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Discrete variations of the fractional Brownian motion in the presence of outliers and an additive noise

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Author(s): Sophie Achard | Jean-François Coeurjolly

Journal: Statistics Surveys
ISSN 1935-7516

Volume: 4;
Start page: 117;
Date: 2010;
Original page

Keywords: Fractional Brownian motion | Hurst exponent estimation | Discrete variations | Robustness | Outliers

ABSTRACT
This paper gives an overview of the problem of estimating the Hurst parameter of a fractional Brownian motion when the data are observed with outliers and/or with an additive noise by using methods based on discrete variations. We show that the classical estimation procedure based on the log-linearity of the variogram of dilated series is made more robust to outliers and/or an additive noise by considering sample quantiles and trimmed means of the squared series or differences of empirical variances. These different procedures are compared and discussed through a large simulation study and are implemented in the R package dvfBm.
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