This article proposes a spatial autoregression (SAR) model with time-varying coefficients. The model incorporates both spatial dependence and the impacts of explanatory variables, and all the coefficients are allowed to flexibly vary according to time. This article further develops a kernel-smoothed estimator (KSE) to estimate the timevarying coefficients. Compared with the maximum likelihood estimator (MLE) obtained at discrete time points, the KSE utilizes the potentially useful information from time neighborhoods. We have theoretically proved the consistency of the proposed KSE. A number of simulation studies show that the KSE is more accurate and performs substantially better than the MLE. Moreover, a real data analysis for a ride-hailing platform in China also shows that the KSE is more stable and interpretable. The proposed model as well as the KSE can be widely applied to data with a large number of cross-sectional units and regularly spaced time points.

中文翻译：

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具有时变系数的空间自回归模型

本文提出了一种具有时变系数的空间自回归（SAR）模型。该模型结合了空间依赖性和解释变量的影响，并且允许所有系数随时间灵活变化。本文进一步开发了一个核平滑估计器 (KSE) 来估计时变系数。与在离散时间点获得的最大似然估计器 (MLE) 相比，KSE 利用了来自时间邻域的潜在有用信息。我们从理论上证明了所提出的 KSE 的一致性。许多模拟研究表明，KSE 比 MLE 更准确并且性能明显更好。此外，对国内某网约车平台的真实数据分析也表明，KSE 更稳定、更易解释。