%0 Journal Article
%T Discrete variations of the fractional Brownian motion in the presence of outliers and an additive noise
%A Sophie Achard
%A Jean-Fran£żois Coeurjolly
%J Statistics Surveys
%D 2010
%I Statistics Surveys
%X 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.
%K Fractional Brownian motion
%K Hurst exponent estimation
%K Discrete variations
%K Robustness
%K Outliers
%U http://projecteuclid.org/euclid.ssu/1276260873