A geostatistical spatio-temporal model to non-fixed locations

Abstract

We investigated a Gaussian conditional geostatistical spatio-temporal model (CGSTM) aiming to fit data observed at non-fixed locations over discrete times, based only on the observed locations. The model specifies the process state at the current time conditioning on the process state in the recent past. Particularly, the process mean uses a weighting function governing the spatio-temporal model evolution and handling the interaction between space and time. The CGSTM provides attractive features, such as it belongs to the dynamic linear model framework, models non-fixed locations over time and easily provides forecasting maps k-steps ahead. Likelihood estimation and inference are based on a Kalman filter-based algorithm. Equivalent closed form of a covariance and precision matrices of the spatio-temporal joint-distribution was obtained. We performed a simulation study considering locations of a real data example, which presents data locations varying over time. A second simulation study was ran using various scenarios for parameter values and number of observations in time and space, observing consistency and unbiasedness of model estimators. Thirdly, The model was fitted to the average monthly rainfall dataset, with 678 temporal registers at 32 stations located in western Parana, Brazil. The rainfall station locations suffered geographical changes from 1961 to 2017. In this modelling, we used explanatory variables and provided forecasting maps.