Bivariate first-order random coefficient integer-valued autoregressive processes based on modified negative binomial operator

References

• Aleksić, M. S., and M. M. Ristić. 2021. A geometric minification integer-valued autoregressive model. Applied Mathematical Modelling 90:265–80. doi: 10.1016/j.apm.2020.08.047.
   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
• Billingsley, P. 1961. Statistical inference for markov processes. Chicago: The University of Chicago Press.
   Google Scholar
• Chen, H., F. Zhu, and X. Liu. 2022. A new bivariate INAR(1) model with time-dependent innovation vectors. Stats 5 (3):819–40. doi: 10.3390/stats5030048.
   Web of Science ®Google Scholar
• Czado, C., T. Gneiting, and L. Held. 2009. Predictive model assessment for count data. Biometrics 65 (4):1254–61. doi: 10.1111/j.1541-0420.2009.01191.x.
   PubMed Web of Science ®Google Scholar
• Ding, X., and D. Wang. 2016. Empirical likelihood inference for INAR(1) model with explanatory variables. Journal of the Korean Statistical Society 45 (4):623–32. doi: 10.1016/j.jkss.2016.05.004.
   Web of Science ®Google Scholar
• Freeland, R. K., and B. P. M. McCabe. 2004. Forecasting discrete-valued low count time series. International Journal of Forecasting 20 (3):427–34. doi: 10.1016/S0169-2070(03)00014-1.
   Web of Science ®Google Scholar
• Gorgi, P. 2020. Beta-negative binomial auto-regressions for modelling integer-valued time series with extreme observations. Journal of the Royal Statistical Society Series B: Statistical Methodology 82 (5):1325–47. doi: 10.1111/rssb.12394.
   Web of Science ®Google Scholar
• Hall, P., and C. C. Heyde. 1980. Martingale limit theory and its application. New York: Academic Press.
   Google Scholar
• Hwang, S. Y., and I. V. Basawa. 1998. Parameter estimation for generalized random coefficient autoregressive processes. Journal of Statistical Planning and Inference 68 (2):323–37. doi: 10.1016/S0378-3758(97)00147-X.
   Web of Science ®Google Scholar
• Jung, R., B. McCabe, and A. Tremaayne. 2016. Model validation and diagnostics. In Handbook of discrete-valued time series, eds. R. A. Davis, H. Holan, R. Lund, and N. Ravishanker, 189–218. Boca Raton, FL: Chapman & Hall.
   Google Scholar
• Karlis, D., and X. Pedeli. 2013. Flexible bivariate INAR(1) processes using copulas. Communications in Statistics - Theory and Methods 42 (4):723–40. doi: 10.1080/03610926.2012.754466.
   Web of Science ®Google Scholar
• Karlsen, H., and D. Tjøstheim. 1988. Consistent estimates for the NEAR(2) and NLAR(2) time series models. Journal of the Royal Statistical Society Series B: Statistical Methodology 50 (2):313–20. doi: 10.1111/j.2517-6161.1988.tb01730.x.
   Google Scholar
• Klenke, A. 2013. Probability theory: A comprehensive course. Berlin: Springer Science & Business Media.
   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. doi: 10.1214/aos/1176344207.
   Web of Science ®Google Scholar
• Li, H., K. Yang, S. Zhao, and D. Wang. 2018. First-order random coefficients integer-valued threshold autoregressive processes. AStA Advances in Statistical Analysis 102 (3):305–31. doi: 10.1007/s10182-017-0306-3.
   Web of Science ®Google Scholar
• Li, H., Z. Liu, K. Yang, X. Dong, and W. Wang. 2023. A pth-order random coefficients mixed binomial autoregressive process with explanatory variables. Computational Statistics, forthcoming :1–24. doi: 10.1007/s00180-023-01396-8.
   Web of Science ®Google Scholar
• Liu, Y., D. Wang, H. Zhang, and N. Shi. 2016. Bivariate zero truncated Poisson INAR(1) process. Journal of the Korean Statistical Society 45 (2):260–75. doi: 10.1016/j.jkss.2015.11.002.
   Web of Science ®Google Scholar
• Monteiro, M., I. Pereira, and M. G. Scotto. 2021. Bivariate models for time series of counts: A comparison study between PBINAR models and dynamic factor models. Communications in Statistics - Simulation and Computation 50 (7):1873–87. doi: 10.1080/03610918.2019.1599015.
   Web of Science ®Google Scholar
• Pedeli, X., and D. Karlis. 2011. A bivariate INAR(1) process with application. Statistical Modelling 11 (4):325–49. doi: 10.1177/1471082X100110040.
   Web of Science ®Google Scholar
• Pedeli, X., and D. Karlis. 2013a. On estimation of the bivariate poisson INAR process. Communications in Statistics - Simulation and Computation 42 (3):514–33. doi: 10.1080/03610918.2011.639001.
