Volume 17, 2013
|Page(s)||307 - 327|
|Published online||17 May 2013|
Local estimation of the Hurst index of multifractional Brownian motion by increment ratio statistic method
INRIA Saclay, 91893
2 Laboratoire de Mathématiques, UMR CNRS 6620 & Université de Clermont-Ferrand 2, France
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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