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

Pierre Raphaël BertrandMehdi FhimaArnaud Guillin — 2013

ESAIM: Probability and Statistics

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 strategy. A simulation study shows the goodness of fit of this estimator.

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