  Limit behaviour of temporal and contemporaneous aggregations of independent
copies of a stationary multitype Galton-Watson branching process with
immigration is studied in the so-called iterated and simultaneous cases,
respectively. In both cases, the limit process is a zero mean Brownian motion
with the same covariance function under third order moment conditions on the
branching and immigration distributions. We specialize our results for
generalized integer-valued autoregressive processes and single-type
Galton-Watson processes with immigration as well.
