Robust High-Dimensional Time-Varying Coefficient Estimation

Donggyu Kim () and Minseok Shin
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Donggyu Kim: Department of Economics, University of California Riverside

No 202417, Working Papers from University of California at Riverside, Department of Economics

Abstract: 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 â„“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 â„“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.

Pages: 55 Pages
Date: 2024-12
New Economics Papers: this item is included in nep-ecm and nep-ets
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