Joint temporal and contemporaneous aggregation of random-coefficient AR(1) processes

We discuss joint temporal and contemporaneous aggregation of N independent copies of AR(1) process with random-coefficient a epsilon [0, 1) when N and time scale n increase at different rate. Assuming that a has a density, regularly varying at a = 1 with exponent -1 < beta < 1, different joint limits of normalized aggregated partial sums are shown to exist when N1/(1+beta)/n tends to (i) infinity, (ii) 0, (iii) 0 < mu < infinity. The limit process arising under (iii) admits a Poisson integral representation on (0, infinity) x C(R) and enjoys 'intermediate' properties between fractional Brownian motion limit in (i) and sub-Gaussian limit in (ii). (C) 2013 Elsevier B.V. All rights reserved.