202
Views
2
CrossRef citations to date
0
Altmetric
Research Article

Multiple values-inflated time series of counts: modeling and inference based on INGARCH scheme

ORCID Icon &
Pages 1297-1317 | Received 09 Jun 2022, Accepted 06 Oct 2022, Published online: 19 Oct 2022

References

  • Al-Osh MA, Aly E-EA. First order autoregressive time series with negative binomial and geometric marginals. Commun Statist-Theory Methods. 1992;21(9):2483–2492.
  • Alzaid A, Al-Osh M. An integer-valued pth-order autoregressive structure (INAR(p)) process. J Appl Probab. 1990;27:314–324.
  • McKenzie E. Some simple models for discrete variate time series1. Amer Water Resour Assoc. 1985;21(4):645–650.
  • Ferland R, Latour A, Oraichi D. Integer-valued GARCH process. J Time Ser Anal. 2006;27(6):923–942.
  • Fokianos K, Rahbek A, Tjøstheim D. Poisson autoregression. J Amer Statist Assoc. 2009;104(488):1430–1439.
  • Weiß CH. An introduction to discrete-valued time series. New York: Wiley; 2018.
  • Christou V, Fokianos K. Quasi-likelihood inference for negative binomial time series models. J Time Ser Anal. 2014;35(1):55–78.
  • Davis RA, Wu R. A negative binomial model for time series of counts. Biometrika. 2009;96(3):735–749.
  • Zhu F. A negative binomial integer-valued GARCH model. J Time Ser Anal. 2011;32(1):54–67.
  • Davis RA, Liu H. Theory and inference for a class of observation-driven models with application to time series of counts. Stat Sin. 2016;26(4):1673–1707.
  • Kim B, Lee S. Robust estimation for general integer-valued time series models. Ann Inst Statist Math. 2020;72(6):1371–1396.
  • Xiong L, Zhu F. Minimum density power divergence estimator for negative binomial integer-valued GARCH models. Commun Math Statist. 2022;10:233–261.
  • Li Q, Chen H, Zhu F. Robust estimation for Poisson integer-valued GARCH models using a new hybrid loss. J Syst Sci Complexity. 2021;34:1578–1596.
  • Chen CWS, Khamthong K, Lee S. Markov switching integer valued generalized autoregressive conditional heteroscedastic models for dengue counts. J R Statist Soc C. 2019;68:963–983.
  • Jazi MA, Jones G, Lai C. First order integer valued AR processes with zero inflated poisson innovations. J Time Ser Anal. 2012;33:954–963.
  • Lee S, Lee Y, Chen CWS. Parameter change test for zero-inflated generalized Poisson autoregressive models. Statistics. 2016;50(3):1–18.
  • Rakitzis AC, Maravelakis PE, Castagliola P. CUSUM control charts for the monitoring of zero-inflated binomial processes. Qual Reliab Eng Int. 2016;32:465–483.
  • Zhu F. Zero-inflated Poisson and negative binomial integer-valued GARCH models. J Statist Plann Inferences. 2012;142(4):826–839.
  • Lee S, Kim D, Seok S. Modelling and inference for counts time series based on zero-infated exponential family INGARCH models. J Stat Comput Simul. 2021;91(11):2227–2248.
  • Alshkaki RSA. On the zero-one inflated Poisson distribution. Int J Statist Distributions Appl. 2016;2:42–48.
  • Qi X, Li Q, Zhu F. Modeling time series of count with excess zeros and ones based on INAR(1) model with zero-and-one inflated Poisson innovations. J Comput Appl Math. 2019;346:572–590.
  • Lee Y, Lee S. CUSUM tests for general nonlinear integer-valued GARCH models: comparison study. Ann Inst Stat Math. 2019;71:1033–1057.
  • Csörg M, Horváth L. Limit theorems in change-point analysis. Vol. 18. New York: John Wiley & Sons Inc; 1997.
  • Lee S, Ha J, Na O, et al. The cusum test for parameter change in time series models. Scand J Statist. 2003;30(4):781–796.
  • Fokianos K, Fried R. Interventions in INGARCH processes. J Time Ser Anal. 2010;31(3):210–225.
  • Fokianos K, Fried R. Interventions in log-linear Poisson autoregression. Stat Modell. 2012;12(4):299–322.
  • Fokianos K, Gombay E, Hussein A. Retrospective change detection for binary time series models. J Statist Plann Inferences. 2014;145:102–112.
  • Franke J, Kirch C, Kamgaing JT. Changepoints in times series of counts. J Time Ser Anal. 2012;33(5):757–770.
  • Hudecová Š. Structural changes in autoregressive models for binary time series. J Statist Plann Inferences. 2013;143(10):1744–1752.
  • Kang J, Lee S. Parameter change test for random coefficient integer-valued autoregressive processes with application to polio data analysis. J Time Ser Anal. 2009;30(2):239–258.
  • Kang J, Lee S. Parameter change test for Poisson autoregressive models. Scand J Statist. 2014;41(4):1136–1152.
  • Lee Y, Lee S, Tjøstheim D. Asymptotic normality and parameter change test for bivariate Poisson INGARCH models. TEST. 2018;27(1):52–69.
  • Lee S. Residual-based CUSUM of squares test for poisson integer-valued GARCH models. J Stat Comput Simul. 2019;89:3182–3195.
  • Lee S, Lee S. Exponential family distribution QMLE-based CUSUM test for integer-valued time series. Commun Statist–Simul Comput. 2021:
  • Weiß CH, Zhu F, Hoshiyar A. Softplus INGARCH models. Stat Sin. 2022;32:1099–1120.

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.