A mixed INAR(p) model with serially dependent innovation with application to some COVID-19 data

References

• Al-Osh, M. A., and A. Aly. 1992. First order autoregressive time series with negative binomial and geometric marginals. Communications in Statistics- Theory and Methods 21 (9):2483–92. doi:10.1080/03610929208830925.
   Web of Science ®Google Scholar
• Al-Osh, M. A., and A. A. Alzaid. 1987. First-order integer-valued autoregressive (INAR(1)) process. Journal of Time Series Analysis 8 (3):261–75. doi:10.1111/j.1467-9892.1987.tb00438.x.
   Google Scholar
• Aly, A., and N. Bouzar. 1994. Explicit stationary distributions for some galton-watson processes with immigration. Communications in Statistics. Stochastic Models 10 (2):499–517. doi:10.1080/15326349408807305.
   Google Scholar
• Alzaid, A., and M. Al-Osh. 1988. First-order integer-valued autoregressive (INAR (1)) process: Distributional and regression properties. Statistica Neerlandica 42 (1):53–61. doi:10.1111/j.1467-9574.1988.tb01521.x.
   Google Scholar
• Alzaid, A. A., and M. Al-Osh. 1990. An integer-valued p th-order autoregressive structure (INAR(p)) process. Journal of Applied Probability 27 (2):314–24. doi:10.2307/3214650.
   Web of Science ®Google Scholar
• Billingsley, P. 1961. Statisrical inference for Markov processes,6-7. Chicago: University of Chicago Press.
   Google Scholar
• Brockwell, P. J., and R. A. Davis. 1987. Time series: Theory and methods. New York: Springer Science & Business Media.
   Google Scholar
• Bu, R., B. McCabe, and K. Hadri. 2008. Maximum likelihood estimation of higher-order integer-valued autoregressive processes. Journal of Time Series Analysis 29 (6):973–94. doi:10.1111/j.1467-9892.2008.00590.x.
   Web of Science ®Google Scholar
• Buckley, F., and P. Pollett. 2010. Limit theorems for discrete-time metapopulation models. Probability Surveys 7:53–83.
   Google Scholar
• Chen, H., Qi. Li, and F. Zhu. 2021. Binomial AR(1) processes with innovational outliers. Communications in Statistics - Theory and Methods 50 (2):446–72. doi:10.1080/03610926.2019.1635704.
   Web of Science ®Google Scholar
• Davis, R. A., K. Fokianos, S. H. Holan, H. Joe, J. Livsey, R. Lund, V. Pipiras, and N. Ravishanker. 2021. Count time series: A methodological review. Journal of the American Statistical Association 116 (535):1533–47. doi:10.1080/01621459.2021.1904957.
   Web of Science ®Google Scholar
• Du, J. G., and Y. Li. 1991. The integer-valued autoregressive (INARp)) model. Journal of Time Series Analysis 12 (2):129–42.
   Google Scholar
• Hall, P., and C. C. Heyde. 1980. Martingale limit theory and its application, Vol. 64. New York: Academic Press.
   Google Scholar
• Huang, J., and F. Zhu. 2022. An alternative test for zero modification in the INAR(1) model with Poisson innovations. Communications in Statistics-Simulation and Computation 52 (3):803–16. doi:10.1080/03610918.2020.1869987.
   Web of Science ®Google Scholar
• Jung, R. C., M. Kukuk, and R. Liesenfeld. 2006. Time series of count data: modeling, estimation and diagnostics. Computational Statistics & Data Analysis 51 (4):2350–64. doi:10.1016/j.csda.2006.08.001.
   Web of Science ®Google Scholar
• Klimko, L. A., and P. I. Nelson. 1978. On conditional least squares estimation for stochastic processes. The Annals of Statistics 6 (3):629–42.
   Web of Science ®Google Scholar
• Latour, A. 1997. The multivariate Ginar(p) process. Advances in Applied Probability 29 (1):228–48. doi:10.2307/1427868.
   Web of Science ®Google Scholar
• Li, C., D. Wang, and H. Zhang. 2015. First-order mixed integer-valued autoregressive processes with zero-inflated generalized power series innovations. Journal of the Korean Statistical Society 44 (2):232–46. doi:10.1016/j.jkss.2014.08.004.
   Web of Science ®Google Scholar
• Li, Q., H. Lian, and F. Zhu. 2016. Robust closed-form estimators for the integer-valued GARCH (1,1) model. Computational Statistics & Data Analysis 101:209–25. doi:10.1016/j.csda.2016.03.006.
