Dynamic Matrix Factor Models: A Covariate-Driven Approach to Varying Factor Loadings
提出一种协变量驱动的矩阵因子模型，允许行和列载荷矩阵随可观测协变量非参数变化，结合核平滑与主成分分析进行估计，并通过蒙特卡洛模拟和国际贸易流量、投资组合收益实证验证其优于传统固定载荷模型。
This paper proposes a covariate-driven matrix factor model in which the row and column loading matrices evolve as nonparametric functions of an observable time-varying covariate sequence. This flexible specification accommodates dynamic factor loadings driven by the temporal characteristics of the covariate. We develop a nonparametric estimation procedure that combines kernel smoothing with principal component analysis (PCA). Under high-dimensional asymptotics, we establish convergence rates for the estimators of the latent factor, dynamic loading matrices, and common component. Furthermore, we propose a formal bootstrap-based hypothesis test for the null hypothesis of constant loadings and a post-estimation smoothing procedure to resolve rotational ambiguity. Monte Carlo simulations and empirical applications to international trade flows and portfolio returns demonstrate the superior performance of the proposed method relative to conventional constant-loading matrix factor models, particularly in settings with complex, covariate-driven structural variation.