Nonseparable, Space-Time Covariance Functions with Dynamical Compact Supports

The paper provides new classes of nonseparable space-time covariance functions with spatial (or temporal) margin belonging to the Generalized Wendland class of compactly supported covariance functions. An interesting feature of our covariances, from the computational viewpoint, is that the compact support is a decreasing function of the temporal (spatial) lag. We provide conditions for the validity of the proposed class, and analyze the problem of differentiability at the origin for the temporal (spatial) margin. A simulation study explores the finite sample properties and the computational burden associated with the maximum likelihood estimation of the covariance parameters. Finally, we use the proposed covariance models on Irish wind speed data and compare them with Gneiting-Mat´ern models in terms of fitting, prediction efficiency and computational burden. Necessary and sufficient conditions together with other results on dynamically varying compact supports are provided in the Online Supplement to this paper.