New Classes of Asymmetric Spatial-Temporal Covariance Models

Environmental spatial data often show complex spatial-temporal dependency structures that are difficult to model and estimate due to the lack of symmetry and other standard assumptions of the covariance function. In this study, we introduce certain types of symmetry in spatialtemporal processes: axial symmetry in time, axial symmetry in space, and diagonal symmetry in space, and propose new classes of asymmetric spatial-temporal covariance models by using spectral representations. We also explain the relationship between symmetry and separability and introduce nonseparable covariance models. Finally, we apply our new classes of covariance models to estimate the spatial-temporal structure of fine Particulate Matter (PM2.5) over the northeastern region of U.S.