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

In this article, 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. 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. Copyright 2008 The Author. Journal compilation 2008 Blackwell Publishing Ltd