Realized Regularized Regressions
TLDR
This paper introduces a continuous-time penalized regression framework for high-frequency data, achieving oracle properties in high dimensions.
Key contributions
- Introduces a continuous-time penalized regression for time-varying coefficients and variable selection with high-frequency data.
- Estimates coefficients via spline basis expansions and least squares from truncated high-frequency increments.
- Establishes consistency and asymptotic distribution for integrated coefficients in finite dimensions.
- Achieves oracle property in high dimensions using a group-wise truncated L1-penalty for variable selection.
Why it matters
This paper offers a robust method for analyzing high-frequency financial data, enabling dynamic coefficient estimation and variable selection. Its oracle property ensures reliable model selection even with many covariates. The empirical application demonstrates its practical utility in uncovering sparse factor structures.
Original 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 $\ell_1$-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.
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