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Estimating the parameters of a fractional Brownian motion by discrete variations of its sample paths. (English) Zbl 0984.62058
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:
62M05Markov processes: estimation
62G20Nonparametric asymptotic efficiency
62G05Nonparametric estimation
62M10Time series, auto-correlation, regression, etc. (statistics)
60J65Brownian motion