Jump regression revisited
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 dYt = βt dZt + dXt 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 ΔYt = βΔZt + ΔXt 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 ΔYt = (β+ ηt) ΔZt for i.i.d. (ηt)t ≥ 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.
Related
- Whitney extension theorem and intrinsic rectifiability of jump sets in Carnot-Carathéodory spaces
- Random Jump Intensities and Bernstein Density Estimation in Ergodic Basic Affine Jump-Diffusion Processes
- Subdiffusive fractional limit of a jump-renewal equation
- Jump of the Milnor Number in Linear Deformations with Fixed Order
- Mixing zone dynamics for the Saffman-Taylor instability with viscosity jump
BibTeX
@misc{vetter2026jump,
title = {{Jump regression revisited}},
author = {Mathias Vetter and Fan Yu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39061},
eprint = {2609.39061},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39061},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Jump regression revisited
AU - Mathias Vetter
AU - Fan Yu
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39061
UR - https://arxiv.org/abs/2609.39061
AB - 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 ≥ 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.
ER -