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Jump regression revisited — arXiv:2609.39061

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.39061
License (as archived): CC0-1.0
Archived: 2026-10-07T14:13:05.769Z
SHA-256 of the archived text: 6d2ea80534fa7e72ee3b328a8224e88aefe12fda5e22280c2dda3fedf0e1945b
Stable URL of this page: https://metraipolis.com/documento/dc_2ef43ff30f73

How to cite

Jump regression revisited — arXiv:2609.39061 — arXiv (en), https://arxiv.org/abs/2609.39061 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_2ef43ff30f73 (Metraipolis archive dc_2ef43ff30f73, sha256 6d2ea80534fa7e72ee3b328a8224e88aefe12fda5e22280c2dda3fedf0e1945b)

BibTeX

@misc{dc2ef43ff30f73,
  title = {Jump regression revisited — arXiv:2609.39061},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.39061},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_2ef43ff30f73; sha256 6d2ea80534fa7e72ee3b328a8224e88aefe12fda5e22280c2dda3fedf0e1945b},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.39061. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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 $dY_t = \beta_t dZ_t + dX_t$ with some residual process $X$, and often with constant or piecewise constant $\beta$. In the case of jump processes such a relationship essentially boils down to $\Delta Y_t = \beta \Delta Z_t + \Delta X_t$ 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 $\Delta Y_t = (\beta + \eta_t) \Delta Z_t$ for i.i.d. $(\eta_t)_{t \ge 0}$. We propose an estimator for $\beta$ based on high-frequency observations of $(Y,Z)$ and discuss consistency and associated central limit theorems in two different asymptotic regimes.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-10-01 in math.ST).
Categorie arXiv: Statistics Theory (math.ST).
Pagina del lavoro: https://arxiv.org/abs/2609.39061 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T14:03:45.736Z dalla pagina https://arxiv.org/catchup/math.ST/2026-10-01?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).