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Articles

Residual-based CUSUM of squares test for Poisson integer-valued GARCH models

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Pages 3182-3195 | Received 18 Apr 2019, Accepted 15 Aug 2019, Published online: 22 Aug 2019

References

  • Al-Osh MA, Aly E-EA. First order autoregressive time series with negative binomial and geometric marginals. Comm Statist Theory Methods. 1992;21:2483–2492. doi: 10.1080/03610929208830925
  • Alzaid A, Al-Osh M. An integer-valued pth-order autoregressive structure (INAR(p)) process. J Appl Probab. 1990;27:314–324. doi: 10.2307/3214650
  • McKenzie E. Some simple models for discrete variate time series. J Am Water Resour Assoc. 1985;21:645–650. doi: 10.1111/j.1752-1688.1985.tb05379.x
  • McKenzie E. Handbook of statistics. Vol. 21. Chapter 16, Discrete variate time series. Boca Raton (FL): CRC Press; 2003. p. 573–606.
  • Weiß CH. Thinning operations for modeling time series of counts-a survey. AStA-Adv Stat Anal. 2008;92:319–341. doi: 10.1007/s10182-008-0072-3
  • Ferland R, Latour A, Oraichi D. Integer-valued GARCH process. J Time Ser Anal. 2006;27:923–942. doi: 10.1111/j.1467-9892.2006.00496.x
  • Fokianos K, Rahbek A, Tjøstheim D. Poisson autoregression. J Am Stat Assoc. 2009;104:1430–1439. doi: 10.1198/jasa.2009.tm08270
  • Heinen A. Modelling time series count data: an autoregressive conditional Poisson model. Available at SSRN 1117187; 2003.
  • Neumann MH. Absolute regularity and ergodicity of Poisson count processes. Bernoulli. 2011;17:1268–1284. doi: 10.3150/10-BEJ313
  • 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.12050
  • Davis RA, Wu R. A negative binomial model for time series of counts. Biometrika. 2009;96:735–749. doi: 10.1093/biomet/asp029
  • 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
  • Zhu F. Zero-inflated Poisson and negative binomial integer-valued GARCH models. J Statist Plann Inferences. 2012;142:826–839. doi: 10.1016/j.jspi.2011.10.002
  • Lee S, Lee Y, Chen CW. Parameter change test for zero-inflated generalized Poisson autoregressive models. Statistics. 2016;50:1–18. doi: 10.1080/02331888.2015.1083020
  • 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.
  • Csörgö M, Horváth L. Limit theorems in change-point analysis. Vol. 18. New York: John Wiley & Sons. Inc.; 1997.
  • Lee S, Ha J, Na O, et al. The cusum test for parameter change in time series models. Scand J Statist. 2003;30:781–796. doi: 10.1111/1467-9469.00364
  • Kang J, Lee S. Parameter change test for random coefficient integer-valued autoregressive processes with application to polio data analysis. J Time Ser Anal. 2009;30:239–258. doi: 10.1111/j.1467-9892.2009.00608.x
  • Fokianos K, Fried R. Interventions in INGARCH processes. J Time Ser Anal. 2010;31:210–225. doi: 10.1111/j.1467-9892.2010.00657.x
  • Fokianos K, Fried R. Interventions in log-linear Poisson autoregression. Stat Modelling. 2012;12:299–322. doi: 10.1177/1471082X1201200401
  • Franke J, Kirch C, Kamgaing JT. Changepoints in times series of counts. J Time Ser Anal. 2012;33:757–770. doi: 10.1111/j.1467-9892.2011.00778.x
  • Hudecová Š. Structural changes in autoregressive models for binary time series. J Statist Plann Inferences. 2013;143:1744–1752. doi: 10.1016/j.jspi.2013.05.009
  • Fokianos K, Gombay E, Hussein A. Retrospective change detection for binary time series models. J Statist Plann Inferences. 2014;145:102–112. doi: 10.1016/j.jspi.2013.08.017
  • Kang J, Lee S. Parameter change test for Poisson autoregressive models. Scand J Statist. 2014;41:1136–1152. doi: 10.1111/sjos.12088
  • Hudecová Š, Hudecová M, Meintanis S. Change detection in INARCH time series of counts. In: Cao R, Gonzalez Manteiga W, Romo J, editors. Nonparametric statistics. Vol. 175. New York: Springer; 2016. p. 47–58.
  • Diop ML, Kengne W. Testing parameter change in general integer-valued time series. J Time Ser Anal. 2017;38:880–894. doi: 10.1111/jtsa.12240
  • Lee Y, Lee S, Tjøstheim D. Asymptotic normality and parameter change test for bivariate Poisson INGARCH models. TEST. 2018;27:52–69. doi: 10.1007/s11749-016-0510-6
  • Lee Y, Lee S. CUSUM tests for general nonlinear inter-valued GARCH models: comparison study. Ann Inst Stat Math. 2019;71:1033–1057. doi: 10.1007/s10463-018-0676-7
  • Lee S, Lee J. Parameter change test for nonlinear time series models with GARCH type errors. J Korean Math Soc. 2015;52:503–522. doi: 10.4134/JKMS.2015.52.3.503
  • Lee S, Tokutsu Y, Maekawa K. The cusum test for parameter change in regression models with ARCH errors. J Japan Statist Soc. 2004;34:173–188. doi: 10.14490/jjss.34.173
  • Oh H, Lee S. Modified residual CUSUM test for location-scale time series models with heteroscedasticity. Ann Inst Stat Math. 2018;71:1059–1091. doi: 10.1007/s10463-018-0679-4
  • Lee S, Park S. The cusum of squares test for scale changes in infinite order moving average processes. Scand J Statist. 2001;28:625–644. doi: 10.1111/1467-9469.00259
  • Woodridge JM, White H. Some invariance principles and central limit theorems for dependent heterogeneous processes. Econ Theory. 1988;4:210–230. doi: 10.1017/S0266466600012032
  • Lee S, Park S, Chen WSC. On Fisher's dispersion test for integer-valued autoregressive Poisson models with applications. Comm Statist Theory Methods. 2017;46:9985–9994. doi: 10.1080/03610926.2016.1228970
  • Lee S. Location and scale-based CUSUM test with application to autoregressive models. Submitted for publication. 2019.
  • Bradley R. Introduction to strong mixing conditions. Vol. 1. Herber City, Utah: Kendrik Press, Inc.; 2007.

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