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We discuss joint temporal and contemporaneous aggregation of $N$ independentcopies of strictly stationary AR(1) and INteger-valued AutoRegressive processesof order 1 (INAR(1)) with random coefficient $\alpha \in (0, 1)$ andidiosyncratic innovations. Assuming that $\alpha$ has a density function of theform $\psi(x) (1 - x)^\beta$, $x \in (0, 1)$, with $\lim_{x\uparrow 1} \psi(x)= \psi_1 \in (0, \infty)$, different Brownian limit processes of appropriatelycentered 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\.eand Surgailis (2014), and Barczy, Ned\'enyi and Pap (2015), where the iteratedlimits are given for every other possible value of the parameter $\beta$ forthe two types of models.

Iterated scaling limits for aggregation of random coefficient AR(1) and INAR(1) processes