Table of Contents Author Guidelines Submit a Manuscript
Table of Contents Alerts

To receive news and publication updates for Mathematical Problems in Engineering, enter your email address in the box below.

Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 217213, 8 pages
http://dx.doi.org/10.1155/2013/217213
Research Article

Stationarity Testing of Accumulated Ethernet Traffic

Zhiping Lu,1 Ming Li,2 and Wei Zhao3

1School of Finance and Statistics, East China Normal University, No. 500, Dong-Chuan Road, Shanghai 200241, China
2School of Information Science and Technology, East China Normal University, No. 500, Dong-Chuan Road, Shanghai 200241, China
3Department of Computer and Information Science, University of Macau, Av. Padre Tomas Pereira, Taipa, Macau

Received 26 January 2013; Revised 12 March 2013; Accepted 13 March 2013

Academic Editor: Shengyong Chen

Copyright © 2013 Zhiping Lu 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. R. M. Loynes, “On the concept of the spectrum for non-stationary processes,” Journal of the Royal Statistical Society Series B, vol. 30, pp. 1–30, 1968. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. M. B. Priestley, “Evolutionary spectra and non-stationary processes,” Journal of the Royal Statistical Society Series B, vol. 27, pp. 204–237, 1965. View at Google Scholar · View at MathSciNet
  3. Z. Guo, L. G. Durand, and H. C. Lee, “Time-frequency distributions of nonstationary signals based on a Bessel kernel,” IEEE Transactions on Signal Processing, vol. 42, no. 7, pp. 1700–1706, 1994. View at Publisher · View at Google Scholar · View at Scopus
  4. N. E. Huang, Z. Shen, S. R. Long et al., “The empirical mode decomposition and the Hubert spectrum for nonlinear and non-stationary time series analysis,” Proceedings of the Royal Society A, vol. 454, no. 1971, pp. 903–995, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  5. A. R. Messina and V. Vittal, “Nonlinear, non-stationary analysis of interarea oscillations via Hilbert spectral analysis,” IEEE Transactions on Power Systems, vol. 21, no. 3, pp. 1234–1241, 2006. View at Publisher · View at Google Scholar · View at Scopus
  6. C. R. Pinnegar and L. Mansinha, “Time-local spectral analysis for nonstationary time series: the s-transform for noisy signals,” Fluctuation and Noise Letters, vol. 3, no. 3, pp. L357–L364, 2003. View at Google Scholar
  7. J. Xiao and P. Flandrin, “Multitaper time-frequency reassignment for nonstationary spectrum estimation and chirp enhancement,” IEEE Transactions on Signal Processing, vol. 55, no. 6, pp. 2851–2860, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. M. Li and W. Zhao, “On 1/f noise,” Mathematical Problems in Engineering, vol. 2012, Article ID 673648, 23 pages, 2012. View at Publisher · View at Google Scholar
  9. Z. Psaradakis, “Blockwise bootstrap testing for stationarity,” Statistics and Probability Letters, vol. 76, no. 6, pp. 562–570, 2006. View at Publisher · View at Google Scholar · View at Scopus
  10. S. Ling, “Estimation and testing stationarity for double-autoregressive models,” Journal of the Royal Statistical Society Series B, vol. 66, no. 1, pp. 63–78, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. P. M. M. Rodrigues and A. Rubia, “A note on testing for nonstationarity in autoregressive processes with level dependent conditional heteroskedasticity,” Statistical Papers, vol. 49, no. 3, pp. 581–593, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. R. Von Sachs and M. H. Neumann, “A wavelet-based test for stationarity,” Journal of Time Series Analysis, vol. 21, no. 5, pp. 597–613, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. P. Abry and D. Veitch, “Wavelet analysis of long-range-dependent traffic patrice abry and darryl veitch,” IEEE Transactions on Information Theory, vol. 44, no. 1, pp. 2–15, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  14. M. Grossglauser and J. C. Bolot, “On the relevance of long-range dependence in network traffic,” IEEE/ACM Transactions on Networking, vol. 7, no. 5, pp. 629–640, 1999. View at Google Scholar · View at Scopus
