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Article Dans Une Revue Statistical Inference for Stochastic Processes Année : 2001

Estimating the parameters of a fractional Brownian motion by discrete variations of its sample paths

Résumé

This paper develops a class of consistent estimators of the parameters of a fractional Brownian motion based on the asymptotic behavior of the k-th absolute moment of discrete variations of its sampled paths over a discrete grid of the interval [0,1]. We derive explicit convergence rates for these types of estimators, valid through the whole range 0 < H < 1 of the self-similarity parameter. We also establish the asymptotic normality of our estimators. The effectiveness of our procedure is investigated in a simulation study.

Dates et versions

hal-00383118 , version 1 (12-05-2009)

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Jean-François Coeurjolly. Estimating the parameters of a fractional Brownian motion by discrete variations of its sample paths. Statistical Inference for Stochastic Processes, 2001, 4 (2), pp.199-227. ⟨10.1023/A:1017507306245⟩. ⟨hal-00383118⟩

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