Abstract: In this study, we develop a new semiparametric approach to model geostatistical data measured repeatedly over time. In addition, we draw inferences about the parameters and components of the underlying spatio-temporal process. Dependence in time and across space is modeled semiparametrically, giving rise to a class of nonseparable and nonstationary spatio-temporal covariance functions. A two-step procedure is devised to estimate the model parameters based on the likelihood of detrended data, and the computational algorithm is efficient owing to the dimension reduction. Extensions to spatio-temporal processes with general mean trends are also considered. Furthermore, the asymptotic properties of our proposed method are established, including consistency and asymptotic normality. A simulation study shows the sound finite-sample properties of the proposed method, and a real-data example is used to compare our method with alternative approaches.

Key words and phrases: Geostatistics, semiparametric methods, spatio-temporal processes.