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 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.

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Field Value
Source https://hal.science/hal-00790344
Author Philippe, Anne, Puplinskaite, Donata, Surgailis, Donatas
Maintainer CCSD
Last Updated May 10, 2026, 10:54 (UTC)
Created May 10, 2026, 10:54 (UTC)
Identifier hal-00790344
Language en
Rights https://about.hal.science/hal-authorisation-v1/
contributor Laboratoire de Mathématiques Jean Leray (LMJL) ; Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST) ; Université de Nantes (UN)-Université de Nantes (UN)-Centre National de la Recherche Scientifique (CNRS)
creator Philippe, Anne
date 2013-02-19T00:00:00
harvest_object_id 940ce930-4fb3-45f8-b53d-ac2e7a1dc629
harvest_source_id 3374d638-d20b-4672-ba96-a23232d55657
harvest_source_title test moissonnage SELUNE
metadata_modified 2026-04-16T00:00:00
relation info:eu-repo/semantics/altIdentifier/arxiv/1302.4815
set_spec type:UNDEFINED