IDEAS home Printed from https://ideas.repec.org/a/gam/jstats/v6y2023i1p18-311d1063472.html
   My bibliography  Save this article

A New Soft-Clipping Discrete Beta GARCH Model and Its Application on Measles Infection

Author

Listed:
  • Huaping Chen

    (School of Mathematics and Statistics, Henan University, Kaifeng 475004, China)

Abstract

In this paper, we develop a novel soft-clipping discrete beta GARCH (ScDBGARCH) model that provides an available method to model bounded time series with under-dispersion, equi-dispersion or over-dispersion. The new model not only allows positive dependence, but also negative dependence. The stochastic properties of the models are established, and these results are, in turn, used in the analysis of the asymptotic properties of the conditional maximum likelihood (CML) estimator of the new model. In addition, we apply the new model to measles infection to show its improved performance.

Suggested Citation

  • Huaping Chen, 2023. "A New Soft-Clipping Discrete Beta GARCH Model and Its Application on Measles Infection," Stats, MDPI, vol. 6(1), pages 1-19, February.
    • Handle: RePEc:gam:jstats:v:6:y:2023:i:1:p:18-311:d:1063472
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2571-905X/6/1/18/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2571-905X/6/1/18/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Galit Shmueli & Thomas P. Minka & Joseph B. Kadane & Sharad Borle & Peter Boatwright, 2005. "A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 127-142, January.
    2. Aknouche, Abdelhakim & Bentarzi, Wissam & Demouche, Nacer, 2018. "On periodic ergodicity of a general periodic mixed Poisson autoregression," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 15-21.
    3. Tobias A. Möller & Christian H. Weiß & Hee-Young Kim & Andrei Sirchenko, 2018. "Modeling Zero Inflation in Count Data Time Series with Bounded Support," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 589-609, June.
    4. Tianqing Liu & Xiaohui Yuan, 2013. "Random rounded integer-valued autoregressive conditional heteroskedastic process," Statistical Papers, Springer, vol. 54(3), pages 645-683, August.
    5. Yao Kang & Dehui Wang & Kai Yang, 2020. "Extended binomial AR(1) processes with generalized binomial thinning operator," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(14), pages 3498-3520, July.
    6. Agosto, Arianna & Cavaliere, Giuseppe & Kristensen, Dennis & Rahbek, Anders, 2016. "Modeling corporate defaults: Poisson autoregressions with exogenous covariates (PARX)," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 640-663.
    7. Esmeralda Gonçalves & Nazaré Mendes-Lopes, 2020. "Signed compound poisson integer-valued GARCH processes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(22), pages 5468-5492, November.
    8. Huaping Chen & Qi Li & Fukang Zhu, 2021. "Binomial AR(1) processes with innovational outliers," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(2), pages 446-472, January.
    9. Huaping Chen & Qi Li & Fukang Zhu, 2022. "A new class of integer-valued GARCH models for time series of bounded counts with extra-binomial variation," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(2), pages 243-270, June.
    10. Christian H. Weiß & Philip K. Pollett, 2014. "Binomial Autoregressive Processes With Density-Dependent Thinning," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(2), pages 115-132, March.
    11. Giulia Carallo & Roberto Casarin & Christian P. Robert, 2020. "Generalized Poisson Difference Autoregressive Processes," Papers 2002.04470, arXiv.org.
    12. Yan Cui & Qi Li & Fukang Zhu, 2020. "Flexible bivariate Poisson integer-valued GARCH model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(6), pages 1449-1477, December.
    13. Jan Bulla & Christophe Chesneau & Maher Kachour, 2017. "A bivariate first-order signed integer-valued autoregressive process," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(13), pages 6590-6604, July.
    14. Mengya Liu & Fukang Zhu & Ke Zhu, 2022. "Modeling normalcy‐dominant ordinal time series: An application to air quality level," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 460-478, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Huaping Chen & Qi Li & Fukang Zhu, 2023. "A covariate-driven beta-binomial integer-valued GARCH model for bounded counts with an application," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(7), pages 805-826, October.
