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Statistical Papers

, Volume 53, Issue 4, pp 935–949 | Cite as

Additive outliers in INAR(1) models

  • Mátyás BarczyEmail author
  • Márton Ispány
  • Gyula Pap
  • Manuel Scotto
  • Maria Eduarda Silva
Regular Article

Abstract

In this paper the integer-valued autoregressive model of order one, contaminated with additive outliers is studied in some detail. Moreover, parameter estimation is also addressed. Supposing that the timepoints of the outliers are known but their sizes are unknown, we prove that the conditional least squares (CLS) estimators of the offspring and innovation means are strongly consistent. In contrast, however, the CLS estimators of the outliers’ sizes are not strongly consistent, although they converge to a random limit with probability 1. We also prove that the joint CLS estimator of the offspring and innovation means is asymptotically normal. Conditionally on the values of the process at the timepoints neighboring to the outliers’ occurrences, the joint CLS estimator of the sizes of the outliers is also asymptotically normal.

Keywords

Integer-valued autoregressive models Additive outliers Conditional least squares estimators Strong consistency Conditional asymptotic normality 

Mathematics Subject Classification (2000)

60J80 62F12 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Mátyás Barczy
    • 1
    Email author
  • Márton Ispány
    • 1
  • Gyula Pap
    • 2
  • Manuel Scotto
    • 3
  • Maria Eduarda Silva
    • 4
  1. 1.Faculty of InformaticsUniversity of DebrecenDebrecenHungary
  2. 2.University of Szeged, Bolyai InstituteSzegedHungary
  3. 3.Departamento de Matemática, Campus Universitário de SantiagoUniversidade de AveiroAveiroPortugal
  4. 4.Faculdade de EconomiaUniversidade do PortoPortoPortugal

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