标题： 部分指定时空自回归模型与人工神经网络 显示英文标题

标题： Partially Specified Space Time Autoregressive Model with Artificial Neural Network

摘要： 时空自回归模型已被广泛应用于科学领域，如经济学、公共财政、政治学、农业经济学、环境研究和交通分析。 经典时空自回归模型是一个用于描述空间相关性的线性模型。 在本工作中，我们扩展了经典模型，以包括相关的外生变量，可能非高斯的、高波动性的误差，以及一个非线性的神经网络组件。 非线性神经网络组件允许更多的模型灵活性，能够学习和建模非线性和复杂的关系。 我们使用最大似然方法进行模型参数估计。 在对时空模型和神经网络组件的一些标准条件下，我们建立了这些估计量的一致性和渐近正态性。 我们通过数值模拟研究来检验有限样本中渐近近似的质量。 为了说明，我们包含了一个现实世界的应用。 显示英文摘要

摘要： The space time autoregressive model has been widely applied in science, in areas such as economics, public finance, political science, agricultural economics, environmental studies and transportation analyses. The classical space time autoregressive model is a linear model for describing spatial correlation. In this work, we expand the classical model to include related exogenous variables, possibly non-Gaussian, high volatility errors, and a nonlinear neural network component. The nonlinear neural network component allows for more model flexibility, the ability to learn and model nonlinear and complex relationships. We use a maximum likelihood approach for model parameter estimation. We establish consistency and asymptotic normality for these estimators under some standard conditions on the space time model and neural network component. We investigate the quality of the asymptotic approximations for finite samples by means of numerical simulation studies. For illustration, we include a real world application.