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Local estimation of the Hurst index of multifractional Brownian motion by increment ratio statistic method
Pierre Raphaël Bertrand, Mehdi Fhima, Arnaud Guillin
Journal:

ESAIM: Probability and Statistics / Volume 17 / 2013

Published online by Cambridge University Press:

17 May 2013, pp. 307-327

Print publication:

2013
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We investigate here the central limit theorem of the increment ratio statistic of amultifractional Brownian motion, leading to a CLT for the time varying Hurst index. Theproofs are quite simple relying on Breuer–Major theorems and an original freezingof time strategy. A simulation study shows the goodness of fit of thisestimator.