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.
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/}
}
TY - JOUR AU - Bertrand, Pierre Raphaël AU - Fhima, Mehdi AU - Guillin, Arnaud TI - Local estimation of the Hurst index of multifractional brownian motion by increment ratio statistic method JO - ESAIM: Probability and Statistics PY - 2013 SP - 307 EP - 327 VL - 17 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2011154/ DO - 10.1051/ps/2011154 LA - en ID - PS_2013__17__307_0 ER -
%0 Journal Article %A Bertrand, Pierre Raphaël %A Fhima, Mehdi %A Guillin, Arnaud %T Local estimation of the Hurst index of multifractional brownian motion by increment ratio statistic method %J ESAIM: Probability and Statistics %D 2013 %P 307-327 %V 17 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2011154/ %R 10.1051/ps/2011154 %G en %F PS_2013__17__307_0
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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