High-Dimensional High-Frequency Regression

Abstract

In this paper, we develop a novel high-dimensional regression inference procedure for high-frequency financial data. Unlike usual high-dimensional regression for low-frequency data, we need to additionally handle the time-varying coefficient problem. To accomplish this, we employ the Dantzig selection scheme and apply a debiasing scheme, which provides well-performing unbiased instantaneous coefficient estimators. With these schemes, we estimate the integrated coefficient, and to further account for the sparsity of the beta process, we apply thresholding schemes. We call this Thresholding dEbiased Dantzig Integrated Beta (TEDI Beta). We establish asymptotic properties of the proposed TEDI Beta estimator. In the empirical analysis, we apply the TEDI Beta procedure to analyzing high-dimensional factor models using high-frequency data.