dvfBm (version 1.0)

perturbFBM: Simulation of a perturbed fBm

Description

Simulation of a sample path of a fractional Brownian motion contaminated by outliers or an additive Gaussian noise

Usage

perturbFBM(n, H, C = 1, type = "no", SNR=NULL,plot = FALSE)

Arguments

n

sample size

H

Hurst parameter

C

scaling coefficient. Default is 1

type

type of perturbation. Possible choices are "no","B0","B1","AO"

SNR

Signal Noise Ratio parameter for the contamination

plot

if plot is TRUE a (2,2) plot of the sample path of the fractional Brownian motion, the fractional Gaussian noise and their contaminated version is produced. Default is FALSE

Value

• returns a vector of length n of a dsicretized sample path of a fractional Brownian motion with parameters (H,C) at times $i=1,...,n$ possibly contaminated by an additive outliers models, a Brownian motion or a Gaussian white noise.

Details

Possible contaminated models are [object Object],[object Object],[object Object],[object Object] See Achard and Coeurjolly (2009) for a more detailed description.

References

S. Achard and J.-F. Coeurjolly (2009). Discrete variations of the fractional Brownian in the presence of outliers and an additive noise. Submitted

See Also

circFBM, dvFBM

Examples

n<-1000;H1<-.3;H2<-.8
## "no"
tmp1<-perturbFBM(n,H1,type="no",plot=TRUE)
tmp2<-perturbFBM(n,H2,type="no",plot=TRUE)
## "AO"
tmp3<-perturbFBM(n,H1,type="AO",SNR=0,plot=TRUE)
tmp4<-perturbFBM(n,H2,type="AO",SNR=-20,plot=TRUE)
## "B0"
tmp5<-perturbFBM(n,H1,type="B0",SNR=10,plot=TRUE)
tmp6<-perturbFBM(n,H2,type="B0",SNR=0,plot=TRUE)
## "B1"
tmp7<-perturbFBM(n,H1,type="B1",SNR=10,plot=TRUE)
tmp8<-perturbFBM(n,H2,type="B1",SNR=0,plot=TRUE)