  In this paper, we develop a novel high-dimensional coefficient estimation
procedure based on high-frequency data. Unlike usual high-dimensional
regression procedure such as LASSO, we additionally handle the heavy-tailedness
of high-frequency observations as well as time variations of coefficient
processes. Specifically, we employ Huber loss and truncation scheme to handle
heavy-tailed observations, while $\ell_{1}$-regularization is adopted to
overcome the curse of dimensionality. To account for the time-varying
coefficient, we estimate local coefficients which are biased due to the
$\ell_{1}$-regularization. Thus, when estimating integrated coefficients, we
propose a debiasing scheme to enjoy the law of large number property and employ
a thresholding scheme to further accommodate the sparsity of the coefficients.
We call this Robust thrEsholding Debiased LASSO (RED-LASSO) estimator. We show
that the RED-LASSO estimator can achieve a near-optimal convergence rate. In
the empirical study, we apply the RED-LASSO procedure to the high-dimensional
integrated coefficient estimation using high-frequency trading data.
