A Kalman filter method for estimation and prediction of space–time data with an autoregressive structure

• Published in: Journal of statistical planning and inference 2019-12, Vol.203, p.117-130
• Main Authors: Lagos-Álvarez, Bernardo, Padilla, Leonardo, Mateu, Jorge, Ferreira, Guillermo
• Format: Article
• Language: English
• Subjects: Kalman filter algorithm; Simple kriging; Space–time geostatistics; Space–time models; State-space system
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/j.jspi.2019.03.005

We propose a new Kalman filter algorithm to provide a formal statistical analysis of space–time data with an autoregressive structure. The Kalman filter technique allows to capture the temporal dependence as well as the spatial correlation structure through state-space equations, and it is aimed to perform statistical inference in terms of both parameter estimation and prediction at unobserved locations. We put in relevance the nugget effect at the observation equation. We test our procedure and compare it with classical kriging prediction via an intensive simulation study. We show that the Kalman filter is superior in both the estimation, without using a plug-in approach, and prediction for spatio-temporal data, providing a suitable formal procedure for the statistical analysis of space–time data. Finally, an application to the prediction of daily air temperature data in some regions of southern Chile is presented. •A space–time autoregressive model is formulated.•Place in relevance the nugget effect at the observation equation does not cause difficulties in the estimation.•The predictions obtained are compared with those of simple kriging.•The use of the proposed model is better than that for the simple kriging, in terms of a prediction gain criterion.