Discrete variations of the fractional brownian motion in the presence of outliers and an additive noise

Statistics Surveys

Volumn 4, Issue , 2010, Pages 117-147

  Achard, Sophie ^a   Coeurjolly, Jean François ^b  

^a CNRS   (France)

^b UNIV GRENOBLE ALPES   (France)

Author keywords

Discrete variations; Fractional Brownian motion; Hurst exponent estimation; Outliers; Robustness

Indexed keywords

EID: 77955524249     PISSN: None     EISSN: 19357516     Source Type: Journal    
DOI: 10.1214/09-SS059     Document Type: Article

References (21)

1. S. Baykut, T. Akgül, and S. Ergintav. Estimation of spectral exponent parameter of 1/f process in additive white background noise. EURASIP Journal on Advances in Signal Processing, 2007(15):1-7, 2007.
2. J. Beran. Statistics for long-memory processes. Chapman & Hall/CRC, 1994.
3. A. Brouste, J. Istas, and S. Lambert-Lacroix. On Fractional Gaussian Random Fields Simulations. Journal of Statistical Software, 23(1): 1-23, 2007.
4. G. Chan and A.T.A. Wood. Estimation of fractal dimension for a class of non-Gaussian stationary processes and fields. Annals of Statistics, 32(3):1222-1260, 2004.
5. J.-F. Coeurjolly. Simulation and identification of the fractional Brownian motion: a bibliographical and comparative study. J. Stat. Softw., 5(7):1-53, November 2000a.
6. J.-F. Coeurjolly. Estimating the parameters of a fractional Brownian motion by discrete variations of its sample paths. Stat. Infer. Stoch. Process., 4(2): 199-227, January 2001.
7. J.-F. Coeurjolly. Identification of multifractional Brownian motion. Bernoulli, 11(6):987-1008, 2005.
8. J.-F. Coeurjolly. Hurst exponent estimation of locally self-similar gaussian processes using sample quantiles. Annals of Statistics, 36(3):1404-1434, 2008.
9. J.-F. Coeurjolly. Inférence statistique pour les mouvements Browniens fractionnaire et multifractinonaire. PhD thesis, Université Joseph Fourier, 2000b.
10. S. Cohen and J. Istas. An universal estimator of local self-similarity. ESAIM: Probability and Statistics, 2002.
11. I. Daubechies. Orthonormal bases of compactly supported wavelets. Communications on Pure and, Applied Mathematics, 41 (7):909-996, 2006.
12. J.L. Doob. Stochastic Processes. Wiley Classics Library, USA, 1953.
13. P. Doukhan, G. Oppenheim, and M.S. Taqqu. Theory and applications of long-range dependence. Birkhauser, 2003.
14. G. Fäy, E. Moulines, F. Roueff, and M.S. Taqqu. Estimators of longmemory: Fourier versus wavelets. Journal of Econometrics, 151(2):159-177, 2009.
15. J. Istas. Quadratic variations of spherical fractional Brownian motions. Stochastic Processes and their Applications, 117 (4):476-486, 2007.
16. J. Istas and G. Lang. Quadratic variations and estimation of the hölder index of a gaussian process. Ann. Inst. H. Poincaré Probab. Statist., 33: 407-436, 1997.
17. J.T. Kent and A.T.A. Wood. Estimating the fractal dimension of a locally self-similar gaussian process using increments. J. Roy. Statist. Soc. Ser. B, 59:679-700, 1997.
18. B. Mandelbrot and J. Van Ness. Fractional brownian motions, fractional noises and applications. SIAM Rev., 10:422-437, 1968.
19. D. B. Percival and A. T. Walden. Wavelet Methods for Time Series Analysis. Cambridge University Press, 2000.
20. F. Richard and H. Biermé. Estimation of anisotropic gaussian fields through radon transform. ESAIM Probab. Stat., 12(1):30-50, 2008.
21. Haipeng Shen, Zhengyuan Zhu, and Thomas C. M. Lee. Robust estimation of the self-similarity parameter in network traffic using wavelet transform. Signal Process., 87(9):2111-2124, 2007.