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

Published online by Cambridge University Press:  17 May 2013

Pierre Raphaël Bertrand ,
Mehdi Fhima  and
Arnaud Guillin
Pierre Raphaël Bertrand
Affiliation:
INRIA Saclay, 91893 Orsay Cedex, France Laboratoire de Mathématiques, UMR CNRS 6620 & Université de Clermont-Ferrand 2, France. arnaud.guillin@math.univ-bpclermont.fr
Mehdi Fhima
Affiliation:
Laboratoire de Mathématiques, UMR CNRS 6620 & Université de Clermont-Ferrand 2, France. arnaud.guillin@math.univ-bpclermont.fr
Arnaud Guillin
Affiliation:
Laboratoire de Mathématiques, UMR CNRS 6620 & Université de Clermont-Ferrand 2, France. arnaud.guillin@math.univ-bpclermont.fr
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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.

Keywords

Increment ratio statisticfractional Brownian motionlocal estimationmultifractional Brownian motionwavelet series representation
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 17 , 2013 , pp. 307 - 327
Copyright
© EDP Sciences, SMAI, 2013

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