In this article, 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 ℓ1-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 ℓ1-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.

https://www.cambridge.org/core/journals/econometric-theory/article/robust-highdimensional-timevarying-coefficient-estimation/508DF3AFB068F35BBB401C854CE34A92