High-Dimensional Time-Varying Coefficient Estimation in Diffusion Models

Abstract

In this paper, we develop a novel high-dimensional time-varying coefficient estimation method, based on high-dimensional It\^o 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.