On MCMC sampling in random coefficients self-exciting integer-valued threshold autoregressive processes

References

• Chen CWS, Lee S. Bayesian causality test for integer-valued time series models with applications to climate and crime data. J R Stat Soc: Ser C (Appl Stat). 2017;66(4):797–814. doi: 10.1111/rssc.12200
   Google Scholar
• Yang K, Li H, Wang D, et al. Random coefficients integer-valued threshold autoregressive processes driven by logistic regression. AStA Adv Stat Anal. 2021;105(4):533–557. doi: 10.1007/s10182-020-00379-0
   Web of Science ®Google Scholar
• Fokianos K, Rahbek A, Tjostheim D. Poisson autoregression. Publicat Am Stat Assoc. 2009;104(488):1430–1439. doi: 10.1198/jasa.2009.tm08270
   Web of Science ®Google Scholar
• Ferland R, Latour A, Oraichi D. Integer-valued GARCH process. J Time Ser Anal. 2006;27(6):923–942. doi: 10.1111/jtsa.2006.27.issue-6
   Web of Science ®Google Scholar
• Li Q, Zhu F. Mean targeting estimator for the integer-valued GARCH(1,1) model. Stat Papers. 2020;61(2):659–679. doi: 10.1007/s00362-017-0958-9
   Web of Science ®Google Scholar
• Al-Osh MA, Alzaid AA. First-order integer-valued autoregressive (INAR(1)) process. J Time Ser Anal. 1987;8(3):261–275. doi: 10.1111/j.1467-9892.1987.tb00438.x
   Google Scholar
• Brännäs K, Quoreshi AMMS. Integer-valued moving average modelling of the number of transactions in stocks. Appl Finan Econom. 2010;20(18):1429–1440. doi: 10.1080/09603107.2010.498343
   Google Scholar
• Davis RA, Fokianos K, Holan SH, et al. Count time series: a methodological review. J Am Stat Assoc. 2021;116(535):1533–1547. doi: 10.1080/01621459.2021.1904957
   Web of Science ®Google Scholar
• Scotto MG, Weiß CH, Gouveia S. Thinning-based models in the analysis of integer-valued time series: a review. Stat Model. 2015;15(6):590–618. doi: 10.1177/1471082X15584701
   Web of Science ®Google Scholar
• Weiß CH. Thinning operations for modeling time series of countsa survey. AStA Adv Stat Anal. 2008;92(3):319–341. doi: 10.1007/s10182-008-0072-3
   Web of Science ®Google Scholar
• Altun E, Khan NM. Modelling with the novel INAR(1)-PTE process. Methodol Comput Appl Probab. 2022;24(3):1735–1751. doi: 10.1007/s11009-021-09878-2
   Web of Science ®Google Scholar
• Li Q, Chen H, Zhu F. Robust estimation for poisson integer-valued GARCH models using a new hybrid loss. J Syst Sci Complex. 2021;34(4):1578–1596. doi: 10.1007/s11424-020-9344-0
   Web of Science ®Google Scholar
• Yang K, Li A, Li H, et al. High-order self-excited threshold integer-valued autoregressive model: estimation and testing. Commun Math Stat. 2023;1–28. doi: 10.1007/s40304-022-00325-3
   Web of Science ®Google Scholar
• Yang K, Yu X, Zhang Q, et al. On MCMC sampling in self-exciting integer-valued threshold time series models. Comput Stat Data Anal. 2022;169:107410. doi: 10.1016/j.csda.2021.107410
   Web of Science ®Google Scholar
• Zhang J, Zhu F, Khan NM. A new INAR model based on Poisson-BE2 innovations. Commun Stat - Theory Methods. 2023;52(17):6063–6077. doi: 10.1080/03610926.2021.2024571
   Web of Science ®Google Scholar
• Steutel FW, van Harn K. Discrete analogues of self-decomposability and stability. Ann Probab. 1979;7(5):893–899. doi: 10.1214/aop/1176994950
   Web of Science ®Google Scholar
• Ristić MM, Bakouch HS, Nastić AS. A new geometric first-order integer-valued autoregressive (NGINAR(1)) process. J Stat Plan Inference. 2009;139(7):2218–2226. doi: 10.1016/j.jspi.2008.10.007
   Web of Science ®Google Scholar
• Yang K, Kang Y, Wang D, et al. Modeling overdispersed or underdispersed count data with generalized poisson integer-valued autoregressive processes. Metrika. 2019;82(7):863–889. doi: 10.1007/s00184-019-00714-9
   Web of Science ®Google Scholar
• Alzaid AA, Al-Osh MA. An integer-valued pth-order autoregressive structure (INAR(p)) process. J Appl Probab. 1990;27(2):314–324. doi: 10.2307/3214650
   Web of Science ®Google Scholar
• Bu R, McCabe B. Model selection, estimation and forecasting in INAR(p) models: A likelihood-based Markov Chain approach. Int J Forecast. 2008;24(1):151–162. doi: 10.1016/j.ijforecast.2007.11.002
   Web of Science ®Google Scholar
• Du JG, Li Y. The integer-valued autoregressive (INAR(p)) model. J Time Ser Anal. 1991;12(2):129–142. doi: 10.1111/j.1467-9892.1991.tb00073.x
   Google Scholar
• Pedeli X, Davison AC, Fokianos K. Likelihood estimation for the INAR(p) model by saddlepoint approximation. J Am Stat Assoc. 2015;110(511):1229–1238. doi: 10.1080/01621459.2014.983230
   Web of Science ®Google Scholar
• Tian S, Wang D, Cui S. A seasonal geometric INAR(1) process based on negative binomial thinning operator. Stat Papers. 2020;61(6):2561–2581. doi: 10.1007/s00362-018-1060-7
   Web of Science ®Google Scholar
• Li H, Yang K, Wang D. Quasi-likelihood inference for self-exciting threshold integer-valued autoregressive processes. Comput Stat. 2017;32(4):1597–1620. doi: 10.1007/s00180-017-0748-9
   Web of Science ®Google Scholar
• Monteiro M, Scotto MG, Pereira I. Integer-valued self-exciting threshold autoregressive processes. Commun Stat Theory Methods. 2012;41(15):2717–2737. doi: 10.1080/03610926.2011.556292
   Web of Science ®Google Scholar
• Wang C, Liu H, Yao J, et al. Self-excited threshold poisson autoregression. J Am Stat Assoc. 2014;109(506):777–787. doi: 10.1080/01621459.2013.872994
   Web of Science ®Google Scholar
• Yang K, Wang D, Jia B, et al. An integer-valued threshold autoregressive process based on negative binomial thinning. Stat Papers. 2018;59(3):1131–1160. doi: 10.1007/s00362-016-0808-1
   Web of Science ®Google Scholar
• Manaa A, Bentarzi M. On a periodic SETINAR model. Commun Stat Simul Comput. 2023;52(3):596–620. doi: 10.1080/03610918.2021.1874416
   Web of Science ®Google Scholar
• Brännäs K. Explanatory variables in the AR(1) count data model. Umea Econom Studies. 1995;381.
