Wavelet Estimation of the Long Memory Parameter for Hermite Polynomial of Gaussian Processes

@inproceedings{Clausel2011WaveletEO,
  title={Wavelet Estimation of the Long Memory Parameter for Hermite Polynomial of Gaussian Processes},
  author={Marianne Clausel and François Roueff and Murad S. Taqqu},
  year={2011}
}
We consider stationary processes with long memory which are non–Gaussian and represented as Hermite polynomials of a Gaussian process. We focus on the corresponding wavelet coefficients and study the asymptotic behavior of the sum of their squares since this sum is often used for estimating the long–memory parameter. We show that the limit is not Gaussian but can be expressed using the non–Gaussian Rosenblatt process defined as a Wiener-Itô integral of order 2. This happens even if the original… CONTINUE READING

References

Publications referenced by this paper.
Showing 1-10 of 38 references

A wavelet analysis of the Rosenblatt process: chaos expansion and estimation of the self-similarity parameter

  • J.-M. Bardet, C. A. Tudor
  • Stochastic Process. Appl.,
  • 2010
Highly Influential
5 Excerpts

On the spectral density of the wavelet coefficients of long memory time series with application to the log-regression estimation of the memory parameter

  • E. Moulines, F. Roueff, M. S. Taqqu
  • J. Time Ser. Anal.,
  • 2007
Highly Influential
9 Excerpts

Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series

  • R. Fox, M. S. Taqqu
  • Ann. Statist.,
  • 1986
Highly Influential
11 Excerpts

Wavelet - based analysis of nonGaussian long - range dependent processes and estimation of the Hurst parameter

  • H. Helgason
  • Lithuanian Mathematical Journal
  • 2011

Wavelet-based analysis of non-Gaussian long-range dependent processes and estimation of the Hurst parameter. Lithuanian

  • P. Abry, H Helgason, V. Pipiras
  • Mathematical Journal,
  • 2011

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