  Many econometric analyses involve spatio--temporal data. A considerable
amount of literature has addressed spatio--temporal models, with Spatial
Dynamic Panel Data (SDPD) being widely investigated and applied. In real data
applications, checking the validity of the theoretical assumptions underlying
the SDPD models is essential but sometimes difficult. At other times, the
assumptions are clearly violated. For example, the spatial matrix is assumed to
be known but it may actually be unknown and needs to be estimated. In such
cases, the performance of the SDPD model's estimator is generally affected.
Motivated by such considerations, we propose a new model (called stationary
SDPD) and a new estimation procedure based on simple and clear assumptions that
can be easily checked with real data. The new model is highly adaptive, and the
estimation procedure has a rate of convergence that is not affected by the
dimension of the time series (under general assumptions), notwithstanding the
relatively high number of parameters to be estimated. The new model may be used
to represent a wide class of multivariate time series, not necessarily
spatio-temporal. So, it can be used as a valid alternative to vector
autoregressive (VAR) models with two immediate advantages: i) a faster rate of
convergence of the estimation procedure and ii) the possibility of estimating
the model even when the dimension is higher than the time series length,
overcoming the curse of dimensionality typical of the VAR models. The
simulation study shows that the new estimation procedure performs well compared
with the classic alternative procedure, even when the spatial matrix is unknown
and therefore estimated.
