Thinning operations for modeling time series of counts—a survey

Original Paper

DOI: 10.1007/s10182-008-0072-3

Cite this article as:
Weiß, C.H. Adv Stat Anal (2008) 92: 319. doi:10.1007/s10182-008-0072-3


The analysis of time series of counts is an emerging field of science. To obtain an ARMA-like autocorrelation structure, many models make use of thinning operations to adapt the ARMA recursion to the integer-valued case. Most popular among these probabilistic operations is the concept of binomial thinning, leading to the class of INARMA models. These models are proved to be useful, especially for processes of Poisson counts, but may lead to difficulties in the case of different count distributions. Therefore, several alternative thinning concepts have been developed. This article reviews such thinning operations and shows how they are successfully applied to define integer-valued ARMA models.


Thinning operations Binomial thinning Count time series INAR(1) models 

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of Statistics, Institute of MathematicsUniversity of WürzburgWürzburgGermany