Spatiotemporal modelling with dynamic deformation for nonstationary covariance structures

Abstract In this paper, we present an innovative spatiotemporal model that allows dynamic variation in the spatial correlation structure over time through dynamic deformation. We propose that temporal deformation occurs smoothly relative to that in the original region. To incorporate this idea, we employ state space models to model dynamic deformation. Generalizing this class of models based on spatial deformation was driven by the need to model monthly average temperature data in the southern region of Brazil. The distinctive traits of this region, characterized by plateaus and mountain ranges and close proximity to the Atlantic Ocean, provide notable geographic diversity. This diversity, in addition to different meteorological phenomena over time, may influence the spatial correlation function. The model parameters are estimated via a Bayesian approach, which requires the use of Markov chain Monte Carlo methods to approximate the posterior distributions of parameters. The model is applied to 15 years of monthly average temperature data from the southern region of Brazil. The primary result of this analysis reveals a significant improvement in temperature modelling when the proposed model is used compared with that when versions that employ static deformation are used.