Realized Regularized Regressions

Abstract


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 L1-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.


JEL Classifications: C14, C22, C58, G12


Keywords: high-frequency regressions, time-varying coefficients, penalized least squares, high-dimensional semimartingales, model selection, systematic risk


Biography


Shifan Yu is a Postdoctoral Researcher at the Oxford-Man Institute of Quantitative Finance, University of Oxford, and a Junior Research Fellow at Corpus Christi College. He is also an Associate Member of the Department of Economics at the University of Oxford and an Honorary Researcher at the Centre for Financial Econometrics, Asset Markets and Macroeconomic Policy at Lancaster University Management School. He obtained his PhD at Lancaster University in 2024. His research interests lie in financial econometrics, with a particular focus on high-frequency financial data and their implications for improved statistical inference on asset price dynamics, volatility, and market microstructure.