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

2013/02/20 by Anne Philippe, Donata Puplinskaite, Donata Puplinskaitė +5 · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1302.4815

openalex publication_date 2013/02/20 · arxiv created 2013/07/06 · arxiv updated 2013/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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(W²) is finite and a mixing density regularly varying at the "unit root" x=1 with exponent β>0. We show that the above partial sums process may exhibit four different limit behaviors depending on βand 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 L₂-space.

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