Local estimation of the Hurst index of multifractional brownian motion by increment ratio statistic method

Pierre Raphaël Bertrand; Mehdi Fhima; Arnaud Guillin

ESAIM: Probability and Statistics (2013)

  • Volume: 17, page 307-327
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Bertrand, Pierre Raphaël, Fhima, Mehdi, and Guillin, Arnaud. "Local estimation of the Hurst index of multifractional brownian motion by increment ratio statistic method." ESAIM: Probability and Statistics 17 (2013): 307-327. <http://eudml.org/doc/274365>.

@article{Bertrand2013,
abstract = {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.},
author = {Bertrand, Pierre Raphaël, Fhima, Mehdi, Guillin, Arnaud},
journal = {ESAIM: Probability and Statistics},
keywords = {increment ratio statistic; fractional brownian motion; local estimation; multifractional brownian motion; wavelet series representation; multifractional Brownian motion},
language = {eng},
pages = {307-327},
publisher = {EDP-Sciences},
title = {Local estimation of the Hurst index of multifractional brownian motion by increment ratio statistic method},
url = {http://eudml.org/doc/274365},
volume = {17},
year = {2013},
}

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
PB - EDP-Sciences
VL - 17
SP - 307
EP - 327
AB - 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.
LA - eng
KW - increment ratio statistic; fractional brownian motion; local estimation; multifractional brownian motion; wavelet series representation; multifractional Brownian motion
UR - http://eudml.org/doc/274365
ER -

References

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