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We propose a parsimonious spatiotemporal model for time series data on aspatial grid. Our model is capable of dealing with high-dimensional time seriesdata that may be collected at hundreds of locations and capturing the spatialnon-stationarity. In essence, our model is a vector autoregressive model thatutilizes the spatial structure to achieve parsimony of autoregressive matricesat two levels. The first level ensures the sparsity of the autoregressivematrices using a lagged-neighborhood scheme. The second level performs aspatial clustering of the non-zero autoregressive coefficients such that nearbylocations share similar coefficients. This model is interpretable and can beused to identify geographical subregions, within each of which, the time seriesshare similar dynamical behavior with homogeneous autoregressive coefficients.The model parameters are obtained using the penalized maximum likelihood withan adaptive fused Lasso penalty. The estimation procedure is easy to implementand can be tailored to the need of a modeler. We illustrate the performance ofthe proposed estimation algorithm in a simulation study. We apply our model toa wind speed time series dataset generated from a climate model over SaudiArabia to illustrate its usefulness. Limitations and possible extensions of ourmethod are also discussed.

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