Many geophysical processes exhibit complex spatiotemporal interaction. In this paper a class of nonstationary statistical models with finite-order autoregressive spatiotemporal dynamics is introduced. The associated prediction problem is solved by implementing the Kalman filter in terms of multivariate versions of the spatial Karhunen-Lo¿ve and wavelet transforms. To illustrate the methodology, the AR(2) spatiotemporal interaction model is considered to represent a spatiotemporal data set from near-surface wind speed. The implementation of the Kalman filter is achieved in terms of the method of moments and the principal component analysis.