280
Views
8
CrossRef citations to date
0
Altmetric
Articles

Generalized Poisson integer-valued autoregressive processes with structural changes

, ORCID Icon, ORCID Icon, &

References

  • M.A. Al-Osh and A.A. Alzaid, First-order integer-valued autoregressive (INAR(1)) process, J. Time Ser. Anal. 8 (1987), pp. 261–275.
  • M. Bourguignon, J. Rodrigues, and M. Santos-Neto, Extended Poisson INAR(1) processes with equidispersion, underdispersion and overdispersion, J. Appl. Stat. 46 (2018), pp. 101–118.
  • C.W.S. Chen and S. Lee, Generalized Poisson autoregressive models for time series of counts, Comput. Statist. Data. Anal. 99 (2016), pp. 51–67.
  • P.C. Consul, Generalized Poisson Distributions: Applications and Properties, Marcel Dekker, Inc., New York, 1989.
  • P.C. Consul and F. Famoye, Generalized Poisson regression model, Comm. Statist. Theory Methods 21 (1992), pp. 89–109.
  • P.C. Consul and F. Famoye, Lagrangian Probability Distributions, Birkhäuser, Boston, 2006.
  • P.C. Consul and G.C. Jain, A generalization of the Poisson distribution, Technometrics 15 (1973), pp. 791–799.
  • Y. Cui and R. Wu, Test of parameter changes in a class of observation-driven models for count time series, Comm. Statist. Theory Methods (2019), DOI: 10.1080/03610926.2019.1565843.
  • J. Franke, C. Kirch, and J.T. Kamgaing, Changepoints in times series of counts, J. Time Ser. Anal. 33 (2012), pp. 757–770.
  • R.K. Freeland, True integer value time series, AStA Adv. Stat. Anal. 94 (2010), pp. 217–229.
  • G. Gurevich and A. Vexler, Retrospective change point detection: From parametric to distribution free policies, Comm. Statist Simulation Comput. 39 (2010), pp. 899–920.
  • H. Karlsen and D. Tjøstheim, Consistent estimates for the NEAR(2) and NLAR time series models, J. R. Stat. Soc. Ser. B 50 (1988), pp. 313–320.
  • A.S. Kashikar, N. Rohan, and T.V. Ramanathan, Integer autoregressive models with structural breaks, J. Appl. Stat. 40 (2013), pp. 2653–2669.
  • H. Li, K. Yang, and D. Wang, Quasi-likelihood inference for self-exciting threshold integer-valued autoregressive processes, Comput. Stat. 32 (2017), pp. 1597–1620.
  • H. Li, K. Yang, S. Zhao, and D. Wang, First-order random coefficients integer-valued threshold autoregressive processes, AStA Adv. Stat. Anal. 102 (2018), pp. 305–331.
  • E. McKenzie, Some simple models for discrete variate time series, JAWAR J. Amer. Water Resources Assoc. 21 (1985), pp. 645–650.
  • T.A. Möller, M.E. Silva, C.H. Weiß, M.G. Scotto, and I. Pereira, Self-exciting threshold binomial autoregressive processes, AStA Adv. Stat. Anal. 100 (2016), pp. 369–400.
  • M. Monteiro, M.G. Scotto, and I. Pereira, Integer-valued self-exciting threshold autoregressive processes, Commun. Stat. – Theor. Meth. 41 (2012), pp. 2717–2737.
  • X. Pedeli, A.C. Davison, and K. Fokianos, Likelihood estimation for the INAR(p) model by saddlepoint approximation, J. Amer. Statist. Assoc. 110 (2015), pp. 1229–1238.
  • M.M. Ristić, H.S. Bakouch, and A.S. Nastić, A new geometric first-order integer-valued autoregressive (NGINAR(1)) process, J. Stat. Plann. Inference. 139 (2009), pp. 2218–2226.
  • S. Schweer, A goodness-of-fit test for integer-valued autoregressive processes, J. Time Ser. Anal. 37 (2016), pp. 77–98.
  • M.G. Scotto, C.H. Weiß, and S. Gouveia, Thinning-based models in the analysis of integer-valued time series: a review, Stat. Modelling. 15 (2015), pp. 590–618.
  • H. Shi and D. Wang, An approximation model of the collective risk model with INAR(1) claim process, Comm. Statist. Theory Methods 43 (2014), pp. 5305–5317.
  • F. Steutel and K. van Harn, Discrete analogues of self-decomposability and stability, Ann. Probab. 7 (1979), pp. 893–899.
  • S. Tian, D. Wang, and S. Cui, A seasonal geometric INAR process based on negative binomial thinning operator, Stat. Papers 61 (2020), pp. 2561–2581.
  • Š. Hudecová, M. Hušková, and S.G. Meintanis, Tests for structural changes in time series of counts, Scand. J. Stat. 44 (2017), pp. 843–865.
  • A. Vexler, Martingale type statistics applied to change points detection, Comm. Statist. Theory Methods 37 (2008), pp. 1207–1224.
  • A. Vexler, C. Wu, A. Liu, B.W. Whitcomb, and E.F. Schisterman, An extension of a change-point problem, Statistics 43 (2009), pp. 213–225.
  • C. Wang, H. Liu, J. Yao, R.A. Davis, and W.K. Li, Self-excited threshold Poisson autoregression, J. Amer. Statist. Assoc. 109 (2014), pp. 776–787.
  • X. Wang, D. Wang, K. Yang, and D. Xu, Estimation and testing for the integer-valued threshold autoregressive models based on negative binomial thinning, Comm. Statist. Simulation Comput. (2019), DOI: 10.1080/03610918.2019.1586929.
  • C.H. Weiß, Thinning operations for modeling time series of counts – a survey, Adv. Stat. Anal. 92 (2008), pp. 319–343.
  • C.H. Weiß, The INARCH(1) model for overdispersed time series of counts, Comm. Statist. Simulation Comput. 39 (2010), pp. 1269–1291.
  • K. Yang, Y. Kang, D. Wang, H. Li, and Y. Diao, Modeling overdispersed or underdispersed count data with generalized Poisson integer-valued autoregressive processes, Metrika 82 (2019), pp. 863–889.
  • K. Yang, D. Wang, B. Jia, and H. Li, An integer-valued threshold autoregressive process based on negative binomial thinning, Statist. Papers 59 (2018b), pp. 1131–1160.
  • K. Yang, D. Wang, and H. Li, Threshold autoregression analysis for finite-range time series of counts with an application on measles data, J. Stat. Comput. Simul. 88 (2018a), pp. 597–614.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.