Local estimation of the Hurst index of multifractional brownian motion by increment ratio statistic method
ESAIM: Probability and Statistics, Tome 17 (2013), pp. 307-327.

We investigate here the central limit theorem of the increment ratio statistic of a multifractional Brownian motion, leading to a CLT for the time varying Hurst index. The proofs are quite simple relying on Breuer-Major theorems and an original freezing of time strategy. A simulation study shows the goodness of fit of this estimator.

DOI : 10.1051/ps/2011154
Classification : 60G22, 662M09
Mots-clés : increment ratio statistic, fractional brownian motion, local estimation, multifractional brownian motion, wavelet series representation 
@article{PS_2013__17__307_0,
     author = {Bertrand, Pierre Rapha\"el and Fhima, Mehdi and Guillin, Arnaud},
     title = {Local estimation of the {Hurst} index of multifractional brownian motion by increment ratio statistic method},
     journal = {ESAIM: Probability and Statistics},
     pages = {307--327},
     publisher = {EDP-Sciences},
     volume = {17},
     year = {2013},
     doi = {10.1051/ps/2011154},
     mrnumber = {3066382},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ps/2011154/}
}
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Bertrand, Pierre Raphaël; Fhima, Mehdi; Guillin, Arnaud. Local estimation of the Hurst index of multifractional brownian motion by increment ratio statistic method. ESAIM: Probability and Statistics, Tome 17 (2013), pp. 307-327. doi : 10.1051/ps/2011154. http://www.numdam.org/articles/10.1051/ps/2011154/

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