Statistical analysis of a spatio-temporal model with location dependent parameters and a test for spatial stationarity

In this paper we define a spatio-temporal model with location dependent parameters to describe temporal variation and spatial nonstationarity. We consider the prediction of observations at unknown locations using known neighbouring observations. Further we propose a local least squares based method to estimate the parameters at unobserved locations. The sampling properties of these estimators are investigated. We also develop a statistical test for spatial stationarity. In order to derive the asymptotic results we show that the spatially nonstationary process can be locally approximated by a spatially stationary process. We illustrate the methods of estimation with some simulations. key words: Autoregressive process, ground ozone data, kriging, local least squares, local stationarity, polynomial interpolation, spatio-temporal models, testing for spatial stationarity.