wavFDPSDF {wmtsa} | R Documentation |
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.
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)")