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  • 1 Institut für Statistik, Technische Universität Graz, Münzgrabenstraße 11, 8010 Graz, Austria
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Abstract  

Aggregated processes appear in many areas of statistics, natural sciences and economics and studying their behavior has a considerable importance from a purely probabilistic point of view as well. Granger (1980) showed that aggregating processes of simple structure can lead to processes with much more complex dynamics, in particular, aggregating random coefficient AR(1) processes can result in long memory processes. This opens a new way to analyze complex processes by constructing such processes from simple ‘building blocks’ via aggregation. The basic statistical problem of aggregation theory is, given a sample {Y1(N), …, Yn(N)} of size n of the N-fold aggregated process, to draw conclusions for the structure of the constituting processes (“disaggregation”) and use this for describing the asymptotic behavior of the aggregated process. Probabilistically, this requires determining the limit distribution of nonlinear functionals of {Y1(N), …, Yn(N)}, which depends sensitively on the relative order of n and N. In this survey paper, we give a detailed asymptotic study of aggregated linear processes with an arbitrary (possibly infinite) number of parameters and apply the results to the disaggregation problem of AR(1) and AR(2) processes. We also discuss the problem of long memory of aggregated processes.

Manuscript Submission: HERE

  • Impact Factor (2019): 0.693
  • Scimago Journal Rank (2019): 0.412
  • SJR Hirsch-Index (2019): 20
  • SJR Quartile Score (2019): Q3 Mathematics (miscellaneous)
  • Impact Factor (2018): 0.664
  • Scimago Journal Rank (2018): 0.412
  • SJR Hirsch-Index (2018): 19
  • SJR Quartile Score (2018): Q2 Mathematics (miscellaneous)

Periodica Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1971
Volumes
per Year
2
Issues
per Year
4
Founder Bolyai János Matematikai Társulat - János Bolyai Mathematical Society
Founder's
Address
H-1055 Budapest, Hungary Falk Miksa u. 12.I/4.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0031-5303 (Print)
ISSN 1588-2829 (Online)

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