A test for stationarity for irregularly spaced spatial data

Abstract The analysis of spatial data is based on a set of assumptions, which in practice need to be checked. A commonly used assumption is that the spatial random field is second order stationary. In this paper, a test for spatial stationarity for irregularly sampled data is proposed. The test is based on a transformation of the data (a type of Fourier transform), where the correlations between the transformed data is close to zero if the random field is second order stationary. On the other hand, if the random field were second order nonstationary, this property does not hold. Using this property a test for second order stationarity is constructed. The test statistic is based on measuring the degree of correlation in the transformed data. The asymptotic sampling properties of the test statistic is derived under both stationarity and nonstationarity of the random field. These results motivate a graphical tool which allows a visual representation of the nonstationary features. The method is illustrated with simulations and a real data example.