# Robust High-Dimensional Time-Varying Coefficient Estimation

## TL;DR

This paper introduces RED-LASSO, a robust method for high-dimensional, time-varying coefficient estimation using high-frequency data, effectively handling heavy tails and sparsity.

## Contribution

The paper develops a novel robust estimation procedure combining Huber loss, debiasing, and thresholding for high-dimensional, time-varying models with heavy-tailed data.

## Key findings

- Achieves near-optimal convergence rates.
- Successfully applied to high-frequency trading data.
- Handles heavy tails and coefficient sparsity effectively.

## Abstract

In this paper, we develop a novel high-dimensional coefficient estimation procedure based on high-frequency data. Unlike usual high-dimensional regression procedures such as LASSO, we additionally handle the heavy-tailedness of high-frequency observations as well as time variations of coefficient processes. Specifically, we employ the Huber loss and a 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 numbers 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.