  15. B. B. Mandelbrot, “Note on the definition and the stationarity of fractional Gaussian noise,” Journal of Hydrology, vol. 30, no. 4, pp. 407–409, 1976. View at Google Scholar · View at Scopus
  16. M. Li and W. Zhao, “Quantitatively investigating locally weak stationarity of modified multifractional Gaussian noise,” Physica A, vol. 391, no. 24, pp. 6268–6278, 2012. View at Google Scholar
  17. B. B. Mandelbrot, Multifractals and 1/f Noise, Springer, New York, NY, USA, 1999. View at MathSciNet
  18. http://ita.ee.lbl.gov/html/contrib/BC.html.
  19. Z. Lu, M. Li, and W. Zhao, “Normality of Ethernet traffic at large time scales,” Mathematical Problems in Engineering, vol. 2013, Article ID 471963, 2013. View at Publisher · View at Google Scholar
  20. D. A. Dickey and W. A. Fuller, “Distribution of the estimators for autoregressive time series with a unit root,” Journal of the American Statistical Association, vol. 74, no. 366, pp. 427–431, 1979. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. S. E. Said and D. A. Dickey, “Testing for unit roots in autoregressive-moving average models of unknown order,” Biometrika, vol. 71, no. 3, pp. 599–607, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. P. C. B. Phillips and P. Perron, “Testing for a unit root in time series regression,” Biometrika, vol. 75, no. 2, pp. 335–346, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. G. Elliott, T. J. Rothenberg, and J. H. Stock, “Efficient tests for an autoregressive unit root,” Econometrica, vol. 64, no. 4, pp. 813–836, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  24. D. Kwiatkowski, P. C. B. Phillips, P. Schmidt, and Y. Shin, “Testing the null hypothesis of stationarity against the alternative of a unit root. How sure are we that economic time series have a unit root?” Journal of Econometrics, vol. 54, no. 1–3, pp. 159–178, 1992. View at Google Scholar · View at Scopus
  25. P. J. Brockwell and R. A. Davis, “Nonstationary and seasonal time series models,” in Introduction to Time Series and Forecasting, pp. 179–196, Springer, New York, NY, USA, 2002. View at Google Scholar
  26. C. B. Foster, Economics and Business Forecasting—Lectures 4, 5 and 6, Lecture notes-Ec 178, University of California, San Diego, Calif, USA, 2005.
  27. M. Lanne and P. Saikkonen, “Reducing size distortions of parametric stationarity tests,” Journal of Time Series Analysis, vol. 24, no. 4, pp. 423–439, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. R. Refinetti, “Non-stationary time series and the robustness of circadian rhythms,” Journal of Theoretical Biology, vol. 227, no. 4, pp. 571–581, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. E. Zivot, “Economic Theory II: Time Series Analysis—Unit Root Tests,” Lecture Notes-Econ 584. University of Washington, 2005, http://faculty.washington.edu/ezivot/econ584/notes/unitroot.pdf.
  30. P. M. Robinson, “Efficient tests of nonstationary hypotheses,” Journal of the American Statistical Association, vol. 89, no. 428, pp. 1420–1437, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  31. L. Ferrara, D. Guegan, and Z. Lu, “Testing fractional order of long memory processes: a monte carlo study,” Communications in Statistics, vol. 39, no. 4, pp. 795–806, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  32. E. G. Bakhoum and C. Toma, “Specific mathematical aspects of dynamics generated by coherence functions,” Mathematical Problems in Engineering, vol. 2011, Article ID 436198, 10 pages, 2011. View at Publisher · View at Google Scholar · View at Scopus
  33. C. Cattani, “On the existence of wavelet symmetries in archaea DNA,” Computational and Mathematical Methods in Medicine, vol. 2012, Article ID 673934, 21 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  34. C. Cattani, G. Pierro, and G. Altieri, “Entropy and multifractality for the myeloma multiple TET 2 gene,” Mathematical Problems in Engineering, vol. 2012, Article ID 193761, 14 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  35. C. Toma, “Advanced signal processing and command synthesis for memory-limited complex systems,” Mathematical Problems in Engineering, vol. 2012, Article ID 927821, 13 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet