带惩罚模型选择的多元时空回归及实证应用
Multivariate Spatio-Temporal Regression with Penalized Model Selection and an Empirical Application
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中文总结 AI 辅助
本文提出多元通用嵌套时空（MGNST）回归框架，结合惩罚模型选择方法，通过蒙特卡洛实验和日本关西地区198个城市的社会经济数据验证了其在分析多元时空依赖结构的有效性。
中文摘要 AI 辅助
本文构建了多元通用嵌套时空（MGNST）回归框架的统计基础，用于分析响应变量间的空间、时间及跨方程依赖关系。四个参数矩阵分别表示空间滞后依赖、空间误差依赖、时间自回归和同期误差协方差，其非对角元素允许依赖在响应变量内部及之间传播。矩阵约束可产生11种模型设定，涵盖多元空间自回归模型、多元空间误差模型、带外生变量的向量自回归模型及独立时空回归模型作为特例。我们利用工具变量秩条件建立可识别性条件，并引入基于有效自由度的惩罚似然估计和信息准则。蒙特卡洛实验检验了三种数据生成模型、三种样本量和三种空间依赖水平。惩罚AIC下的正确选择率通常随样本量和空间依赖强度增加而提高，参数恢复效果随样本量增大而改善。针对日本关西地区198个城市的社会经济数据，惩罚AIC选择了完整的MGNST模型，而惩罚BIC选择了按响应变量独立的空间误差模型。尽管选择了不同复杂度的模型，两种准则均支持时间持续性和空间误差依赖。pAIC选择的MGNST模型将响应变量中的强空间自相关降至可忽略的残差水平，证明其在识别和比较多元时空依赖结构方面的实用性。
英文摘要
This paper develops the statistical foundations of a multivariate general nesting spatio-temporal (MGNST) regression framework for analyzing spatial, temporal, and cross-equation dependence among responses. Four parameter matrices represent spatial lag dependence, spatial error dependence,temporal autoregression, and contemporaneous error covariance. Their off-diagonal elements allow dependence to propagate within and across responses. Matrix restrictions yield eleven specifications encompassing multivariate spatial autoregressive models, multivariate spatial error models, vector autoregressive models with exogenous variables, and independent spatio-temporal regressions as special cases. We establish identifiability conditions using instrumental-variable rank conditions and introduce penalized likelihood estimation and information criteria based on effective degrees of freedom. Monte Carlo experiments examine three data-generating models, three sample sizes, and three levels of spatial dependence. Correct-selection rates under penalized AIC generally increase with sample size and the strength of spatial dependence, while parameter recovery improves as the sample size increases. For socioeconomic data from 198 municipalities in Japan's Kansai region, penalized AIC selects the full MGNST model, whereas penalized BIC selects a response-wise independent spatial error model. Despite selecting models of different complexity, both criteria support temporal persistence and spatial error dependence. The pAIC-selected MGNST model reduces strong spatial autocorrelation in the responses to negligible residual levels, demonstrating its usefulness for identifying and comparing multivariate spatio-temporal dependence structures.
