  We propose a parsimonious spatiotemporal model for time series data on a
spatial grid. Our model is capable of dealing with high-dimensional time series
data that may be collected at hundreds of locations and capturing the spatial
non-stationarity. 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 non-zero autoregressive coefficients such that nearby
locations share similar coefficients. This model is interpretable and can be
used to identify geographical subregions, within each of which, the time series
share similar dynamical behavior with homogeneous autoregressive coefficients.
The model parameters are obtained using the penalized maximum likelihood with
an adaptive fused Lasso penalty. The estimation procedure is easy to implement
and can be tailored to the need of a modeler. We illustrate the performance of
the proposed estimation algorithm in a simulation study. We apply our model to
a wind speed time series dataset generated from a climate model over Saudi
Arabia to illustrate its usefulness. Limitations and possible extensions of our
method are also discussed.
