Robust High-Dimensional Time-Varying Coefficient Estimation
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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 ℓ_1-regularization is adopted to overcome the curse of dimensionality under a sparse coefficient structure. To account for the time-varying coefficient, we estimate local high-dimensional coefficients which are biased estimators due to the ℓ_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 with only finite γth moment for any γ>2. In the empirical study, we apply the RED-LASSO procedure to the high-dimensional integrated coefficient estimation using high-frequency trading data.
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