Spatio-temporal generalized complex covariance models based on convolution

Modeling covariance functions, with values on a complex domain, is essential for geostatistical interpolation or stochastic simulation of complex-valued random fields in space or space-time. However, little has been done for complex spatio-temporal modeling. For this aim, the construction of new classes of spatio-temporal complex-valued covariance models, based on convolution, is provided. Indeed, starting from the Lajaunie and Bejaoui models extended to a space-time domain, generalized families of complex models are obtained through the integration with respect to a positive measure. A procedure for fitting the two parts of the spatio-temporal complex models and for defining the density function considered for the integration is also illustrated. The computational details of this procedure are discussed through a case study on a spatio-temporal dataset of sea currents and the performance of these classes of models is assessed.