Testing Spatial Stationarity and Segmenting Spatial Processes into Stationary Components

In geostatistics, the process of interest is commonly assumed to be stationary in a spatial region, particularly when only a single realization of data at finite locations is available. In this research, we develop a test for stationarity utilizing robust local estimates of spatial covariances. The test statistic is derived from clustering the data locations using Voronoi tessellations. If the stationary assumption is violated, we provide a method to show the nonstationary features by partitioning the region into stationary sub-regions. We further determine the best number of partitions using Bayesian information criterion. The proposed method is computationally efficient and applicable to irregularly spaced data. Its effectiveness is demonstrated through some simulation studies and an application to a precipitation dataset in Colorado.