wavFDPSDF: Spectral density function for a fractionally differenced...
In wconstan/wmtsa: Wavelet Methods for Time Series Analysis

Description Usage Arguments Value References See Also Examples

Returns the spectral density function (SDF) for a fractionally differenced (FD) process. Given a unit sampling rate, the SDF for an FD proces is

variance / abs(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.

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

`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`.

the SDF values corresponding to the FD model parameters.

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

wavFDPBand, wavFDPBlock, wavFDPTime.

## 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)")