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 E W 2  < ∞ and a mixing density regularly varying at the ‘unit root’ x  = 1 with exponent β  > 0. We show that the previous partial sums process may exhibit four different limit behaviors depending on β and the Lévy 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 ϕ ( x ) in a suitable L 2 space.