Contemporaneous aggregation of triangular array of random-coefficient AR(1) processes.

Anne Philippe (1) , Donata Puplinskaite (1, 2) , Donatas Surgailis (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 Vilnius Institute of Mathematics and Informatics

We discuss contemporaneous aggregation of independent copies of a triangular array of random-coefficient AR(1) 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. Partial sums process of $ is discussed under the assumption E( W^2 ) is finite and a mixing density regularly varying at the ''unit root'' x=1 with exponent \beta >0. We show that the above partial sums process may exhibit four different limit behaviors depending on \beta and the Lévy triplet of W. Finally, we study the disaggregation problem in spirit of Leipus et al. (2006) and obtain the weak consistency of the corresponding estimator of the mixing distribution in a suitable L_2-space.

Mots clés: partial sums process; Aggregation; infinitely divisible distribution; random-coefficient AR(1) process; long memory; partial sums process.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Anne Philippe, Donata Puplinskaite, Donatas Surgailis. Contemporaneous aggregation of triangular array of random-coefficient AR(1) processes.. 2013. ⟨hal-00790344v2⟩