Abstract
We develop a new approach for modeling non‐stationary spatial–temporal processes on the basis of data sampled at fixed locations over time. The approach applies a basis function formulation and a constrained penalized least squares method recently proposed for estimating non‐stationary spatial‐only covariance functions. In this article, we further incorporate the temporal dependence into this framework and model the spatial–temporal process as the sum of a spatial–temporal stationary process and a linear combination of known basis functions with temporal dependent coefficients. A group lasso penalty is devised to select the basis functions and estimate the parameters simultaneously. In addition, a blockwise coordinate descent algorithm is applied for implementation. This algorithm computes the constrained penalized least squares solutions along a regularization path very rapidly. The resulting dynamic model has a state‐space form, thereby the optimal spatial–temporal predictions can be computed efficiently using the Kalman filter. Moreover, the methodology is applied to a wind speed data set observed at the western Pacific Ocean for illustration.