Examining the properties of the estimators of the spatial unilateral autoregressive model by bootstrapping

Abstract

Many methods and procedures have been developed and proposed to overcome the estimation problem in spatial modeling, for example, by defining classes of models called separable models and the unilateral models. A special type of spatial models that received much attention is the spatial unilateral autoregressive models denoted as AR(p1,1) model. Several procedures have been proposed to estimate the parameters of this model. These include the Yule-Walker, the least squares and the maximum likelihood methods. In this paper, we examine the properties of these estimators for the first-order model, i.e. the AR(1,1) model. The examination is done by measuring the accuracy of these estimators for AR(1,1) model based on the value of the standard error of the estimates. To achieve this objective, bootstrap method based on resampling the residuals is used to obtain the standard error of the estimates.