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Binomial AR(1) processes with innovational outliers

Author

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  • Huaping Chen
  • Qi Li
  • Fukang Zhu

Abstract

Binomial integer-valued AR processes have been well studied in the literature, but there is little progress in modeling bounded integer-valued time series with outliers. In this paper, we first review some basic properties of the binomial integer-valued AR(1) process and then we introduce binomial integer-valued AR(1) processes with two classes of innovational outliers. We focus on the joint conditional least squares (CLS) and the joint conditional maximum likelihood (CML) estimates of models’ parameters and the probability of occurrence of the outlier. Their large-sample properties are illustrated by simulation studies. Artificial and real data examples are used to demonstrate good performances of the proposed models.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:lstaxx:v:50:y:2021:i:2:p:446-472
    DOI: 10.1080/03610926.2019.1635704
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Sascha Henninger & Martin Schneider & Arne Leitte, 2021. "Smart Sirens—Civil Protection in Rural Areas," Sustainability, MDPI, vol. 14(1), pages 1-10, December.

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