Robust estimation for general integer-valued autoregressive models based on the exponential-polynomial divergence

References

• Ferland R, Latour A, Oraichi D. Integer-valued GARCH processes. J Time Ser Anal. 2006;27:923–942. doi: 10.1111/jtsa.2006.27.issue-6
   Web of Science ®Google Scholar
• Fokianos K, Rahbek A, Tjøstheim D. Poisson autoregression. J Am Stat Assoc. 2009;104:1430– 1439. doi: 10.1198/jasa.2009.tm08270
   Web of Science ®Google Scholar
• Davis RA, Wu R. A negative binomial model for time series of counts. Biometrika. 2009;96:735–749. doi: 10.1093/biomet/asp029
   Web of Science ®Google Scholar
• Zhu F. A negative binomial integer-valued GARCH model. J Time Ser Anal. 2011;32:54–67. doi: 10.1111/jtsa.2010.32.issue-1
   Web of Science ®Google Scholar
• Christou V, Fokianos K. Quasi-likelihood inference for negative binomial time series models. J Time Ser Anal. 2014;35:55–78. doi: 10.1111/jtsa.v35.1
   Web of Science ®Google Scholar
• Zhu F. Modeling overdispersed or underdispersed count data with generalized poisson integer-valued garch models. J Math Anal Appl. 2012;389:58–71. doi: 10.1016/j.jmaa.2011.11.042
   Web of Science ®Google Scholar
• Zhu F. Zero-inflated Poisson and negative binomial integer-valued GARCH models. J Stat Plan Inference. 2012;142:826–839. doi: 10.1016/j.jspi.2011.10.002
   Web of Science ®Google Scholar
• Lee S, Lee Y, Chen CWS. Parameter change test for zero-inflated generalized Poisson autoregressive models. Statistics. 2016;50:540–557. doi: 10.1080/02331888.2015.1083020
   Web of Science ®Google Scholar
• Davis RA, Liu H. Theory and inference for a class of observation-driven models with application to time series of counts. Stat Sin. 2016;26:1673–1707.
   Web of Science ®Google Scholar
• Weiß CH. An introduction to discrete-valued time series. New York: Wiley; 2018.
   Google Scholar
• Brègman LM. The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming. USSR Comput Math Math Phys. 1967;7:200–217. doi: 10.1016/0041-5553(67)90040-7
   Google Scholar
• Basu A, Harris IR, Hjort NL, et al. Robust and efficient estimation by minimizing a density power divergence. Biometrika. 1998;85:549–559. doi: 10.1093/biomet/85.3.549
   Web of Science ®Google Scholar
• Kang J, Lee S. Minimum density power divergence estimator for Poisson autoregressive models. Comput Stat Data Anal. 2014;80:44–56. doi: 10.1016/j.csda.2014.06.009
   Web of Science ®Google Scholar
• Kim B, Lee S. Robust estimation for zero-inflated Poisson autoregressive models based on density power divergence. J Stat Comput Simul. 2017;87:2981–2996. doi: 10.1080/00949655.2017.1351563
   Web of Science ®Google Scholar
• Xiong L, Zhu F. Minimum density power divergence estimator for negative binomial integer-valued GARCH models. Commun Math Stat. 2022;10:233–261. doi: 10.1007/s40304-020-00221-8
   Web of Science ®Google Scholar
• Kim B, Lee S. Robust estimation for general integer-valued time series models. Ann Inst Stat Math. 2020;72:1371–1396. doi: 10.1007/s10463-019-00728-0
   Web of Science ®Google Scholar
• Diop ML, Kengne W. Density power divergence for general integer-valued time series with multivariate exogenous covariate. arXiv:2006.11948. 2020.
   Google Scholar
• Lee S, Kim D, Kim B. Modeling and inference for multivariate time series of counts based on the INGARCH scheme. Comput Stat Data Anal. 2023;177:107579. doi: 10.1016/j.csda.2022.107579
   Web of Science ®Google Scholar
• Xiong L, Zhu F. Robust estimation for the one-parameter exponential family integer-valued GARCH(1,1) models based on a modified Tukey's biweight function. Comput Stat. 2022. in press.
   Web of Science ®Google Scholar
• Singh P, Mandal A, Basu A. Robust inference using the exponential-polynomial divergence. J Stat Theory Pract. 2021;15:29. doi: 10.1007/s42519-020-00162-z
   Web of Science ®Google Scholar
• Mukherjee T, Mandal A, Basu A. The B-exponential divergence and its generalizations with applications to parametric estimation. Stat Methods Appl. 2019;28:241–257. doi: 10.1007/s10260-018-00444-8
   Web of Science ®Google Scholar
• Kang J, Lee S. Parameter change test for Poisson autoregressive models. Scand J Stat. 2014;41:1136–1152. doi: 10.1111/sjos.v41.4
   Web of Science ®Google Scholar
• Lee Y, Lee S. CUSUM test for general nonlinear integer-valued GARCH models: comparison study. Ann Inst Stat Math. 2019;71:1033–1057. doi: 10.1007/s10463-018-0676-7
   Web of Science ®Google Scholar
• Fujisawa H, Eguchi S. Robust estimation in the normal mixture model. J Stat Plan Inference. 2006;136:3989–4011. doi: 10.1016/j.jspi.2005.03.008
   Web of Science ®Google Scholar
• Durio A, Isaia ED. The minimum density power divergence approach in building robust regression models. Informatica. 2011;22:43–56. doi: 10.15388/Informatica.2011.313
   Web of Science ®Google Scholar
• Toma A, Broniatowski M. Dual divergence estimators and tests: robustness results. J Multivar Anal. 2011;102:20–36. doi: 10.1016/j.jmva.2010.07.010
   Web of Science ®Google Scholar
• Warwick J, Jones MC. Choosing a robustness tuning parameter. J Stat Comput Simul. 2005;75:581–588. doi: 10.1080/00949650412331299120
   Web of Science ®Google Scholar
• Basak S, Basu A. The extended Bregman divergence and parametric estimation. Statistics. 2022;56:699–718. doi: 10.1080/02331888.2022.2070622
   Web of Science ®Google Scholar
• Basak S, Basu A, Jones MC. On the ‘optimal’ density power divergence tuning parameter. J Appl Stat. 2021;48:536–556. doi: 10.1080/02664763.2020.1736524
   PubMed 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;34:1578–1596. doi: 10.1007/s11424-020-9344-0
   Web of Science ®Google Scholar