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.

[1]  Mikyoung Jun,et al.  An Approach to Producing Space–Time Covariance Functions on Spheres , 2007, Technometrics.

[2]  Mike Rees,et al.  5. Statistics for Spatial Data , 1993 .

[3]  D. Myers,et al.  Problems in space-time kriging of geohydrological data , 1990 .

[4]  D. Myers,et al.  Variograms with zonal anisotropies and noninvertible kriging systems , 1990 .

[5]  J. Zidek,et al.  Bayesian Spatial Prediction of Random Space-Time Fields With Application to Mapping PM2.5 Exposure , 2002 .

[6]  Montserrat Fuentes,et al.  Modeling and predicting complex space–time structures and patterns of coastal wind fields , 2005 .

[7]  T. Gneiting.  Nonseparable, Stationary Covariance Functions for Space–Time Data , 2002 .

[8]  Dale L. Zimmerman,et al.  Testing for directional symmetry in spatial dependence using the periodogram , 2005 .

[9]  Richard H. Jones,et al.  Models for Continuous Stationary Space-Time Processes , 1997 .

[10]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[11]  M. Stein.  Space–Time Covariance Functions , 2005 .

[12]  Noel A Cressie,et al.  Statistics for Spatial Data. , 1992 .

[13]  Shahrokh Rouhani,et al.  Space-Time Kriging of Groundwater Data , 1989 .

[14]  I. Rodríguez‐Iturbe,et al.  The design of rainfall networks in time and space , 1974 .

[15]  R. J. Martin,et al.  Testing axial symmetry and separability of lattice processes , 2005 .

[16]  N. Cressie,et al.  Classes of nonseparable, spatio-temporal stationary covariance functions , 1999 .