Estimating the Parameters of a Fractional Brownian Motion by Discrete Variations of its Sample Paths
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- Coeurjolly, JF. Statistical Inference for Stochastic Processes (2001) 4: 199. doi:10.1023/A:1017507306245
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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.