Adaptively varying-coefficient spatiotemporal models

Summary.  We propose an adaptive varying-coefficient spatiotemporal model for data that are observed irregularly over space and regularly in time. The model is capable of catching possible non-linearity (both in space and in time) and non-stationarity (in space) by allowing the auto-regressive coefficients to vary with both spatial location and an unknown index variable. We suggest a two-step procedure to estimate both the coefficient functions and the index variable, which is readily implemented and can be computed even for large spatiotemporal data sets. Our theoretical results indicate that, in the presence of the so-called nugget effect, the errors in the estimation may be reduced via the spatial smoothing—the second step in the estimation procedure proposed. The simulation results reinforce this finding. As an illustration, we apply the methodology to a data set of sea level pressure in the North Sea.