In this paper, we propose a novel high-dimensional time-varying coefficient estimator for noisy high-frequency observations. In high-frequency finance, we often observe that noises dominate a signal of an underlying true process. Thus, we cannot apply usual regression procedures to analyze noisy high-frequency observations. To handle this issue, we first employ a smoothing method for the observed variables. However, the smoothed variables 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 Thresholded dEbiased Nonconvex LASSO (TEN-LASSO) estimator. Furthermore, this paper establishes the concentration properties of the TEN-LASSO estimator and discusses a nonconvex optimization algorithm.

翻译：本文针对含噪声高频观测数据，提出了一种新颖的高维时变系数估计方法。在高频金融中，噪声常主导潜在真实过程的信号，因此通常的回归方法无法直接用于分析含噪高频观测数据。为解决该问题，我们首先对观测变量采用平滑方法进行处理。然而，平滑后的变量仍包含不可忽略的噪声。为应对这些不可忽略的噪声及高维性，我们为每个局部系数提出了一种非凸惩罚回归方法。该方法可得到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，利用去偏后的局部系数估计量获得无偏的积分系数估计量。进一步，为考虑系数的稀疏结构，我们对去偏后的积分系数估计量采用阈值化方案。我们将该方案称为阈值去偏非凸LASSO（TEN-LASSO）估计量。此外，本文建立了TEN-LASSO估计量的集中性质，并讨论了非凸优化算法。