The spatial 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 spatial autoregressive model is a linear model for describing spatial correlation. In this work, we expand the classical model to include time lagged observations, 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 spatial/space-time model and neural network component. We investigate the quality of the asymptotic approximations for finite samples by means of numerical simulation studies. Next, we discuss the model selection in the proposed space-time autoregressive model. We employ the Shakeout noise injection method to conduct feature selection and use the likelihood ratio test for the time lag order selection. We evaluate the performance of Shakeout noise injection technique in a simulated dataset and also investigate the asymptotic approximation of the likelihood ratio test statistics by simulations. Finally, we apply our proposed spatial and space-time autoregressive models to a real world application.

Creator

• Wang, Wenqian

DOI

• https://doi.org/10.21985/n2-nw0y-1z06

Subject

• Mathematics
• Geography
• Statistics

Language

• en

Alternate Identifier

• etdadmin_upload_663006
• http://dissertations.umi.com/northwestern:14671

Keyword

• Neural network
• Maximum likelihood method
• Spatial analysis
• Noise injection

Date created

• 2019-01-01

Resource type

• Dissertation

Rights statement

• In Copyright