A new INAR(1) process with bounded support for counts showing equidispersion, underdispersion and overdispersion

  • Yao Kang
  • Dehui WangEmail author
  • Kai Yang
Regular Article


The present work introduces a mixture INAR(1) model based on the mixing Pegram and binomial thinning operators with a finite range \(\{0,1,\ldots ,n\}\). The new model can be used to handle equidispersion, underdispersion, overdispersion, zero-inflation and multimodality. Several probabilistic and statistical properties are explored. Estimators of the model parameters are derived by the conditional maximum likelihood method. The asymptotic properties and numerical results of the estimators are also studied. In addition, the forecasting problem is addressed. Applications to real data sets are given to show the application of the new model.


Binomial AR(1) processes Pegram operator Binomial thinning operator Parameter estimation Forecasting 



We gratefully acknowledge the anonymous reviewers for their serious work and thoughtful suggestions that have helped us improve this paper substantially. This work is supported by National Natural Science Foundation of China (No. 11731015, 11571051, 11501241, 11871028), Natural Science Foundation of Jilin Province (No. 20150520053JH, 20170101057JC, 20180101216JC), Program for Changbaishan Scholars of Jilin Province (2015010), and Science and Technology Program of Jilin Educational Department during the “13th Five-Year” Plan Period (No. 2016316).


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of MathematicsJilin UniversityChangchunChina
  2. 2.School of Mathematics and StatisticsChangchun University of TechnologyChangchunChina

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