A group lasso approach for non-stationary spatial-temporal covariance estimation

We develop a new approach for modeling non-stationary spatialtemporal 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 spatialtemporal process as the sum of a spatialtemporal 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 spatialtemporal 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. Copyright (C) 2011 John Wiley & Sons, Ltd.