Applications of Mathematics

, Volume 63, Issue 1, pp 79–105 | Cite as

A Zero-Inflated Geometric INAR(1) Process with Random Coefficient

  • Hassan S. Bakouch
  • Mehrnaz Mohammadpour
  • Masumeh Shirozhan


Many real-life count data are frequently characterized by overdispersion, excess zeros and autocorrelation. Zero-inflated count time series models can provide a powerful procedure to model this type of data. In this paper, we introduce a new stationary first-order integer-valued autoregressive process with random coefficient and zero-inflated geometric marginal distribution, named ZIGINARRC(1) process, which contains some sub-models as special cases. Several properties of the process are established. Estimators of the model parameters are obtained and their performance is checked by a small Monte Carlo simulation. Also, the behavior of the inflation parameter of the model is justified. We investigate an application of the process using a real count climate data set with excessive zeros for the number of tornados deaths and illustrate the best performance of the proposed process as compared with a set of competitive INAR(1) models via some goodness-of-fit statistics. Consequently, forecasting for the data is discussed with estimation of the transition probability and expected run length at state zero. Moreover, for the considered data, a test of the random coefficient for the proposed process is investigated.


ndomized binomial thinning geometric minima estimation likelihood ratio test mixture distribution realization with random size 

MSC 2010



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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2018

Authors and Affiliations

  • Hassan S. Bakouch
    • 1
  • Mehrnaz Mohammadpour
    • 2
  • Masumeh Shirozhan
    • 2
  1. 1.Department of Mathematics, Faculty of ScienceTanta UniversityTantaEgypt
  2. 2.Department of Statistics, Faculty of Mathematical SciencesUniversity of MazandaranBabolsarIran

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