   Web of Science ®Google Scholar
• Liu, X., H. Jiang, and D. Wang. 2023. Estimation of parameters in the MDDRCINAR(p) model. Journal of Statistical Computation and Simulation 93 (6):983–1010. doi:10.1080/00949655.2021.1970163.
   Web of Science ®Google Scholar
• Liu, X., and D. Wang. 2019. Estimation of parameters in the DDRCINAR(p) model. Brazilian Journal of Probability and Statistics 33 (3):638–73.
   Web of Science ®Google Scholar
• Liu, X., D. Wang, D. Deng, J. Cheng, and F. Lu. 2021. Maximum likelihood estimation of the DDRCINAR(p) model. Communications in Statistics - Theory and Methods 50 (24):6231–55. doi:10.1080/03610926.2020.1741627.
   Web of Science ®Google Scholar
• Liu, Z., Q. Li, and F. Zhu. 2020. Random environment binomial thinning integer-valued autoregressive process with Poisson or geometric marginal. Brazilian Journal of Probability and Statistics 34:251–72.
   Web of Science ®Google Scholar
• Liu, Z., Qi. Li, F. Zhu. 2021. Semiparametric integer-valued autoregressive models on Z. Canadian Journal of Statistics 49 (4):1317–37. doi:10.1002/cjs.11621.
   Web of Science ®Google Scholar
• McKenzie, Ed. 1985. Some simple models for discrete variate time series 1. JAWRA Journal of the American Water Resources Association 21 (4):645–50. doi:10.1111/j.1752-1688.1985.tb05379.x.
   Google Scholar
• Qi, X., Qi. Li, and F. Zhu. 2019. Modeling time series of count with excess zeros and ones based on INAR(1) model with zero-and-one inflated Poisson innovations. Journal of Computational and Applied Mathematics 346:572–90. doi:10.1016/j.cam.2018.07.043.
   Web of Science ®Google Scholar
• Ristić, M. M., H. S. Bakouch, and A. S. Nastić. 2009. A new geometric first-order integer-valued autoregressive (NGINAR(1)) process. Journal of Statistical Planning and Inference 139 (7):2218–26. doi:10.1016/j.jspi.2008.10.007.
   Web of Science ®Google Scholar
• Ristić, M. M., and A. S. Nastić. 2012. A mixed INAR(p) model. Journal of Time Series Analysis 33 (6):903–15. doi:10.1111/j.1467-9892.2012.00806.x.
   Web of Science ®Google Scholar
• Ristić, M. M., A. S. Nastić, and H. S. Bakouch. 2012. Estimation in an integer-valued autoregressive process with negative binomial marginals (NBINAR(1)). Communications in Statistics- Theory and Methods 41 (4):606–18. doi:10.1080/03610926.2010.529528.
   Web of Science ®Google Scholar
• Ristić, M. M., A. S. Nastić, and A. V. Miletić Ilić. 2013. A geometric time series model with dependent Bernoulli counting series. Journal of Time Series Analysis 34 (4):466–76. doi:10.1111/jtsa.12023.
   Web of Science ®Google Scholar
• Shirozhan, M., M. Mohammadpour, and H. S. Bakouch. 2019. A new geometric INAR(1) model with mixing pegram and generalized binomial thinning operators. Iranian Journal of Science and Technology, Transactions A: Science 43 (3):1011–20. doi:10.1007/s40995-017-0345-3.
   Google Scholar
• Steutel, F. W., and K. Van Harn. 1979. Discrete analogues of self-decomposability and stability. Annals of Probability 7 (5):893–9.
   Web of Science ®Google Scholar
• Weiß, C. H. 2008. The combined INAR(p) models for time series of counts. Statistics and Probability Letters 78 (13):1817–22.
   Web of Science ®Google Scholar
• Weiß, C. H. 2015. A poisson INAR(1) model with serially dependent innovations. Metrika 78 (7):829–51.
   Web of Science ®Google Scholar
• Zhang, J., F. Zhu, and N. Mamode Khan, 2022. A new INAR model based on Poisson BE2 innovations. Communications in Statistics-Theory and Method 52 (17):6063–77. doi:10.1080/03610926.2021.2024571.
   Google Scholar
• Zheng, H, and I. V. Basawa. 2008. First-order observation-driven integer-valued autoregressive processes. Statistics & Probability Letters 78 (1):1–9. doi:10.1016/j.spl.2007.04.017.
   Web of Science ®Google Scholar