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

By temporal and contemporaneous aggregation, doubly indexed partial sums of independent copies of random coefficient AR(1) or INAR(1) processes are studied. Iterated limits of the appropriately centered and scaled aggregated partial sums are shown to exist. The paper completes the results of Pilipauskaitė and Surgailis (2014) and Barczy et al. (2015).