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

We discuss joint temporal and contemporaneous aggregation of NN independent copies of AR(1) process with random-coefficient a∈[0,1)a∈[0,1) when NN and time scale nn increase at different rate. Assuming that aa has a density, regularly varying at a=1a=1 with exponent −1<β<1−1<β<1, different joint limits of normalized aggregated partial sums are shown to exist when N1/(1+β)/nN1/(1+β)/n tends to (i) ∞∞, (ii) 00, (iii) 0<μ<∞0<μ<∞. The limit process arising under (iii) admits a Poisson integral representation on (0,∞)×C(R)(0,∞)×C(R) and enjoys ‘intermediate’ properties between fractional Brownian motion limit in (i) and sub-Gaussian limit in (ii).