In this paper, we propose a novel high-dimensional time-varying coefficient estimator for noisy high-frequency observations with a factor structure. In high-frequency finance, we often observe that noises dominate the signal of underlying true processes and that covariates exhibit a factor structure due to their strong dependence. Thus, we cannot apply usual regression procedures to analyze high-frequency observations. To handle the noises, we first employ a smoothing method for the observed dependent and covariate processes. Then, to handle the strong dependence of the covariate processes, we apply Principal Component Analysis (PCA) and transform the highly correlated covariate structure into a weakly correlated structure. However, the variables from PCA still contain non-negligible noises. To manage these non-negligible noises and the high dimensionality, we propose a nonconvex penalized regression method for each local coefficient. This method produces consistent but biased local coefficient estimators. To estimate the integrated coefficients, we propose a debiasing scheme and obtain a debiased integrated coefficient estimator using debiased local coefficient estimators. Then, to further account for the sparsity structure of the coefficients, we apply a thresholding scheme to the debiased integrated coefficient estimator. We call this scheme the Factor Adjusted Thresholded dEbiased Nonconvex LASSO (FATEN-LASSO) estimator. Furthermore, this paper establishes the concentration properties of the FATEN-LASSO estimator and discusses a nonconvex optimization algorithm.

翻译：本文针对具有因子结构的含噪高频观测数据，提出了一种新颖的高维时变系数估计方法。在高频金融领域，我们常观察到噪声主导了潜在真实过程的信号，且协变量因其强依赖性而呈现出因子结构。因此，无法应用常规回归程序来分析高频观测数据。为处理噪声，我们首先对观测到的因变量和协变量过程采用平滑方法。接着，为处理协变量过程的强依赖性，我们应用主成分分析（PCA），将高度相关的协变量结构转换为弱相关结构。然而，来自PCA的变量仍包含不可忽略的噪声。为处理这些不可忽略的噪声以及高维问题，我们针对每个局部系数提出了一种非凸惩罚回归方法。该方法产生一致但有偏的局部系数估计量。为估计积分系数，我们提出了一种去偏方案，并利用去偏后的局部系数估计量获得了一个去偏的积分系数估计量。随后，为进一步考虑系数的稀疏结构，我们对去偏后的积分系数估计量应用阈值方案。我们将此方案称为因子调整阈值去偏非凸LASSO（FATEN-LASSO）估计量。此外，本文建立了FATEN-LASSO估计量的集中性质，并讨论了一种非凸优化算法。