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

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Abstract

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 inline image in (4). Partial sums process of inline image is discussed under the assumption EW2 < ∞ 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 inline image in spirit of Leipus et al. (2006) and obtain the weak consistency of the corresponding estimator of ϕ(x) in a suitable L2 space.

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