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Mathematical Problems in Engineering
Volume 2016, Article ID 9505794, 8 pages
http://dx.doi.org/10.1155/2016/9505794
Research Article

Empirical Likelihood Inference for First-Order Random Coefficient Integer-Valued Autoregressive Processes

College of Mathematics, Jilin Normal University, Siping 136000, China

Received 21 June 2015; Accepted 4 November 2015

Academic Editor: Mustafa Tutar

Copyright © 2016 Zhiwen Zhao and Wei Yu. 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. R. A. Davis, T. M. Dunsmuir, and Y. Wang, “Modeling time series of count data,” in Asymptotics, Nonparametrics and Time Series, pp. 63–114, Marcel-Dekker, New York, NY, USA, 1999. View at Google Scholar
  2. I. L. MacDonald and W. Z. Zucchini, Hidden Markov and Other Models for Discrete-Valued Time Series, Chapman & Hall, London, UK, 1997.
  3. T. Fukasawa and I. V. Basawa, “Estimation for a class of generalized state-space time series models,” Statistics & Probability Letters, vol. 60, no. 4, pp. 459–473, 2002. View at Publisher · View at Google Scholar · View at Scopus
  4. F. W. Steutel and K. V. Harn, “Discrete analogues of self-decomposability and stability,” The Annals of Probability, vol. 7, no. 5, pp. 893–899, 1979. View at Publisher · View at Google Scholar · View at MathSciNet
  5. 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 MathSciNet · View at Scopus
  6. H. Zheng, I. V. Basawa, and S. Datta, “Inference for pth-order random coefficient integer-valued autoregressive processes,” Journal of Time Series Analysis, vol. 27, no. 3, pp. 411–440, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. J. Kang and S. Lee, “Parameter change test for random coefficient integer-valued autoregressive processes with application to polio data analysis,” Journal of Time Series Analysis, vol. 30, no. 2, pp. 239–258, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  8. H. Zhang, D. Wang, and F. Zhu, “The empirical likelihood for first-order random coefficient integer-valued autoregressive processes,” Communications in Statistics. Theory and Methods, vol. 40, no. 3, pp. 492–509, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  9. H. Zhang, D. Wang, and F. Zhu, “Empirical likelihood inference for random coefficient INAR(p) process,” Journal of Time Series Analysis, vol. 32, no. 3, pp. 195–203, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. A. Roitershtein and Z. Zhong, “On random coefficient INAR(1) processes,” Science China Mathematics, vol. 56, no. 1, pp. 177–200, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. A. B. Owen, “Empirical likelihood ratio confidence intervals for a single functional,” Biometrika, vol. 75, no. 2, pp. 237–249, 1988. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. A. B. Owen, “Empirical likelihood ratio confidence region,” The Annals of Statistics, vol. 18, no. 1, pp. 90–120, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  13. A. B. Owen, “Empirical likelihood for linear models,” The Annals of Statistics, vol. 19, no. 4, pp. 1725–1747, 1991. View at Publisher · View at Google Scholar · View at MathSciNet
  14. C.-S. Chuang and N. H. Chan, “Empirical likelihood for autoregressive models, with applications to unstable time series,” Statistica Sinica, vol. 12, no. 2, pp. 387–407, 2002. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  15. S. X. Chen, W. Härdle, and M. Li, “An empirical likelihood goodness-of-fit test for time series,” Journal of the Royal Statistical Society—Series B: Statistical Methodology, vol. 65, no. 3, pp. 663–678, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. N. H. Chan and S. Ling, “Empirical likelihood for GARCH models,” Econometric Theory, vol. 22, no. 3, pp. 403–428, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. S. X. Chen and J. T. Gao, “An adaptive empirical likelihood test for parametric time series regression models,” Journal of Econometrics, vol. 141, no. 2, pp. 950–972, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. P. Guggenberger and R. J. Smith, “Generalized empirical likelihood tests in time series models with potential identification failure,” Journal of Econometrics, vol. 142, no. 1, pp. 134–161, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. J. Li, W. Liang, S. He, and X. Wu, “Empirical likelihood for the smoothed LAD estimator in infinite variance autoregressive models,” Statistics & Probability Letters, vol. 80, no. 17-18, pp. 1420–1430, 2010. View at Publisher · View at Google Scholar · View at Scopus
  20. Z.-W. Zhao and D.-H. Wang, “Empirical likelihood for an autoregressive model with explanatory variables,” Communications in Statistics. Theory and Methods, vol. 40, no. 3, pp. 559–570, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. Z.-W. Zhao, D.-H. Wang, and C.-X. Peng, “Coefficient constancy test in generalized random coefficient autoregressive model,” Applied Mathematics and Computation, vol. 219, no. 20, pp. 10283–10292, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. P. Hall and C. C. Heyde, Martingale Limit Theory and Its Application, Academic Press, New York, NY, USA, 1980. View at MathSciNet