Effects of trends and seasonalities on robustness of the Hurst parameter estimators

Author(s): X. Ye ; X. Xia ; J. Zhang ; Y. Chen
DOI: 10.1049/iet-spr.2012.0050

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Author(s): X. Ye ¹ ; X. Xia ¹ ; J. Zhang ¹ ; Y. Chen ^{2, 3}
- Affiliations: 1: Department of Electrical, Electronic and Computer Engineering, University of Pretoria, Pretoria, South Africa
  2: MESA Lab, School of Engineering, University of California, Merced, Merced, USA
  3: Electrical and Computer Engineering Department, Utah State University, Logan, USA
Source: Volume 6, Issue 9, December 2012, p. 849 – 856
DOI: 10.1049/iet-spr.2012.0050 , Print ISSN 1751-9675, Online ISSN 1751-9683

Long-range dependence (LRD) is discovered in time series arising from different fields, especially in network traffic and econometrics. Detecting the presence and the intensity of LRD plays a crucial role in time-series analysis and fractional system identification. The existence of LRD is usually indicated by the Hurst parameters. Up to now, many Hurst parameter estimators have been proposed in order to identify the LRD property involved in a time series. Since different estimators have different accuracy and robustness performances, in this study, 13 most popular Hurst parameter estimators are summarised and their estimation performances are investigated. LRD processes with known Hurst parameters are generated as the control data set for the robustness evaluation. In addition, three types of LRD processes are also obtained as the test signals by adding noises in terms of means, trends and seasonalities to the control data set. All 13 Hurst parameter estimators are applied to these LRD processes to estimate the existing Hurst parameters. The estimation results are documented and quantified by the standard errors. Conclusions of the accuracy and robustness performances of the estimators are drawn by comparing the estimation results.

References

1. 1)
  - M.S. Taqqu , V. Teverovsky . Robustness of Whittle type estimators for time series with long-range dependence. Stochastic Models , 4 , 723 - 757
2. 2)
  - B.B. Mandelbrot , J.W. Van Ness . Fractional Brownian motion, fractional noises and applications. SIAM Rev. , 4 , 422 - 437
3. 3)
  - J.B. Bassingthwaighte , G.M. Raymond . Evaluation of the dispersional analysis method for fractal time series. Ann. Biomed. Eng. , 4 , 491 - 505
4. 4)
  - J. Beran . (1994) Statistics for long-memory processes.
5. 5)
  - J. Geweke , S. Porter-Hudak . The estimation and application of long memory time series models. J. Time Ser. Anal. , 4 , 221 - 238
6. 6)
  - Koutsoyiannis, D.: `Supplementary material for the paper climate change, the Hurst phenomenon, and hydrological statistics', Technical Report, 2003, http://www.itia.ntua.gr/getfile/537/2/2003HSJHurstSuppl.pdf, accessed October 2012.
7. 7)
  - H.E. Hurst . Long-term storage capacity of reservoirs. Trans. Am. Soc. Civ. Eng. , 3 , 770 - 799
8. 8)
  - P.J. Brockwell , R.A. Davis . (2002) Introduction to time series and forecasting.
9. 9)
  - M. Li , W. Zhao . Representation of a stochastic traffic bound. IEEE Trans. Parallel Distrib. Syst. , 9 , 1368 - 1372
10. 10)
  - Sheng, H., Chen, Y.Q., Qiu, T.: `Robustness analysis of Hurst estimators for multifractional Gaussian process', Proc. Fourth IFACWorkshop Fractional Differentiation and its Applications, 2010, Badajoz, Spain, p. 1–6.
11. 11)
  - M.S. Taqqu , V. Teverovsky , W. Willinger . Estimators for long-range dependence: an empirical study. Fractals , 785 - 788
12. 12)
  - Sun, R., Chen, Y.Q., Li, Q.: `The modeling and prediction of Great Salt Lake elevation time series based on ARFIMA', Proc. ASME 2007 Int. Design Engineering Technical Conf. and Computers and Information in Engineering Conf. 2007, 2007, Las Vegas, Nevada, USA, p. 1–11.
13. 13)
  - H. Sheng , Y.Q. Chen , T. Qiu . On the robustness of hurst estimators. IET Signal Processing , 2 , 209 - 225
14. 14)
  - D. Koutsoyiannis . Climate change, the Hurst phenomenon, and hydrological statistics. Hydrol. Sci. J. , 1 , 3 - 24
15. 15)
  - R.G. Clegg . A practical guide to measuring the Hurst parameter. Int. J. Simul., Syst. Sci. Technol. , 2 , 3 - 14
16. 16)
  - T. Higuchi . Approach to an irregular time series on the basis of the fractal theory. Phys. D: Nonlinear Phenom. , 2 , 277 - 283
17. 17)
  - P. Grigolini , L. Palatella , G. Raffaelli . Asymmetric anomalous diffusion: an efficient way to detect memory in time series. Fractals , 4 , 439 - 449
18. 18)
  - H. Kettani , J.A. Gubner . A novel approach to the estimation of the long-range dependence parameter. IEEE Trans. Circuits Syst. , 6 , 463 - 467
19. 19)
  - A. Montanari , M.S. Taqqu , V. Teverovsky . Estimating long-range dependence in the presence of periodicity: an empirical study. Math. Comput. Model. , 217 - 228
20. 20)
  - Blok, H.J.: `On the nature of the stock market: simulations and experiments', 2000, PhD, University of British Columbia, Department of Physics and Astronomy.
21. 21)
  - P. Abry , D. Veitch . Wavelet analysis of long-range-dependent traffic. IEEE Trans. Inf. Theory , 1 , 2 - 15
22. 22)
  - J. Gubner . (2006) Probability and random processes for electrical and computer engineers.
23. 23)
  - M. Li , W. Zhao . Quantitatively investigating locally weak stationarity of modified multifractional Gaussian noise. Phy. A , 6268 - 6278

Effects of trends and seasonalities on robustness of the Hurst parameter estimators

Effects of trends and seasonalities on robustness of the Hurst parameter estimators

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