CONTEMPORANEOUS AGGREGATION OF TRIANGULAR ARRAY OF RANDOM-COEFFICIENT AR(1) PROCESSES

We discuss contemporaneous aggregation of independent copies of a triangular array of random-coefficient processes with i.i.d. innovations belonging to the domain of attraction of an infinitely divisible law W. The limiting aggregated process is shown to exist, under general assumptions on W and the mixing distribution, and is represented as a mixed infinitely divisible moving average {X(t)} in (4). Partial sums process of {X(t)} is discussed under the assumption EW2<and a mixing density regularly varying at the unit root' x=1 with exponent >0. We show that the previous partial sums process may exhibit four different limit behaviors depending on and the Levy triplet of W. Finally, we study the disaggregation problem for {X(t)} in spirit of Leipus et al. (2006) and obtain the weak consistency of the corresponding estimator of phi(x) in a suitable L-2 space.