Realized Regularized Regressions

TL;DR

This paper introduces a continuous-time penalized regression method for estimating time-varying coefficients and selecting variables in high-frequency financial data, with theoretical guarantees and empirical validation.

Contribution

It develops a novel spline-based penalized regression framework for high-frequency data, establishing consistency, asymptotic distribution, and oracle properties in high-dimensional settings.

Findings

Sparse factor structure identified across stocks and industry portfolios.

Group-wise penalized estimator achieves model selection consistency.

Method performs well in empirical high-frequency financial data.

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 It\^o 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.