Skip to main content
Article thumbnail
Location of Repository

Robust estimation of the Hurst parameter and selection of an onset scaling.

By Juhyun Park and Cheolwoo Park


We consider the problem of estimating the Hurst parameter for long-range dependent processes using wavelets. Wavelet techniques have been shown to effectively exploit the asymptotic linear relationship that forms the basis of constructing an estimator. However, it has been noticed that the commonly adopted standard wavelet estimator is vulnerable to various non-stationary phenomena that increasingly occur in practice, and thus leads to unreliable results. In this paper, we propose a new wavelet method for estimating the Hurst parameter that is robust to such non-stationarities as peaks, valleys, and trends. We point out that the new estimator arises as a simple alternative to the standard estimator and does not require an additional correction term that is subject to distributional assumptions. Additionally, we address the issue of selecting scales for the wavelet estimator, which is critical to properly exploiting the asymptotic relationship. We propose a new method based on standard regression diagnostic tools, which is easy to implement, and useful for providing informative goodness-of-fit measures. Several simulated examples are used for illustration and comparison. The proposed method is also applied to the estimation of the Hurst parameter of Internet traffic packet counts data

Year: 2009
OAI identifier:
Provided by: Lancaster E-Prints

Suggested articles


  1. (1996). A course in large sample theory. doi
  2. (1999). A wavelet based joint estimator for the parameters of LRD. doi
  3. (2005). Asymptotic self-similarity and wavelet estimation for long-range dependent fractional autoregressive integrated moving average time series with stable innovations. doi
  4. (2004). Dependent SiZer: goodnessof-¯t tests for time series models. doi
  5. (2002). Estimation of the self-similarity parameter in linear fractional stable motion. doi
  6. (2004). Estimation of the self-similarity parameter using the wavelet transform. doi
  7. (1995). Gaussian semiparametric estimation of long range dependence. doi
  8. (1997). Limit Theorems in Change-Point Analysis.
  9. (2003). On the automatic selection of the onset of scaling. doi
  10. (2005). On the wavelet spectrum diagnostic for Hurst parameter estimation in the analysis of Internet tra±c. doi
  11. (2000). Parametric statistical change point analysis. BirkhÄ auser, doi
  12. (2004). Robust Analysis of Linear Models. doi
  13. (2007). Robust estimation of the self-similarity parameter in network tra±c using wavelet transform. doi
  14. (2003). Self-similarity and long-range dependence through the wavelet lens. in Theory and Applications of Long-range Dependence. BirkhÄ auser,
  15. (1996). Self-similarity in World Wide Web tra±c evidence and possible causes. doi
  16. (1994). Statistics for Long-Memory Processes. doi
  17. (2000). Tables of integrals, series and products. doi
  18. (2004). Variable Heavy Tails in Internet Tra±c. doi
  19. (1998). Wavelet analysis of long-range dependent tra±c. doi
  20. (2003). Wavelet estimation for the Hurst parameter in stable processes. doi
  21. (2000). Wavelet estimator of long-range dependent processes. Statistical Inference for Stochastic Processes 3, 85-99.ROBUST HURST doi
  22. (2007). Wide Area tra±c: the failure of Poisson modeling.

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.