{
  "abstract": "We study multiscale inference based on realized power variations when the continuous component of an observed process is rougher than a Brownian semimartingale. The continuous component is locally Gaussian with scaling exponent $H<1/2$, and the model may additionally contain discontinuous activity. Realized $p$-variation then scales as $\\Delta_n^{pH-1}$, generating distinct regimes according to whether $pH$ is below, at, or above one. At the critical boundary $pH=1$, a continuous rough process may share the same first-order two-scale activity signature as a process containing jumps, creating an identification problem outside the usual semimartingale framework. We develop joint inference across several powers rather than relying on a single activity statistic. For the fractional Brownian benchmark, we derive a joint central limit theorem for the multi-power signatures and a roughness estimator computed from the same sample. This leads to a feasible quadratic specification statistic $Q_n$ whose null limit is chi-square. Under $n^{-1/2}$-local departures from the rough scaling relation, $Q_n$ has a noncentral chi-square limit, yielding an explicit asymptotic power function, while fixed identifiable alternatives are detected consistently. Gaussian Volterra extensions are obtained under explicit local-scaling and correlation-summability conditions. Monte Carlo experiments document the finite-sample size--power trade-off associated with using high powers and examine robustness to infinite-activity jumps, microstructure noise, and irregular sampling.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Jules Sadefo Kamdem"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8akvfp74wm9g4.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "8akvfp74wm9g4",
  "issns": [],
  "landing_url": "https://hal.science/hal-05756191v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.info"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "0.qfin"
    ],
    [
      "hal",
      "0.stat"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05756191/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-05-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8akvfp74wm9g4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:36Z",
      "native_id": "hal-05756191",
      "source": "hal",
      "url": "https://hal.science/hal-05756191v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.stat",
      "subfield": "statistics"
    }
  ],
  "title": "Multi-Power Inference Beyond Semimartingales: Rough Gaussian Activity and Jumps",
  "title_text": "Multi-Power Inference Beyond Semimartingales: Rough Gaussian Activity and Jumps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:36Z",
  "url": "https://research.draconitic.com/paper/8akvfp74wm9g4",
  "venue": "HAL",
  "versions": []
}