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Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 580583, 10 pages
http://dx.doi.org/10.1155/2010/580583
Research Article

Detection of Outliers and Patches in Bilinear Time Series Models

Department of Mathematics, Southeast University, Nanjing 210096, China

Received 10 January 2010; Accepted 10 February 2010

Academic Editor: Ming Li

Copyright © 2010 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. M. Li and W. Zhao, “Representation of a stochastic traffic bound,” IEEE Transactions on Parallel and Distributed Systems, preprint.
  2. B. Abraham and G. E. P. Box, “Bayesian analysis of some outlier problems in time series,” Biometrika, vol. 66, no. 2, pp. 229–236, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. R. S. Tsay, “Time series model specification in the presence of outliers,” Journal of the American Statistical Association, vol. 81, pp. 132–141, 1986.
  4. G. M. Ljung, “On outlier detection in time series,” Journal of the Royal Statistical Society. Series B, vol. 55, no. 2, pp. 559–567, 1993. View at Zentralblatt MATH · View at MathSciNet
  5. A. Justel, D. Peña, and R. S. Tsay, “Detection of outlier patches in autoregressive time series,” Statistica Sinica, vol. 11, no. 3, pp. 651–673, 2001. View at Zentralblatt MATH · View at MathSciNet
  6. 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
  7. P. Chen, F. R. Yan, Y. Y. Wu, and Y. Chen, “Detection of outliers in ARMAX time series models,” Advances in Systems Science and Applications, vol. 9, pp. 97–103, 2009.
  8. P. Chen and Y. Chen, “The identification of outliers in ARMAX models via genetic algorithm,” to appear in Kybernetes.
  9. M. Li, “Fractal time series—a tutorial review,” Mathematical Problems in Engineering, vol. 2010, Article ID 157264, 26 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. H.-B. Wang and B.-C. Wei, “Separable lower triangular bilinear model,” Journal of Applied Probability, vol. 41, no. 1, pp. 221–235, 2004. View at Zentralblatt MATH · View at MathSciNet
  11. H.-B. Wang, “Parameter estimation and subset selection for separable lower triangular bilinear models,” Journal of Time Series Analysis, vol. 26, no. 5, pp. 743–757, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. 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
  13. T. Subba Rao, “On the theory of bilinear time series models,” Journal of the Royal Statistical Society B, vol. 43, no. 2, pp. 244–255, 1981. View at Zentralblatt MATH · View at MathSciNet
  14. T. Subba Rao and M. M. Gabr, An Introduction to Bispectral Analysis and Bilinear Time Series Models, vol. 24 of Lecture Notes in Statistics, Springer, New York, NY, USA, 1984. View at MathSciNet
  15. W. K. Kim, L. Billard, and I. V. Basawa, “Estimation for the first-order diagonal bilinear time series model,” Journal of Time Series Analysis, vol. 11, no. 3, pp. 215–229, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. S. A. O. Sesay and T. Subba Rao, “Difference equations for higher-order moments and cumulants for the bilinear time series model BL(p,0,p,1),” Journal of Time Series Analysis, vol. 12, no. 2, pp. 159–177, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. C. W. J. Granger and A. P. Andersen, An Introduction to Bilinear Time Series Models, Vandenhoeck & Ruprecht, Göttingen, Germany, 1978. View at MathSciNet
  18. R. E. McCulloch and R. S. Tsay, “Bayesian analysis of autoregressive time series via the Gibbs sampler,” Journal of Time Series Analysis, vol. 15, no. 2, pp. 235–250, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet