Statistical Papers

, Volume 29, Issue 1, pp 281–300 | Cite as

Integer-valued moving average (INMA) process

  • M. Al-Osh
  • A. A. Alzaid


A simple model for a stationary sequence of dependent integer-valued random variables {Xn} is given. The sequence to be called integer-valued moving average (INMA) process, is taken as the “survivals” of i.i.d. non-negative integervalued random variables. It is argued that the model’s structure reflects to some extent the mechanism generating real life data for many counting process and consequently it is useful for modelling such processes. Various properties for the special case in which {Xn} is Poisson INMA (1) process, such as the joint distribution, regression, time reversibility, along with the conditional and partial correlations, are discussed in details. Extension of the INMA of first order to higher order moving average is considered.

Key words

Integer-valued moving average process Poisson INMA (1) regression reversibility conditional and partial correlations 


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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • M. Al-Osh
    • 1
  • A. A. Alzaid
    • 1
  1. 1.Department of Statistics College of ScienceKing Saud UniversityRiyadhSaudi Arabia

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