Space‐time autoregressive estimation and prediction with missing data based on Kalman filtering

Abstract

SummaryWe propose a Kalman filter algorithm to provide a formal statistical analysis of space‐time data with an autoregressive structure in time. 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 parameter estimation and prediction at unobserved locations. We thus develop space‐time estimation and prediction methods in the presence of missing data, through the Kalman filter, in order to obtain accurate estimates of model parameters and reliable space‐time predictions. Our findings are illustrated through an application on daily air temperatures in some regions of southern Chile, where the dataset shows a number of missing data in many locations.