamic-regret bounds relative to time-varying, current-information comparators. Simulations isolate score scaling, link geometry, persistence, and coordinatewise gains. Across twelve equity indices, the bounded discounted-logistic gain records a lower out-of-sample mean negative log score than the constant gain in eleven markets, although market-level evidence is mixed. It also avoids the extreme transients of the numerically capped exponential-link benchmark.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.09218",
  "author_total": 3,
  "authors": [
    {
      "name": "Fabrizio Lillo"
    },
    {
      "name": "Giulia Livieri"
    },
    {
      "name": "Gianluca Palmari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8jtbk15a1zpth.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.09218",
  "fulltext_url": null,
  "id": "8jtbk15a1zpth",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.09218",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1803|Stock Market Forecasting Methods"
    ]
  ],
  "openalex": "W7202196823",
  "pdf_url": "https://arxiv.org/pdf/2608.09218",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8jtbk15a1zpth.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2608.09218",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.09218"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Online Learning of Scale Parameters in Score-Driven Filters",
  "title_text": "Online Learning of Scale Parameters in Score-Driven Filters",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:33Z",
  "url": "https://research.draconitic.com/paper/8jtbk15a1zpth",
  "venue": "arXiv",
  "versions": []
}