wFGN: The Whittle estimator for a contaminated fGn

In wonsang/wfGn: Estimation of the Hurst Parameter for Contaminated Fractional Gaussian Noises

Description

Whittle estimator of the Hurst parameter of a fractional Gaussian noise contaminated by additive outliers or noise.

Usage

wFGN(x, istart=1, iend=length(x), nloop=1, init=c(0.55,0.01), 
		ndeps=c(1e-7,1e-2), noise=TRUE, pertype="per", minfun="qeta", 
		weights=c(1,1,0), cluster=FALSE, print.level=2)

Arguments

x	a time series
istart	the index of start. Default is 1
iend	the index of end. Default is the length of x.
nloop	the number of sub-series. The Hurst parameter of each sub-series is estimated respectively. Default is 1.
init	the initial search values of Hurst parameter and SNR. Default is c(0.55,0.01).
ndeps	A vector of step sizes for optimization. Default is c(1e-7,1e-2).
noise	Enable the assumption of noise corruption. Default is TRUE.
pertype	type of periodogram. Possible modes are "per","taper".
minfun	type of minimization function. Possible modes are "qeta","lp","csum", and "combi".
weights	A vector of weights for each minimization function when minfun="combi".
cluster	A vector of machine names for parallel processing. For details, refer to the manual of package genoud.
print.level	The logic value which controls the printing level. Four levels are available: 0 (minimal), 1 (normal), 2 (detailed), and 3 (debug). Default is 2. Refer to the manual of package rgenoud for details.

Details

The Hurst parameter of a pure or corrupted fractional Gaussian noise is estimated by a modified Whittle estimator. The most parts of this function were adopted from the S-PLUS codes originally developed by Jan Beran. See Beran (1994) for details.

Value

thetavector	a vector of scaling coefficient and Hurst parameter
Hlow	the lower limit of 95\% confidence interval of Hurst parameter
Hup	the upper limit of 95\% confidence interval of Hurst parameter
SNR	the signal-to-noise ratio
fest	the spectral density of an estimated fGn

Author(s)

Wonsang You

References

Wonsang You (2010) Modified Whittle's Maximum Likelihood Estimator for Fractional Gaussian Noises Contaminated by Additive Noises, Technical Reports of the Leibniz Institute for Neurobiology, TR10015.

Jan Beran (1994) Statistics for Long-Memory Processes, Chapman & Hall.

See Also

circFGN, perturbFGN, wFGN.eval

Examples

n<-1000; H1<-0.2; H2<-0.7
ts1 <- circFGN(n,H1)
dat1 <- wFGN(ts1,noise=FALSE)
ts2 <- perturbFGN(n,H2,type="WN",SNR=10)
dat2 <- wFGN(ts2,pertype="per",minfun="combi")

wonsang/wfGn documentation built on May 14, 2019, 9:25 p.m.