   Google Scholar
• Ding X, Wang D. Empirical likelihood inference for INAR(1) model with explanatory variables. J Korean Stat Soc. 2016;45(4):623–632. doi: 10.1016/j.jkss.2016.05.004
   Web of Science ®Google Scholar
• Freeland RK, McCabe BPM. Analysis of low count time series data by poisson autoregression. J Time Ser Anal. 2004;25(5):701–722. doi: 10.1111/jtsa.2004.25.issue-5
   Web of Science ®Google Scholar
• Gomes D, Canto e Castro L. Generalized integer-valued random coefficient for a first order structure autoregressive (RCINAR) process. J Stat Plan Inference. 2009;139(12):4088–4097. doi: 10.1016/j.jspi.2009.05.037
   Web of Science ®Google Scholar
• Qian L, Zhu F. A new minification integer-valued autoregressive process driven by explanatory variables. Aust New Zealand J Stat. 2022;64(4):478–494. doi: 10.1111/anzs.v64.4
   Web of Science ®Google Scholar
• Li H, Yang K, Zhao S, et al. First-order random coefficients integer-valued threshold autoregressive processes. AStA Adv Stat Anal. 2018;102(3):305–331. doi: 10.1007/s10182-017-0306-3
   Web of Science ®Google Scholar
• Chen CWS, Lee S, Khamthong K. Bayesian inference of nonlinear hysteretic integer-valued GARCH models for disease counts. Comput Stat. 2021;36(1):261–281. doi: 10.1007/s00180-020-01018-7
   Web of Science ®Google Scholar
• Bolstad WM. Introduction to Bayesian statistics. Hoboken (NJ): Wiley; 2007.
   Google Scholar
• Neal P, Subba Rao T. MCMC for integer-valued ARMA processes. J Time Ser Anal. 2007;28(1):92–110. doi: 10.1111/jtsa.2007.28.issue-1
   Web of Science ®Google Scholar
• Enciso-Mora V, Neal P, Rao TS. Integer valued AR processes with explanatory variables. Sankhyā: Ind J Stat, Ser B. 2009;71:248–263.
   Google Scholar
• Bisaglia L, Canale A. Bayesian nonparametric forecasting for INAR models. Comput Stat Data Anal. 2016;100:70–78. doi: 10.1016/j.csda.2014.12.011
   Web of Science ®Google Scholar
• Zhang R, Wang D. Bayesian empirical likelihood inference for the generalized binomial AR(1) models. J Korean Stat Soc. 2022;51(4):977–1004. doi: 10.1007/s42952-022-00171-7
   Web of Science ®Google Scholar
• Li H, Wang H, Yang K, et al. A nonparametric Bayesian analysis for meningococcal disease counts based on integer-valued threshold time series models. Commun Stat – Theory Methods. 2022;1–18. doi: 10.1080/03610926.2022.2059683
   Web of Science ®Google Scholar
• Lu F, Wang D. First-order integer-valued autoregressive process with Markov-switching coefficients. Commun Stat Theory Methods. 2022;51(13):4313–4329. doi: 10.1080/03610926.2020.1813302
   Web of Science ®Google Scholar
• Möller TA, Silva ME, Weiß CH, et al. Self-exciting threshold binomial autoregressive processes. AStA Adv Stat Anal. 2016;100(4):369–400. doi: 10.1007/s10182-015-0264-6
   Web of Science ®Google Scholar
• Li D, Tong H. Nested sub-sample search algorithm for estimation of threshold models. Stat Sin. 2016;26(4):1543–1554. doi:10.5705/ss.2013.394t
   Web of Science ®Google Scholar
• Huang J, Zhu F, Deng D. A mixed generalized poisson INAR model with applications. J Stat Comput Simul. 2023;93(11):1851–1878. doi: 10.1080/00949655.2022.2155161
   Web of Science ®Google Scholar
• Spiegelhalter DJ, Best NG, Carlin BP, et al. Bayesian measures of model complexity and fit. J R Stat Soc, Ser B. 2002;64(4):583–639. doi: 10.1111/1467-9868.00353
   Google Scholar
• Jung RC, Kukuk M, Liesenfeld R. Time series of count data: modeling, estimation and diagnostics. Comput Stat Data Anal. 2006;51(4):2350–2364. doi: 10.1016/j.csda.2006.08.001
   Web of Science ®Google Scholar