   Web of Science ®Google Scholar
• Pedeli, X., and D. Karlis. 2013b. Some properties of multivariate INAR(1) processes. Computational Statistics & Data Analysis 67:213–25. doi: 10.1016/j.csda.2013.05.019.
   Web of Science ®Google Scholar
• Popović, P. M. 2015. Random coefficient bivariate INAR(1) process. Facta Universitatis, Series: Mathematics and Informatics 30:263–80.
   Web of Science ®Google Scholar
• Popović, P. M., M. M. Ristić, and A. S. Nastić. 2016. A geometric bivariate time series with different marginal parameters. Statistical Papers 57 (3):731–53. doi: 10.1007/s00362-015-0677-z.
   Web of Science ®Google Scholar
• Qian, L., and F. Zhu. 2022. A new minification integer-valued autoregressive process driven by explanatory variables. Australian & New Zealand Journal of Statistics 64 (4):478–94. doi: 10.1111/anzs.12379.
   Web of Science ®Google Scholar
• Qian, L., Q. Li, and F. Zhu. 2020. Modelling heavy-tailedness in count time series. Applied Mathematical Modelling 82:766–84. doi: 10.1016/j.apm.2020.02.001.
   Web of Science ®Google Scholar
• Ristić, M. M., A. S. Nastić, K. Jayakumar, and H. S. Bakouch. 2012. A bivariate INAR(1) time series model with geometric marginals. Applied Mathematics Letters 25 (3):481–5. doi: 10.1016/j.aml.2011.09.040.
   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
• Scotto, M. G., C. H. Weiß, M. E. Silva, and I. Pereira. 2014. Bivariate binomial autoregressive models. Journal of Multivariate Analysis 125:233–51. doi: 10.1016/j.jmva.2013.12.014.
   Web of Science ®Google Scholar
• Su, B., and F. Zhu. 2021. Comparison of BINAR(1) models with bivariate negative binomial innovations and explanatory variables. Journal of Statistical Computation and Simulation 91 (8):1616–34. doi: 10.1080/00949655.2020.1863965.
   Web of Science ®Google Scholar
• Tzougas, G., and A. P. di Cerchiara. 2021. The multivariate mixed negative binomial regression model with an application to insurance a posteriori ratemaking. Insurance: Mathematics and Economics 101:602–25. doi: 10.1016/j.insmatheco.2021.10.001.
   Web of Science ®Google Scholar
• Wang, Z. K. 1982. Stochastic process. Beijing: Scientific Press.
   Google Scholar
• Weiß, C. H. 2018. An introduction to discrete-valued time series. Hoboken, NJ, USA: John Wiley & Sons.
   Google Scholar
• Yang, K., H. Li, D. Wang, and C. Zhang. 2021. Random coefficients integer-valued threshold autoregressive processes driven by logistic regression. AStA Advances in Statistical Analysis 105 (4):533–57. doi: 10.1007/s10182-020-00379-0.
   Web of Science ®Google Scholar
• Yang, K., N. Xu, H. Li, Y. Zhao, and X. Dong. 2023a. Multivariate threshold integer-valued autoregressive processes with explanatory variables. Applied Mathematical Modelling 124:142–66. doi: 10.1016/j.apm.2023.07.030.
   Web of Science ®Google Scholar
• Yang, K., X. Yu, Q. Zhang, and X. Dong. 2022. On MCMC sampling in self-exciting integer-valued threshold time series models. Computational Statistics & Data Analysis.169:107410. doi: 10.1016/j.csda.2021.107410.
   Web of Science ®Google Scholar
• Yang, K., Y. Zhao, H. Li, and D. Wang. 2023b. On bivariate threshold Poisson integer-valued autoregressive processes. Metrika 86 (8):931–63. doi: 10.1007/s00184-023-00899-0.
   Web of Science ®Google Scholar
• Yu, M., D. Wang, K. Yang, and Y. Liu. 2020. Bivariate first-order random coefficient integer-valued autoregressive processes. Journal of Statistical Planning and Inference 204:153–76. doi: 10.1016/j.jspi.2019.05.004.
   Web of Science ®Google Scholar
• Zhang, Q., D. Wang, and X. Fan. 2020. A negative binomial thinning-based bivariate INAR(1) process. Statistica Neerlandica 74 (4):517–37. doi: 10.1111/stan.12210.
   Web of Science ®Google Scholar
• Zheng, H., I. V. Basawa, and S. Datta. 2007. First-order random coefficient integer-valued autoregressive processes. Journal of Statistical Planning and Inference 137 (1):212–29. doi: 10.1016/j.jspi.2005.12.003.
   Web of Science ®Google Scholar