A dimension-reduced approach to space-time Kalman filtering
Many physical/biological processes involve variability over both space and time. As a result of difficulties caused by large datasets and the modelling of space, time and spatio-temporal interactions, traditional space-time methods are limited. In this paper, we present an approach to space-time prediction that achieves dimension reduction and uses a statistical model that is temporally dynamic and spatially descriptive. That is, it exploits the unidirectional flow of time, in an autoregressive framework, and is spatially 'descriptive' in that the autoregressive process is spatially coloured. With the inclusion of a measurement equation, this formulation naturally leads to the development of a spatio-temporal Kalman filter that achieves dimension reduction in the analysis of large spatio-temporal datasets. Unlike other recent space-time Kalman filters, our model also allows a non-dynamic spatial component. The method is applied to a dataset of near-surface winds over the topical Pacific ocean. Spatial predictions with this dataset are improved by considering the additional non-dynamic spatial process. The improvement becomes more pronounced as the signal-to-noise ratio decreases. 1999 Biometrika Trust.