Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2013, Article ID 910828, 9 pages
http://dx.doi.org/10.1155/2013/910828
Research Article

Outlier Detection in Adaptive Functional-Coefficient Autoregressive Models Based on Extreme Value Theory

1Department of Mathematics, Southeast University, Nanjing, Jiangsu 210096, China
2School of Finance and Statistics, East China Normal University, Shanghai 200241, China
3Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 10027, USA

Received 26 January 2013; Accepted 12 March 2013

Academic Editor: Ming Li

Copyright © 2013 Ping Chen 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. C. C. Aggarwal, Outlier Analysis, Springer, New York ,NY, USA, 2013.
  2. X. Jie, M. Li, W. Zhao, and S. Y. Chen, “Bound maxima as a traffic feature under DDOS flood attacks,” Mathematical Problems in Engineering, vol. 2012, Article ID 419319, 20 pages, 2012. View at Publisher · View at Google Scholar
  3. M. Li and W. Zhao, “On bandlimitedness and lag-limitedness of fractional Gaussian noise,” Physica A, vol. 392, no. 9, pp. 1955–1961, 2013. View at Google Scholar
  4. M. Li, Y.-Q. Chen, J.-Y. Li, and W. Zhao, “Hölder scales of sea level,” Mathematical Problems in Engineering, Article ID 863707, 22 pages, 2012. View at Publisher · View at Google Scholar
  5. C. W. S. Chen, “Detection of additive outliers in bilinear time series,” Computational Statistics & Data Analysis, vol. 24, no. 3, pp. 283–294, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. M. Li, “Fractal time series—a tutorial review,” Mathematical Problems in Engineering, Article ID 157264, 26 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. Z. Cai, J. Fan, and Q. Yao, “Functional-coefficient regression models for nonlinear time series,” Journal of the American Statistical Association, vol. 95, no. 451, pp. 941–956, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. F. Battaglia, “Outliers in functional autoregressive time series,” Statistics & Probability Letters, vol. 72, no. 4, pp. 323–332, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. F. Battaglia and L. Orfei, “Outlier detection and estimation in nonlinear time series,” Journal of Time Series Analysis, vol. 26, no. 1, pp. 107–121, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. P. Chen, L. Li, Y. Liu, and J.-G. Lin, “Detection of outliers and patches in bilinear time series models,” Mathematical Problems in Engineering, Article ID 580583, 10 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. P. Chen, J. Yang, and L. Y. Li, “Synthetic Detection of Change Point and Outliers in Bilinear Time SeriesModels,” International Journal of Systems Science. In press.
  12. R. A. Martin, “Extreme value analysis of optimal level-crossing prediction for linear Gaussian processes,” Journal of Time Series Analysis, vol. 33, no. 4, pp. 583–607, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  13. K. Zhu and S. Ling, “Likelihood ratio tests for the structural change of an AR(p) model to a threshold AR(p) model,” Journal of Time Series Analysis, vol. 33, no. 2, pp. 223–232, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  14. P. Chareka, F. Matarise, and R. Turner, “A test for additive outliers applicable to long-memory time series,” Journal of Economic Dynamics & Control, vol. 30, no. 4, pp. 595–621, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. W.-K. Fung, Z.-Y. Zhu, B.-C. Wei, and X. He, “Influence diagnostics and outlier tests for semiparametric mixed models,” Journal of the Royal Statistical Society B, vol. 64, no. 3, pp. 565–579, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. A. M. Río, Extreme value theory-based P values in time series outlier detection [Ph.D. thesis], University of Wisconsin Madison, 2005.
  17. J. Fan and Q. Yao, Nonlinear time series, Springer Series in Statistics, Springer, New York, NY, USA, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  18. M. R. Leadbetter and H. Rootzén, “Extremal theory for stochastic processes,” The Annals of Probability, vol. 16, no. 2, pp. 431–478, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet