  We introduce parsimonious parameterisations for multivariate autoregressive
count time series models for spatio-temporal data, including possible
regressions on covariates. The number of parameters is reduced by specifying
spatial neighbourhood structures for possibly huge matrices that take into
account spatio-temporal dependencies. Consistency and asymptotic normality of
the parameter estimators are obtained under mild assumptions by employing
quasi-maximum likelihood methodology. This is used to obtain an asymptotic Wald
test for testing the significance of individual or group effects. Several
simulations and two data examples support and illustrate the methods proposed
in this paper.
