Autoregressive Model With Spatial Dependence and Missing Data

We study herein an autoregressive model with spatially correlated error terms and missing data. A logistic regression model with completely observed covariates is used to model the missingness mechanism. An autoregressive model is used to accommodate time series dependence, and a spatial error model is used to capture spatial dependence. To estimate the model, a weighted least squares estimator is developed for the temporal component, and a weighted maximum likelihood estimator is developed for the spatial component. The asymptotic properties for both estimators are investigated. The finite sample performance is assessed through extensive simulation studies. A real data example about Beijing’s PM${}_{2.5}$ level data is illustrated.