References
- Steutel FW, van Harn K. Discrete analogues of self-decomposability and stability. Ann Probab. 1979;7:893–899. doi: 10.1214/aop/1176994950
- Aghababaei Jazia M, Jones G, Lai CD. First-order integer valued AR processes with zero inflated Poisson innovations. J Time Ser Anal. 2012;33:954–963. doi: 10.1111/j.1467-9892.2012.00809.x
- Al-Osh MA, Alzaid AA. First-order integer-valued autoregressive (INAR(1)) process. J Time Ser Anal. 1987;8:261–275. doi: 10.1111/j.1467-9892.1987.tb00438.x
- Aly EEAA, Bouzar N. On some integer-valued autoregressive moving average models. J Multivariate Anal. 1994b;50:132–151. doi: 10.1006/jmva.1994.1038
- Alzaid AA, Al-Osh MA. Some autoregressive moving average processes with generalized Poisson marginal distributions. Ann Inst Statist Math. 1993;45:223–232. doi: 10.1007/BF00775809
- Bakouch HS, Ristić MM. Zero truncated Poisson integer-valued AR(1) model. Metrika. 2010;72:265–280. doi: 10.1007/s00184-009-0252-5
- Kim H, Lee S. On first-order integer-valued autoregressive process with Katz family innovations. J Statist Comput Simul. 2017;87:546–562. doi: 10.1080/00949655.2016.1219356
- McKenzie E. Autoregressive moving-average processes with negative binomial and geometric distributions. Adv Appl Probab. 1986;18:679–705. doi: 10.2307/1427183
- Mohammadpour M, Bakouch HS, Shirozhan M. Poisson–Lindley INAR(1) model with applications. J Statist. 2018;32:262–280.
- Ristic MM, Bakouch HS, Nastić AS. A new geometric first-order integer-valued autoregressive (NGINAR(1)) process. J Statist Plann Inference. 2009;139:2218–2226. doi: 10.1016/j.jspi.2008.10.007
- Schweer S, Weiß CH. Compound Poisson INAR(1) processes: stochastic properties and testing for overdispersion. Comput Statist Data Anal. 2014;77:267–284. doi: 10.1016/j.csda.2014.03.005
- Shirozhan M, Mohammadpour M, Bakouch HS. A new geometric INAR(1) model with mixing Pegram and generalized binomial thinning operators. Iranian J Sci Technol Trans Sci. 2019;43:1011–1020. doi: 10.1007/s40995-017-0345-3
- Weiß CH. Integer-Valued autoregressive models for counts showing under dispersion. J Appl Statist. 2013;40:1931–1948. doi: 10.1080/02664763.2013.800034
- Kim HY, Park Y. A non-stationary integer-valued autoregressive model. Statist Papers. 2008;49:485–502. doi: 10.1007/s00362-006-0028-1
- Zhang H, Wang D, Zhu D. Inference for INAR(p) processes with signed generalized power series thinning operator. J Statist Plann Inference. 2010;140:667–683. doi: 10.1016/j.jspi.2009.08.012
- Doukhan P, Latour A, Oraichi D. Simple integer-valued bilinear time series model. Appl Probab. 2006;38:559–578. doi: 10.1239/aap/1151337085
- Drost FC, Akker VDR, Werker BJM. Note on integer-valued bilinear time series. Stat Prob Lett. 2008;38:559–578.
- Bentarzi M, Bentarzi W. Periodic integer-valued bilinear time series model. Comm Statist Theor Meth. 2017;46:1184–1201. doi: 10.1080/03610926.2015.1014107
- Mohammadpour M, Bakouch HS, Ramzani S. An integer-valued bilinear time series model via two random operators. Math Comp Model Dyn. 2019;25(4):429–446. doi: 10.1080/13873954.2019.1652655
- Subba Rao T. On the theory of bilinear time series model. J R Statist Soc B. 1981;43:244–255.
- Keenan DM. A Tukey non-additivity type test for time series nonlinearity. Biometrika. 1985;72:39–44. doi: 10.1093/biomet/72.1.39
- Ferland R, Latour A, Qraichi D. Integer-valued GARCH process. J Time Ser Anal. 2006;27:923–942. doi: 10.1111/j.1467-9892.2006.00496.x
- Zhu F. A negative binomial integer-valued GARCH model. J Time Ser Anal. 2011;32:54–67. doi: 10.1111/j.1467-9892.2010.00684.x
- Pascual L, Romo J, Ruiz E. Bootstrap predictive inference for ARIMA processes. J Time Ser Anal. 2004;25:449–465. doi: 10.1111/j.1467-9892.2004.01713.x