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

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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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Achard, S., & Coeurjolly, J. F. (2010). Discrete variations of the fractional brownian motion in the presence of outliers and an additive noise. Statistics Surveys, 4, 117–147. https://doi.org/10.1214/09-SS059

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