Ultra-high-dimensional spot support screening in continuous-time regression
Abstract
We study variable screening for high-frequency continuous-time regression, targeting the support of the spot regression coefficient. Under coordinatewise truncation and finite-variation jumps, uniform entrywise bounds for local correlation estimates yield the rate {(log p)/n}α/(2α+1) under a local averaged α-Hölder condition, up to confidence and grid factors. These bounds imply sure screening for the marginal support. To retain the regression support under local dependence, we propose partial-residual spot iterative screening with pathwise Lepski adaptation. Under sparse eigenvalues and standardized beta-min, the procedure has the sure screening property and requires only correlation columns associated with the current active set. A list-size minimax lower bound applies to both support targets and matches the localization and multiplicity order of the marginal-screening bound when log(p/d)asymplog p. Simulations and a high-frequency factor application illustrate the procedures.
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BibTeX
@misc{zhu2026ultrahighdimensional,
title = {{Ultra-high-dimensional spot support screening in continuous-time regression}},
author = {Haibin Zhu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.08582},
eprint = {2608.08582},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.08582},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Ultra-high-dimensional spot support screening in continuous-time regression
AU - Haibin Zhu
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2608.08582
UR - https://arxiv.org/abs/2608.08582
AB - We study variable screening for high-frequency continuous-time regression, targeting the support of the spot regression coefficient. Under coordinatewise truncation and finite-variation jumps, uniform entrywise bounds for local correlation estimates yield the rate {(log p)/n}^α/(2α+1) under a local averaged α-Hölder condition, up to confidence and grid factors. These bounds imply sure screening for the marginal support. To retain the regression support under local dependence, we propose partial-residual spot iterative screening with pathwise Lepski adaptation. Under sparse eigenvalues and standardized beta-min, the procedure has the sure screening property and requires only correlation columns associated with the current active set. A list-size minimax lower bound applies to both support targets and matches the localization and multiplicity order of the marginal-screening bound when log(p/d)asymplog p. Simulations and a high-frequency factor application illustrate the procedures.
ER -