Realized Regularized Regressions
We develop a continuous-time penalized regression framework for the estimation of time-varying coefficients and variable selection when both the response and covariates are Itô semimartingales with jumps. The coefficient paths are approximated by spline basis expansions and estimated via least squares from truncated high-frequency increments. In a finite-dimensional setting, we establish consistency and derive a feasible asymptotic distribution for the integrated coefficient estimator under infill asymptotics. We then extend the framework to high-dimensional settings in which the number of candidate covariates diverges, and show that a group-wise penalized estimator with a truncated $\ell_1$-penalty attains the oracle property, which delivers both consistent model selection and coefficient estimation. An empirical application to a large panel of more than two hundred high-frequency factors documents sparse factor structure across a large cross-section of stocks and industry portfolios.