  We discuss joint temporal and contemporaneous aggregation of $N$ independent
copies of strictly stationary AR(1) and INteger-valued AutoRegressive processes
of order 1 (INAR(1)) with random coefficient $\alpha \in (0, 1)$ and
idiosyncratic innovations. Assuming that $\alpha$ has a density function of the
form $\psi(x) (1 - x)^\beta$, $x \in (0, 1)$, with $\lim_{x\uparrow 1} \psi(x)
= \psi_1 \in (0, \infty)$, different Brownian limit processes of appropriately
centered and scaled aggregated partial sums are shown to exist in case
$\beta=1$ when taking first the limit as $N \to \infty$ and then the time scale
$n \to \infty$, or vice versa. This paper completes the one of Pilipauskait\.e
and Surgailis (2014), and Barczy, Ned\'enyi and Pap (2015), where the iterated
limits are given for every other possible value of the parameter $\beta$ for
the two types of models.
