AStA Advances in Statistical Analysis

, Volume 100, Issue 4, pp 369–400 | Cite as

Self-exciting threshold binomial autoregressive processes

  • Tobias A. Möller
  • Maria Eduarda Silva
  • Christian H. WeißEmail author
  • Manuel G. Scotto
  • Isabel Pereira
Original Paper


We introduce a new class of integer-valued self-exciting threshold models, which is based on the binomial autoregressive model of order one as introduced by McKenzie (Water Resour Bull 21:645–650, 1985. doi: 10.1111/j.1752-1688.1985.tb05379.x). Basic probabilistic and statistical properties of this class of models are discussed. Moreover, parameter estimation and forecasting are addressed. Finally, the performance of these models is illustrated through a simulation study and an empirical application to a set of measle cases in Germany.


Thinning operation Threshold models Binomial models Count processes 



The authors thank the referees for carefully reading the article and for their comments, which greatly improved the article. This work was supported by Portuguese funds through the CIDMA—Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (FCT-Fundação para a Ciência e a Tecnologia), within project UID/MAT/04106/2013.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Tobias A. Möller
    • 1
  • Maria Eduarda Silva
    • 2
  • Christian H. Weiß
    • 1
    Email author
  • Manuel G. Scotto
    • 3
  • Isabel Pereira
    • 4
  1. 1.Department of Mathematics and StatisticsHelmut Schmidt UniversityHamburgGermany
  2. 2.Center for Research and Development in Mathematics and Applications (CIDMA), Faculty of EconomicsUniversity of PortoPortoPortugal
  3. 3.CEMAT and Department of MathematicsIST University of LisbonLisbonPortugal
  4. 4.Center for Research and Development in Mathematics and Applications (CIDMA), Department of MathematicsUniversity of AveiroAveiroPortugal

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