Lpvar: Log Periodogram Variance Function

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

Description

Log Periodogram Variance Function to be minimized to estimate the parameters of a fractional Gaussian noise.

Usage

Lpvar(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 log periodogram variance function is determined as

ε (f)\equiv \log ≤ft ( \frac{I(f)}{S_X(f)} \right )+γ .

See Percival and Walden (2000) for details. Some parts of this function were adopted from the S-PLUS codes originally developed by Jan Beran.

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.

Percival and Walden (2000) Wavelet Methods for Time Series Analysis, Cambridge University Press.

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

See Also

Qeta, Csum, QLCfun

Examples

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

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