A1007
Title: Robust high-dimensional time-varying coefficient estimation
Authors: Minseok Shin - KAIST (Korea, South) [presenting]
Donggyu Kim - KAIST (Korea, South)
Abstract: A novel high-dimensional coefficient estimation procedure based on high-frequency data is developed. Unlike usual high-dimensional regression procedures such as LASSO, the heavy-tailedness of high-frequency observations as well as time variations of coefficient processes, are additionally handled. Specifically, Huber loss and truncation schemes are employed to handle heavy-tailed observations, while l1-regularization is adopted to overcome the curse of dimensionality under a sparse coefficient structure. To account for the time-varying coefficient, local high-dimensional coefficients are estimated, which are biased estimators due to the l1-regularization. Thus, when estimating integrated coefficients, a debiasing scheme is proposed to enjoy the law of large number property and a thresholding scheme is employed to accommodate the sparsity of the coefficients further. This Robust is called thrEsholding Debiased LASSO (RED-LASSO) estimator. It is shown that the RED-LASSO estimator can achieve a near-optimal convergence rate with only a finite $b$-th moment for any $b>2$. In the empirical study, the RED-LASSO procedure is applied to the high-dimensional integrated coefficient estimation using high-frequency trading data.
