Vector Autoregressive Models with Spatially Structured Coefficients for Time Series on a Spatial Grid

Motivated by the need to analyze readily available data collected in space and time, especially in environmental sciences, we propose a parsimonious spatiotemporal model for time series data on a spatial grid. In essence, our model is a vector autoregressive model that utilizes the spatial structure to achieve parsimony of autoregressive matrices at two levels. The first level ensures the sparsity of the autoregressive matrices using a lagged-neighborhood scheme. The second level performs a spatial clustering of the nonzero autoregressive coefficients such that within some subregions, nearby locations share the same autoregressive coefficients while across different subregions the coefficients may have distinct values. The model parameters are estimated using the penalized maximum likelihood with an adaptive fused Lasso penalty. The estimation procedure can be tailored to accommodate the need and prior knowledge of a modeler. Performance of the proposed estimation algorithm is examined in a simulation study. Our method gives reliable estimation results that are interpretable and especially useful to identify geographical subregions, within each of which, the time series have similar dynamical behavior with homogeneous autoregressive coefficients. We apply our model to a wind speed time series dataset generated from a climate model over Saudi Arabia to illustrate its power in explaining the dynamics by the spatially structured coefficients. Moreover, the estimated model can be useful for building stochastic weather generators as an approximation of the computationally expensive climate model.