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Estimators of long-memory: Fourier versus wavelets

  • Faÿ, Gilles
  • Moulines, Eric
  • Roueff, François
  • Taqqu, Murad S.
Registered author(s):

    Semi-parametric estimation methods of the long-memory exponent of a time series have been studied in several papers, some applied, others theoretical, some using Fourier methods, others using a wavelet-based technique. In this paper, we compare the Fourier and wavelet approaches to the local regression method and to the local Whittle method. We provide an overview of these methods, describe what has been done and indicate the available results and the conditions under which they hold. We discuss their relative strengths and weaknesses both from a practical and a theoretical perspective. We also include a simulation-based comparison. The software written to support this work is available on demand and we illustrate its use at the end of the paper.

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    File URL: http://www.sciencedirect.com/science/article/B6VC0-4VWB1DH-3/2/326878bbcf90fd13526c74e2dc417094
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    Article provided by Elsevier in its journal Journal of Econometrics.

    Volume (Year): 151 (2009)
    Issue (Month): 2 (August)
    Pages: 159-177

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    Handle: RePEc:eee:econom:v:151:y:2009:i:2:p:159-177
    Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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    1. E. Moulines & F. Roueff & M. S. Taqqu, 2007. "On the Spectral Density of the Wavelet Coefficients of Long-Memory Time Series with Application to the Log-Regression Estimation of the Memory Parameter," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(2), pages 155-187, 03.
    2. repec:cep:stiecm:/1997/323 is not listed on IDEAS
    3. Faÿ, Gilles & Moulines, Eric & Soulier, Philippe, 2004. "Edgeworth expansions for linear statistics of possibly long-range-dependent linear processes," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 275-288, February.
    4. ANDREWS, DONALD W & Sun, Yixiao X, 2002. "Adaptive Local Polynomial Whittle Estimation of Long-Range Dependence," University of California at San Diego, Economics Working Paper Series qt9wt048tt, Department of Economics, UC San Diego.
    5. Clifford Hurvich & Eric Moulines & Philippe Soulier, 2004. "Estimating Long Memory in Volatility," Econometrics 0412006, EconWPA.
    6. Violetta Dalla & Liudas Giraitis & Javier Hidalgo, 2006. "Consistent estimation of the memory parameter for nonlinear time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(2), pages 211-251, 03.
    7. Rohit Deo & Clifford Hurvich & Yi Lu, 2005. "Forecasting Realized Volatility Using a Long Memory Stochastic Volatility Model: Estimation, Prediction and Seasonal Adjustment," Econometrics 0501002, EconWPA.
    8. Hurvich, Clifford M. & Moulines, Eric & Soulier, Philippe, 2002. "The FEXP estimator for potentially non-stationary linear time series," Stochastic Processes and their Applications, Elsevier, vol. 97(2), pages 307-340, February.
    9. Robinson, Peter M. & Henry, Marc, 2003. "Higher-order kernel semiparametric M-estimation of long memory," Journal of Econometrics, Elsevier, vol. 114(1), pages 1-27, May.
    10. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
    11. Velasco, Carlos, 2000. "Non-Gaussian Log-Periodogram Regression," Econometric Theory, Cambridge University Press, vol. 16(01), pages 44-79, February.
    12. repec:cep:stiecm:/2006/497 is not listed on IDEAS
    13. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas, 2007. "Nonstationarity-extended local Whittle estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 1353-1384, December.
    14. Hurvich, Clifford & Lang, Gabriel & Soulier, Philippe, 2005. "Estimation of Long Memory in the Presence of a Smooth Nonparametric Trend," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 853-871, September.
    15. Stoev, Stilian & Taqqu, Murad S. & Park, Cheolwoo & Michailidis, George & Marron, J.S., 2006. "LASS: a tool for the local analysis of self-similarity," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2447-2471, May.
    16. Shimotsu, Katsumi & Phillips, Peter C.B., 2006. "Local Whittle estimation of fractional integration and some of its variants," Journal of Econometrics, Elsevier, vol. 130(2), pages 209-233, February.
    17. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(04), pages 549-582, August.
    18. J. Bardet & G. Lang & E. Moulines & P. Soulier, 2000. "Wavelet Estimator of Long-Range Dependent Processes," Statistical Inference for Stochastic Processes, Springer, vol. 3(1), pages 85-99, January.
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