  We propose a series-based nonparametric specification test for a regression
function when data are spatially dependent, the `space' being of a general
economic or social nature. Dependence can be parametric, parametric with
increasing dimension, semiparametric or any combination thereof, thus covering
a vast variety of settings. These include spatial error models of varying types
and levels of complexity. Under a new smooth spatial dependence condition, our
test statistic is asymptotically standard normal. To prove the latter property,
we establish a central limit theorem for quadratic forms in linear processes in
an increasing dimension setting. Finite sample performance is investigated in a
simulation study, with a bootstrap method also justified and illustrated, and
empirical examples illustrate the test with real-world data.
