{
  "abstract": "Prediction intervals from probabilistic time-series forecasters are commonly assessed by marginal coverage, the long-run proportion of observations falling inside the intervals. However, forecast errors in time series are often serially dependent and heteroskedastic, so prediction intervals can attain near-nominal marginal coverage while miscovering systematically during periods of larger local error variance. We identify and address this failure mode, which we call \\emph{local scale miscalibration}. We first document the phenomenon using time-series foundation models (TSFMs): across several real-world series, their native intervals often attain near-nominal marginal coverage while exhibiting substantial temporal variation in local coverage, alternating between overcoverage and undercoverage over shorter windows. We then propose Volatility-Corrected Prediction Intervals (VCPI), a post-hoc calibration procedure that uses the base forecaster's predictive scale as a baseline, models the volatility of standardized forecast residuals with a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model, and applies a multiplicative correction to produce locally adaptive prediction intervals. We justify VCPI both theoretically and empirically, comparing it against model-agnostic conformal counterparts. We provide a theoretical analysis of interval adaptation of the proposed method following abrupt changes in volatility. Empirically, we evaluate VCPI on Chronos, Moirai, and TimesFM across four real-world datasets and find that it produces more stable local coverage than conformal baselines while maintaining near-nominal marginal coverage and comparable interval width.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31621",
  "author_total": 2,
  "authors": [
    {
      "name": "Jason B. Cho"
    },
    {
      "name": "David S. Matteson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f5m1yfkb5vgzv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31621",
  "fulltext_url": null,
  "id": "f5m1yfkb5vgzv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31621",
  "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",
      "stat.ME"
    ],
    [
      "openalex",
      "1803|Forecasting Techniques and Applications"
    ]
  ],
  "openalex": "W7223358256",
  "pdf_url": "https://arxiv.org/pdf/2610.31621",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f5m1yfkb5vgzv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:43Z",
      "native_id": "2610.31621",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31621"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Volatility-Corrected Prediction Intervals: Locally Adaptive Uncertainty Quantification for Probabilistic Time-Series Forecasting",
  "title_text": "Volatility-Corrected Prediction Intervals: Locally Adaptive Uncertainty Quantification for Probabilistic Time-Series Forecasting",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:43Z",
  "url": "https://research.draconitic.com/paper/f5m1yfkb5vgzv",
  "venue": "arXiv",
  "versions": []
}