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 ∈ [ 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 < β < 1 , different joint limits of normalized aggregated partial sums are shown to exist when N 1 / ( 1 + β ) / n tends to (i) ∞ , (ii) 0 , (iii) 0 < μ < ∞ . The limit process arising under (iii) admits a Poisson integral representation on ( 0 , ∞ ) × C ( R ) and enjoys ‘intermediate’ properties between fractional Brownian motion limit in (i) and sub-Gaussian limit in (ii).