| Issue |
ESAIM: PS
Volume 17, 2013
|
|
|---|---|---|
| Page(s) | 307 - 327 | |
| DOI | https://doi.org/10.1051/ps/2011154 | |
| Published online | 17 May 2013 | |
Local estimation of the Hurst index of multifractional Brownian motion by increment ratio statistic method
1
INRIA Saclay, 91893
Orsay Cedex,
France
2
Laboratoire de Mathématiques, UMR CNRS 6620 & Université
de Clermont-Ferrand 2, France
arnaud.guillin@math.univ-bpclermont.fr
Received: 22 October 2010
Revised: 13 April 2011
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.
Mathematics Subject Classification: 60G22 / 662M09
Key words: Increment ratio statistic / fractional Brownian motion / local estimation / multifractional Brownian motion / wavelet series representation
© EDP Sciences, SMAI, 2013
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