Csum: Cumulative Qeta Difference Function

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

Description

Cumulative Qeta Difference Function to be minimized to estimate the parameters of a fractional Gaussian noise.

Usage

Csum(eta,n,yper,snr,pertype)

Arguments

eta	a positive value of the Hurst exponent which is less than 1.
n	the number of time points.
yper	a vector of periodogram with length of the largest integer less than (n-1)/2
snr	the signal-to-noise ratio.
pertype	the type of periodogram. Possible modes are "per","taper".

Details

Let I(f_i) and S(f_i) be respectively the periodogram of a given perturbed fractional Gaussian noise and the spectral density of perturbed fGn with Hurst exponent eta and the signal-to-noise ratio SNR where f_i=2π *i/n with i=1,...,(n-1)/2. Then, the value of cumulative Qeta difference function is determined as

η =\frac{1}{m^*}∑_{t=1}^{m^*}≤ft ( I_t-S_t \right )^2

where

I_t=∑_{j=1}^{t}I(f_j)/∑_{j=1}^{m^*}I(f_j) and S_t=∑_{j=1}^{t}S_X(f_j)/∑_{j=1}^{m^*}S_X(f_j).

Some parts of this function were adopted from the S-PLUS codes originally developed by Jan Beran. See Beran (1994) for details.

Value

A,B,Tn	defined in Qeta.
z	the test statistics
pval	the p-value
fspec	a vector of spectral density with length of the largest integer less than (m-1)/2.
theta1	a value of the first component of theta.
value	a value for minimization

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

Qeta, Lpvar, QLCfun

Examples

n<-1000; H<-0.7; SNR<-10
ts <- perturbFGN(n,H,type="WN",SNR=SNR)
yper<-per(ts)
ts.csum<-Csum(H,n,yper,snr=SNR,pertype="per")

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