We analyze a varying-coefficient dynamic spatial autoregressive model with spatial fixed effects. One salient feature of the model is the incorporation of multiple spatial weight matrices through their linear combinations with varying coefficients, which help solve the problem of choosing the most "correct" one for applied econometricians who often face the availability of multiple expert spatial weight matrices. We estimate and make inferences on the model coefficients and coefficients in basis expansions of the varying coefficients through penalized estimations, establishing the oracle properties of the estimators and the consistency of the overall estimated spatial weight matrix, which can be time-dependent. We further consider two applications of our model in change point detections in dynamic spatial autoregressive models, providing theoretical justifications in consistent change point locations estimation and practical implementations. Simulation experiments demonstrate the performance of our proposed methodology, and a real data analysis is also carried out.

翻译：本文分析了一种具有空间固定效应的变系数动态空间自回归模型。该模型的一个显著特征是通过变系数线性组合纳入了多个空间权重矩阵，这有助于解决应用计量经济学家常面临的问题：当存在多个专家提供的空间权重矩阵时，如何选择最"正确"的一个。我们通过惩罚估计方法对模型系数及变系数基展开中的系数进行估计与推断，建立了估计量的oracle性质以及整体估计空间权重矩阵（可具有时间依赖性）的一致性。我们进一步探讨了该模型在动态空间自回归模型变点检测中的两项应用，为变点位置估计的一致性提供了理论依据，并给出了实际实施方案。模拟实验验证了所提方法的性能，并进行了实际数据分析。