wmtsa (version 2.0-2)

wavFDPSDF: Spectral density function for a fractionally differenced process

Description

Returns the spectral density function (SDF) for a fractionally differenced (FD) process. Given a unit sampling rate, the SDF for an FD proces is $$ {\sigma_\varepsilon^2 \over |2 \sin(\pi f)|^{2 \delta}}, $$ where $variance$ is the innovations variance, $delta$ is the FD parameter, and $f$ is the normalized frequency for $|f| < 1/2$.

Usage

wavFDPSDF(f, delta=0.45, variance=1, response=NULL)

Arguments

f

a numeric value representing normalized frequency where the sampling interval is unity.

delta

the FD parameter. Default: 0.45.

response

a list containing the objects frequency and sqrgain which represent, respectively, a numeric normalized frequency vector corresponding to a wavelet squared gain response at a particular wavelet decomposition level. This argument typically will not be set by the user. Rather, it is used internally by FD process maximum likelihood estimators. Default: NULL.

variance

the FD innovations variance. Default: 1.

Value

the SDF values corresponding to the FD model parameters.

References

D. B. Percival and A. T. Walden, Wavelet Methods for Time Series Analysis, Cambridge University Press, 2000, 340--92.

See Also

wavFDPBand, wavFDPBlock, wavFDPTime.

Examples

## create a normalized frequency vector 
f <- seq(from=1e-2, to=1/2, length=100)

## calculate the FDP SDF for delta=0.45 and unit 
## innovations variance 
S <- wavFDPSDF(f, delta=0.45, variance=1)

## plot the results 
plot(f, S,log="xy", xlab="Frequency", ylab="SDF of FDP(0.45, 1)")