In this paper, we develop a novel high-dimensional time-varying coefficient estimation method, based on high-dimensional Itô diffusion processes. To account for high-dimensional time-varying coefficients, we first estimate local (or instantaneous) coefficients using a time-localized Dantzig selection scheme under a sparsity condition, which results in biased local coefficient estimators due to the regularization. To handle the bias, we propose a debiasing scheme, which provides well-performing unbiased local coefficient estimators. With the unbiased local coefficient estimators, we estimate the integrated coefficient, and to further account for the sparsity of the coefficient process, we apply thresholding schemes. We call this Thresholding dEbiased Dantzig (TED). We establish asymptotic properties of the proposed TED estimator. In the empirical analysis, TED achieves a higher average out-of-sample $R^2$ across assets than benchmark estimators in most periods. Industry-related factors play a central role in explaining asset returns. The estimated integrated coefficients show pronounced time variation associated with firm-specific events and seasonal patterns.

翻译：本文提出了一种基于高维伊藤扩散过程的新型高维时变系数估计方法。为处理高维时变系数，我们首先在稀疏性条件下采用时间局部化的Dantzig选择方案估计局部（或瞬时）系数，该方案会因正则化导致局部系数估计量存在偏差。为处理该偏差，我们提出了一种去偏方案，该方案能提供性能良好的无偏局部系数估计量。利用这些无偏局部系数估计量，我们估计积分系数，并进一步通过阈值化方案处理系数过程的稀疏性。我们将此方法称为阈值化去偏Dantzig估计器。我们建立了所提出的TED估计量的渐近性质。在实证分析中，在大多数时期内，TED在资产上的平均样本外$R^2$高于基准估计量。行业相关因子在解释资产收益率方面起着核心作用。估计得到的积分系数显示出与公司特定事件和季节性模式相关的显著时变特征。