    2. Huaping Chen & Qi Li & Fukang Zhu, 2022. "A new class of integer-valued GARCH models for time series of bounded counts with extra-binomial variation," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(2), pages 243-270, June.
    3. Yao Kang & Shuhui Wang & Dehui Wang & Fukang Zhu, 2023. "Analysis of zero-and-one inflated bounded count time series with applications to climate and crime data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 34-73, March.
    4. Yao Kang & Dehui Wang & Kai Yang, 2021. "A new INAR(1) process with bounded support for counts showing equidispersion, underdispersion and overdispersion," Statistical Papers, Springer, vol. 62(2), pages 745-767, April.
    5. William Kengne, 2023. "On consistency for time series model selection," Statistical Inference for Stochastic Processes, Springer, vol. 26(2), pages 437-458, July.
    6. Qi Li & Fukang Zhu, 2020. "Mean targeting estimator for the integer-valued GARCH(1, 1) model," Statistical Papers, Springer, vol. 61(2), pages 659-679, April.
    7. Huaping Chen & Fukang Zhu & Xiufang Liu, 2022. "A New Bivariate INAR(1) Model with Time-Dependent Innovation Vectors," Stats, MDPI, vol. 5(3), pages 1-22, August.
    8. Gauss Cordeiro & Josemar Rodrigues & Mário Castro, 2012. "The exponential COM-Poisson distribution," Statistical Papers, Springer, vol. 53(3), pages 653-664, August.
    9. Mevin B. Hooten & Michael R. Schwob & Devin S. Johnson & Jacob S. Ivan, 2023. "Multistage hierarchical capture–recapture models," Environmetrics, John Wiley & Sons, Ltd., vol. 34(6), September.
    10. Can Zhou & Yan Jiao & Joan Browder, 2019. "How much do we know about seabird bycatch in pelagic longline fisheries? A simulation study on the potential bias caused by the usually unobserved portion of seabird bycatch," PLOS ONE, Public Library of Science, vol. 14(8), pages 1-19, August.
    11. Christian Weiß, 2015. "A Poisson INAR(1) model with serially dependent innovations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(7), pages 829-851, October.
    12. Paolo Gorgi & Siem Jan Koopman, 2020. "Beta observation-driven models with exogenous regressors: a joint analysis of realized correlation and leverage effects," Tinbergen Institute Discussion Papers 20-004/III, Tinbergen Institute.
    13. Darcy Steeg Morris & Kimberly F. Sellers, 2022. "A Flexible Mixed Model for Clustered Count Data," Stats, MDPI, vol. 5(1), pages 1-18, January.
    14. Joseph B. Kadane & Ramayya Krishnan & Galit Shmueli, 2006. "A Data Disclosure Policy for Count Data Based on the COM-Poisson Distribution," Management Science, INFORMS, vol. 52(10), pages 1610-1617, October.
    15. Aknouche, Abdelhakim & Demouche, Nacer, 2018. "Ergodicity conditions for a double mixed Poisson autoregression," MPRA Paper 88843, University Library of Munich, Germany.
    16. Dennis Kristensen & Young Jun Lee, 2019. "Local Polynomial Estimation of Time-Varying Parameters in Nonlinear Models," Papers 1904.05209, arXiv.org, revised Aug 2023.
    17. Puppo, L. & Pedroni, N. & Maio, F. Di & Bersano, A. & Bertani, C. & Zio, E., 2021. "A Framework based on Finite Mixture Models and Adaptive Kriging for Characterizing Non-Smooth and Multimodal Failure Regions in a Nuclear Passive Safety System," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    18. Cavaliere, Giuseppe & Lu, Ye & Rahbek, Anders & Stærk-Østergaard, Jacob, 2023. "Bootstrap inference for Hawkes and general point processes," Journal of Econometrics, Elsevier, vol. 235(1), pages 133-165.
    19. Imelda Trejo & Nicolas W Hengartner, 2022. "A modified Susceptible-Infected-Recovered model for observed under-reported incidence data," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-23, February.
    20. Fernando Bonassi & Rafael Stern & Cláudia Peixoto & Sergio Wechsler, 2015. "Exchangeability and the law of maturity," Theory and Decision, Springer, vol. 78(4), pages 603-615, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jstats:v:6:y:2023:i:1:p:18-311:d:1063472. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.