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Models for Z+-Valued Time Series Based on Thinning

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International Encyclopedia of Statistical Science

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Introduction

Developing models for integer-valued time series has received increasing attention in the past two decades. Integer-valued time series are useful in modeling dependent count data. They are also useful in the simulation of dependent discrete random variables with specified distribution and correlation structure.

Lawrance and Lewis (1977) and Gaver and Lewis (1980) were the first authors to construct autoregressive processes with non-Gaussian marginals. This has essentially motivated all the research on integer-valued time series. The present review is far from being exhaustive. Our focus is on models for Z +-valued first-order autoregressive processes INAR(1). We will consider five approaches which are based on “thinning” for developing these models.

First construction

To introduce integer-valued autoregressive moving average processes, McKenzie (1986, 1988) and Al-Osh and Alzaid (1987) used the binomial thinning operator ⊙of Steutel and van Harn (1979). The operation ⊙is...

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References and Further Reading

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Author information

Authors and Affiliations

  1. Kuwait University, Safat, Kuwait

    Emad-Eldin A. A. Aly (Professor)

Authors
  1. Emad-Eldin A. A. Aly
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Editors and Affiliations

  1. Department of Statistics and Informatics, Faculty of Economics, University of Kragujevac, City of Kragujevac, Serbia

    Miodrag Lovric

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Aly, EE.A.A. (2011). Models for Z+-Valued Time Series Based on Thinning. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_371

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