The Kriged Kalman filter

Abstract

In recent years there has been growing interest in spatial-temporal modelling, partly due to the potential of large scale data in pollution and global climate monitoring to answer important environmental questions. We consider the Kriged Kalman filter (KKF), a powerful modelling strategy which combines the two wellestablished approaches of (a) Kriging, in the field of spatial statistics, and (b) the Kalman filter, in general state space formulations of multivariate time series analysis. We give a brief introduction to the model and describe its various properties, and highlight that the model allows prediction in time as well as in space, simultaneously. Some special cases of the time series model are considered. We give some procedures to implement the model, also illustrated through a practical example. The paper concludes with a discussion.