dvFBM: Discrete Variations estimate for a contaminated fBm

In dvfBm: Discrete variations of a fractional Brownian motion

Description

Robust estimator of the Hurst parameter of a fractional Brownian possibly contaminated by additive outliers and/or an additive noise.

Usage

dvFBM(fbm, nma = "i2", M1 = 1, M2 = 5, method = c("ST", "Q", "TM", 
	"B1-ST", "B1-Q", "B1-TM", "B0-ST", "B0-Q", "B0-TM"), 
	par = list(), llplot = FALSE)

Arguments

fbm	data
nma	name of the filter used for filtering the data. See filt for possible choices. Default is "i2"
M1	Minimum value of the dilatation factor. Default is 1.
M2	Maximum value of the dilatation factor. Default is 5.
method	Type of the discrete variations method.
par	Parameters depending on method. If method is "Q","B0-Q","B1-Q", a list with two vectors vecp and vecc is needed. If method is "TM","B0-TM","B1-TM", a list with two real numbers beta1 and beta2 is needed.
llplot	If true a plot of \log(U_n^{a^m}) against \log(m) for m=M_1,...,M_2 is produced.

Details

An estimate of the Hurst exponent parameter is provided without estimating the scaling coefficient C and σ (parameter related to an additive noise). The standard method ST is based on filtering the data with dilated versions of the initial filter (whose name is nma). Other methods are improvements. Methods TM and Q are based on trimmed-means and sample quantiles respectively. Methods B0 and B1 exploit the fact that the contamination is a Brownian motion or a Gaussian white noise. Other methods are combinations of the two last classes. See Achard and Coeurjolly (2009) for more details.

Value

Returns the Hurst parameter estimate

Author(s)

J.-F. Coeurjolly

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, perturbFBM

Examples

n<-10000;H<-.8
## no
z<-perturbFBM(n,H,type="no",plot=FALSE)
dvFBM(z,method="ST")
dvFBM(z,method="TM",par=list(beta1=.1,beta2=.1))
dvFBM(z,method="B0-Q",par=list(vecp=.5,vecc=1))
dvFBM(z,method="B1-ST")
## AO
z<-perturbFBM(n,H,type="AO",SNR=-20,plot=FALSE)
dvFBM(z,nma="d4",method="ST")
dvFBM(z,nma="d4",method="TM",par=list(beta1=.1,beta2=.1))
## B0
z<-perturbFBM(n,H,type="B0",SNR=0,plot=FALSE)
dvFBM(z,M2=10,method="ST")
dvFBM(z,M2=10,method="B0-ST")
## B1
z<-perturbFBM(n,H,type="B1",SNR=0,plot=FALSE)
dvFBM(z,method="ST")
dvFBM(z,method="B1-ST")

Example output

Loading required package: wmtsa
log(M1:M2) 
 0.8116682 
log(M1:M2) 
 0.8151357 
log(M1:M2) 
  0.658582 
log(M1:M2) 
 0.7528026 
log(M1:M2) 
 0.7410485 
log(M1:M2) 
 0.8353641 
log(M1:M2) 
 0.6586828 
log(M1:M2) 
   0.75618 
log(M1:M2) 
 0.4224629 
log(M1:M2) 
 0.7535343 

dvfBm documentation built on May 29, 2017, 9:08 p.m.