Ultra-high-dimensional spot support screening in continuous-time regression

We study variable screening for high-frequency continuous-time regression, targeting the support of the spot regression coefficient. We establish uniform entrywise bounds for local estimates of the marginal correlation vector and covariate correlation matrix under coordinatewise truncation and finite-variation jumps. Under a local averaged $\alpha$-H"older condition, the rate is $\{(\log p)\mathrm{/}n{\}}^{\alpha \mathrm{/}(2\alpha +1)}$, up to logarithmic factors. This yields sure screening for the marginal support. We also derive a list-size minimax lower bound that matches the localization and multiplicity order when the retained list size $d$ satisfies $\log (p\mathrm{/}d)\asymp \log p$. For regression-support recovery 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. Simulation studies and a high-frequency factor application illustrate its performance.