- Statist. Surv.
- Volume 4 (2010), 117-147.
Discrete variations of the fractional Brownian motion in the presence of outliers and an additive noise
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.
Statist. Surv., Volume 4 (2010), 117-147.
First available in Project Euclid: 11 June 2010
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Achard, Sophie; Coeurjolly, Jean-François. Discrete variations of the fractional Brownian motion in the presence of outliers and an additive noise. Statist. Surv. 4 (2010), 117--147. doi:10.1214/09-SS059. https://projecteuclid.org/euclid.ssu/1276260873