{
  "abstract": "Regression analysis for stochastic processes has been an important topic over the last decades. Typically, regressing a dependent process $Y$ on an explanatory $Z$ results in an integral relationship of the form $dY_t = β_t dZ_t + dX_t$ with some residual process $X$, and often with constant or piecewise constant $β$. In the case of jump processes such a relationship essentially boils down to $ΔY_t = βΔZ_t + ΔX_t$ on the level of the jumps. Here the residual process $X$ is such that it never jumps together with $Z$, and so any jump in $Y$ is either exactly proportional to $Z$ or purely idiosyncratic. In this paper we discuss a related setup which appears more realistic and is closer to classical regression, namely $ΔY_t = (β+ η_t) ΔZ_t$ for i.i.d. $(η_t)_{t \\ge 0}$. We propose an estimator for $β$ based on high-frequency observations of $(Y,Z)$ and discuss consistency and associated central limit theorems in two different asymptotic regimes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39061",
  "author_total": 2,
  "authors": [
    {
      "name": "Mathias Vetter"
    },
    {
      "name": "Fan Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6csf9cppyjmp7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39061",
  "fulltext_url": null,
  "id": "6csf9cppyjmp7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39061",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7215069031",
  "pdf_url": "https://arxiv.org/pdf/2609.39061",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6csf9cppyjmp7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39061",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39061"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Jump regression revisited",
  "title_text": "Jump regression revisited",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:58Z",
  "url": "https://research.draconitic.com/paper/6csf9cppyjmp7",
  "venue": "arXiv",
  "versions": []
}