Testing Lack of Symmetry in Spatial-Temporal Processes.

Symmetry and separability of spatial-temporal covariances are the main assumptions that are frequently taken for granted in most applications because of the simplicity of constructing covariance structure. However, many studies in environmental sciences show that real data have complex spatial-temporal dependency structures resulting from lack of symmetry or violation of other standard assumptions of the covariance function. In this study, we propose new formal tests for lack of symmetry by using spectral representations of the spatial-temporal covariance functions. The advantage of the proposed tests is that classical analysis of variance (ANOVA) models can be used for detecting lack of symmetry inherent in spatial-temporal processes. We evaluate the performance of the tests with simulation studies and we apply them to air pollution data.