wmtsa (version 1.1-1)

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 $\sigma_\varepsilon^2$ 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. T

variance

the FD innovations variance. Default: 1.

Value

• the SDF values corresponding to the FD model parameters.

concept

fractionally differenced (FD) processspectral density function generation

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)")