Exact confidence intervals for the hurst parameter of a fractional brownian motion

Electronic Journal of Statistics

Volumn 3, Issue , 2009, Pages 416-425

  Breton, Jean Christophe ^a   Nourdin, Ivan ^b   Peccati, Giovanni ^c  

^a UNIVERSITÉ DE LA ROCHELLE   (France)

^b SORBONNE UNIVERSITÉ   (France)

^c UNIVERSITÉ PARIS OUEST NANTERRE LA DÉFENSE   (France)

Author keywords

Concentration inequalities; Exact confidence intervals; Fractional brownian motion; Hurst parameter

Indexed keywords

EID: 70450259195     PISSN: 19357524     EISSN: None     Source Type: Journal    
DOI: 10.1214/09-EJS366     Document Type: Article

References (15)

1. J. Beran (1994). Statistics for Long-Memory Processes. Chapman and Hall.
2. Ch. Borell (1978). Tail probabilities in Gauss space. In Vector Space Measures and Applications, Dublin, 1977. Lecture Notes in Math. 644, 71-82. Springer-Verlag.
3. J.-C. Breton and I. Nourdin (2008). Error bounds on the non-normal approximation of Hermite power variations of fractional Brownian motion. Electron. Comm. Probab. 13, 482-493.
4. P. Breuer and P. Major (1983). Central limit theorems for nonlinear functionals of Gaussian fields. J. Multivariate Anal. 13(3), 425-441.
5. J.F. Coeurjolly (2001). Estimating the parameters of a fractional Brownian motion by discrete variations of its sample paths. Statist. Inf. Stoch. Proc. 4, 199-227.
6. R. Fox and M.S. Taqqu (1986). Large sample properties of parameter estimates for strongly dependent stationary Gaussian time series. Ann. Stat. 14(2), 517-532.
7. L. Giraitis and P.M. Robinson (2003). Edgeworth expansion for semiparametric Whittle estimation of long memory. Ann. Stat. 31(4), 1325-1375.
8. J. Istas and G. Lang (1997). Quadratic variations and estimation of the local Hölder index of a Gaussian process. Ann. Inst. H. Poincaré Probab. Statist. 33(4), 407-436.
9. I. Nourdin and G. Peccati (2008). Stein’s method on Wiener chaos. Probab. Theory Rel. Fields, to appear.
10. I. Nourdin and F.G. Viens (2008). Density formula and concentration inequalities with Malliavin calculus. Available at: www.proba.jussieu.fr/pageperso/nourdin/nourdin-viens.pdf.
11. D. Nualart (2006). The Malliavin calculus and related topics. Springer-Verlag, Berlin, 2nd edition.
12. V. Pipiras and M.S. Taqqu (2003). Fractional calculus and its connection to fractional Brownian motion. In: Long Range Dependence, 166-201, Birkhäuser, Basel.
13. D. Nualart and S. Ortiz-Latorre (2008). Central limit theorem for multiple stochastic integrals and Malliavin calculus. Stoch. Proc. Appl. 118(4), 614-628.
14. I. Shigekawa (1978). Absolute continuity of probability laws of Wiener functionals. Proc. Japan. Acad., 54(A), 230-233.
15. C.A. Tudor and F.G. Viens (2007). Variations and estimators for selfsimilarity parameters via Malliavin calculus. Ann. Probab., to appear.