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Zbl 0984.62058
Coeurjolly, Jean-François
Estimating the parameters of a fractional Brownian motion by discrete variations of its sample paths. (English)
[J] Stat. Inference Stoch. Process. 4, No.2, 199-227 (2001). ISSN 1387-0874; ISSN 1572-9311/e

Summary: 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.

MSC 2000:: *62M05 Markov processes: estimation
62G20 Nonparametric asymptotic efficiency
62G05 Nonparametric estimation
62M10 Time series, etc. (statistics)
60J65 Brownian motion

Keywords: fractional Gaussian noise; discrete variations; consistency; fractional Brownian motion; self-similarity

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