Qeta: Qeta function

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

Description

Function to be minimized to obtain the maximum likelihood of a fractional Gaussian noise.

Usage

Qeta(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 is determined as

B=\frac{2π}{n}∑_{i}2\times ≤ft [ \frac{I(f_i)}{S(f_i)} \right ]^2.

Also, A and Tn are defined as follows.

A=\frac{2π}{n}∑_{i}2\times ≤ft [ \frac{I(f_i)}{S(f_i)} \right ], T_n=\frac{A}{B^2}

The most 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 the above section
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)

Jan Beran (original) and Wonsang You (modifying)

References

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

See Also

Csum, Lpvar, QLCfun

Examples

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

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