  This article studies identification and estimation for the network vector
autoregressive model with nonstationary regressors. In particular, network
dependence is characterized by a nonstochastic adjacency matrix. The
information set includes a stationary regressand and a node-specific vector of
nonstationary regressors, both observed at the same equally spaced time
frequencies. Our proposed econometric specification correponds to the NVAR
model under time series nonstationarity which relies on the local-to-unity
parametrization for capturing the unknown form of persistence of these
node-specific regressors. Robust econometric estimation is achieved using an
IVX-type estimator and the asymptotic theory analysis for the augmented vector
of regressors is studied based on a double asymptotic regime where both the
network size and the time dimension tend to infinity.
