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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 231592, 5 pages
http://dx.doi.org/10.1155/2014/231592
Research Article

Integer-Valued Moving Average Models with Structural Changes

1Statistics School, Southwestern University of Finance and Economics, Chengdu 611130, China
2School of Economics, Southwestern University of Finance and Economics, Chengdu 611130, China

Received 2 March 2014; Revised 22 June 2014; Accepted 7 July 2014; Published 21 July 2014

Academic Editor: Wuquan Li

Copyright © 2014 Kaizhi Yu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. E. McKenzie, “Some simple models for discrete variate time series,” Water Resources Bulletin, vol. 21, no. 4, pp. 635–644, 1985. View at Publisher · View at Google Scholar · View at Scopus
  2. E. McKenzie, “Autoregressive moving-average processes with negative-binomial and geometric marginal distributions,” Advances in Applied Probability, vol. 18, no. 3, pp. 679–705, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. M. A. Al-Osh and A. A. Alzaid, “First order integer-valued autoregressive INAR(1) process,” Journal of Time Series Analysis, vol. 8, no. 3, pp. 261–275, 1987. View at Publisher · View at Google Scholar · View at MathSciNet
  4. A. A. Alzaid and M. Al-Osh, “An integer-valued pth-order autoregressive structure INAR(p) process,” Journal of Applied Probability, vol. 27, no. 2, pp. 314–324, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  5. J. G. Du and Y. Li, “The integer-valued autoregressive (INAR(p)) model,” Journal of Time Series Analysis, vol. 12, no. 2, pp. 129–142, 1991. View at Publisher · View at Google Scholar · View at MathSciNet
  6. M. Al-Osh and A. A. Alzaid, “Integer-valued moving average (INMA) process,” Statistical Papers, vol. 29, no. 4, pp. 281–300, 1988. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. E. McKenzie, “Some ARMA models for dependent sequences of Poisson counts,” Advances in Applied Probability, vol. 20, no. 4, pp. 822–835, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  8. R. Ferland, A. Latour, and D. Oraichi, “Integer-valued GARCH process,” Journal of Time Series Analysis, vol. 27, no. 6, pp. 923–942, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. K. Fokianos and R. Fried, “Interventions in INGARCH processes,” Journal of Time Series Analysis, vol. 31, no. 3, pp. 210–225, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. C. H. Weiß, “The INARCH(1) model for overdispersed time series of counts,” Communications in Statistics: Simulation and Computation, vol. 39, no. 6, pp. 1269–1291, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  11. F. Zhu, “A negative binomial integer-valued GARCH model,” Journal of Time Series Analysis, vol. 32, no. 1, pp. 54–67, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. F. Zhu, “Modeling overdispersed or underdispersed count data with generalized Poisson integer-valued GARCH models,” Journal of Mathematical Analysis and Applications, vol. 389, no. 1, pp. 58–71, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. F. Zhu and D. Wang, “Diagnostic checking integer-valued ARCH(p) models using conditional residual autocorrelations,” Computational Statistics and Data Analysis, vol. 54, no. 2, pp. 496–508, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  14. L. Györfi, M. Ispány, G. Pap, and K. Varga, “Poisson limit of an inhomogeneous nearly critical INAR(1) model,” Acta Universitatis Szegediensis, vol. 73, no. 3-4, pp. 789–815, 2007. View at Google Scholar · View at MathSciNet
  15. H. S. Bakouch and M. M. Ristić, “Zero truncated Poisson integer-valued AR(1) model,” Metrika, vol. 72, no. 2, pp. 265–280, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. M. Kachour and J. F. Yao, “First-order rounded integer-valued autoregressive ((RINAR(1)) process,” Journal of Time Series Analysis, vol. 30, no. 4, pp. 417–448, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. H.-Y. Kim and Y. Park, “A non-stationary integer-valued autoregressive model,” Statistical Papers, vol. 49, no. 3, pp. 485–502, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. H. Zheng, I. V. Basawa, and S. Datta, “First-order random coefficient integer-valued autoregressive processes,” Journal of Statistical Planning and Inference, vol. 137, no. 1, pp. 212–229, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  19. D. Gomes and L. Canto e Castro, “Generalized integer-valued random coefficient for a first order structure autoregressive (RCINAR) process,” Journal of Statistical Planning and Inference, vol. 139, no. 12, pp. 4088–4097, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. M. M. Ristić, A. S. Nastić, K. Jayakumar, and H. S. Bakouch, “A bivariate INAR(1) time series model with geometric marginals,” Applied Mathematics Letters, vol. 25, no. 3, pp. 481–485, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. X. Pedeli and D. Karlis, “A bivariate INAR(1) process with application,” Statistical Modelling, vol. 11, no. 4, pp. 325–349, 2011. View at Google Scholar
  22. P. Thyregod, J. Carstensen, H. Madsen, and K. Arnbjerg-Nielsen, “Integer valued autoregressive models for tipping bucket rainfall measurements,” Environmetrics, vol. 10, no. 4, pp. 395–411, 1999. View at Publisher · View at Google Scholar · View at Scopus
  23. M. Monteiro, M. G. Scotto, and I. Pereira, “Integer-valued self-exciting threshold autoregressive processes,” Communications in Statistics: Theory and Methods, vol. 41, no. 15, pp. 2717–2737, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. Š. Hudecová, “Structural changes in autoregressive models for binary time series,” Journal of Statistical Planning and Inference, vol. 143, no. 10, pp. 1744–1752, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. A. DasGupta, Asymptotic Theory of Statistics and Probability, Springer, New York, NY, USA, 2008. View at MathSciNet
  26. P. J. Brockwell and R. A. Davis, Time Series: Theory and Methods, Springer, New York, NY, USA, 1991. View at Publisher · View at Google Scholar · View at MathSciNet
  27. K. Yu, D. Shi, and H. Zou, “The random coefficient discretevalued time series model,” Statistical Research, vol. 28, no. 4, pp. 106–112, 2011. View at Google Scholar
  28. K. BräKnnäK and A. Hall, “Estimation in integer-valued moving average models,” Applied Stochastic Models in Business and Industry, vol. 17, no. 3, pp. 277–291, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus