Local estimation of the Hurst index of multifractional Brownian motion by Increment Ratio Statistic method

2010/10/23 by Pierre R. Bertrand, Bertrand, Pierre R., Mehdi Fhima +3
Mathematics · #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST) #math.PR #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1010.4849

arxiv created 2010/10/23 · arxiv updated 2010/10/27

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.

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