Predrag Popović, Miroslav Ristić, Milena Stojanović

DOI Number
First page
Last page


In this manuscript we introduce a mixture integer-valued autoregressive model with a structural break. The introduced model is a mixture of an INAR(1) model with the binomial thinning operator and an INAR(1) model with the negative binomial thinning operator. Some properties of the introduced model are derived. The unknown parameters of the model are estimated by some methods and the performances of the obtained estimators are checked by simulations. At the end of the paper, two possible applications of the model are provided and discussed.


Binomial thinning, Integer-valued autoregressive model, Mixture of INAR models, Structural break, Negative binomial thinning.

Full Text:



M.A. Al-Osh and A.A. Alzaid: First-order integer-valued autoregressive (INAR(1)) process, J. Time Ser. Anal. 8(3) (1987), 261–275.

A. Aue and L. Horv´ath: Structural breaks in time series, J. Time Ser. Anal. 34(1) (2013), 1–16.

P.J. Avery and D.A. Henderson: Detecting a changed segment in DNA sequences, J. Royal Stat. Soc.: Series C (Appl. Stat.) 48(4) (1999), 489–503.

C.W.S. Chen and S. Lee: Generalized Poisson autoregressive models for time series of counts, Comput. Stat. Data Anal. 99 (2016), 51–67.

Y. Cui and R. Wu: Test of parameter changes in a class of observation-driven models for count time series, Commun. Stat. - Theory Methods (2019), 1–27.

J. Franke, C. Kirch and J.T. Kamgaing: Changepoints in times series of counts, J. Time Ser. Anal. 33(5) (2012), 757–770.

D.V. Hinkley and E.A. Hinkley: Inference about the change-point in a sequence of binomial variables, Biometrika 57(3) (1970), 477–488.

L. Horv´ath: The maximum likelihood method for testing changes in the parameters of normal observations, Ann. Stat. (1993), 671–680.

ˇS. Hudecov´a: Structural changes in autoregressive models for binary time series, J. Stat. Plan. Inference 143(10) (2013), 1744–1752.

ˇS. Hudecov´a, M. Huˇskov´a and S. Meintanis: Detection of changes in INAR models, Stochastic models, statistics and their applications (2015), 11–18.

A.S. Kashikar, N. Rohan and T.V. Ramanathan: Integer autoregressive models with structural breaks, J. Appl. Stat. 40(12) (2013), 2653–2669.

H. Kim and S. Lee: On residual CUSUM statistic for PINAR(1) model in statistical design and diagnostic of control chart, Commun. Stat. - Simul. Comput. (2019), 1–25.

E. McKenzie: Some simple models for discrete variate time series, JAWRA J. Amer. Water Res. Assoc. 21(4) (1985), 645–650.

M.M. Risti´c, H.S. Bakouch and A.S. Nasti´c: A new geometric first-order integervalued autoregressive (NGINAR(1)) process, J. Stat. Plan. Inference 139(7) (2009), 2218–2226.

K. Yu, H. Zou and D. Shi: Integer-valued moving average models with structural changes, Math. Probl. Eng. 2014 (2014).

DOI: https://doi.org/10.22190/FUMI230203007P


  • There are currently no refbacks.

© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)