Spectral desnity function for a fractionally differenced process.
USAGE:
wavFDPSDF( f, delta = 0.45, variance = 1 )
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 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.
REQUIRED ARGUMENTS:
f
A numeric value representing normalized frequency where the sampling interval is
unity.
OPTIONAL ARGUMENTS:
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:
result
The SDF values corresponding to the FD model parameters.
REFERENCES:
(1) D. B. Percival and A. T. Walden, ``Wavelet Methods for Time Series Analysis'',
Cambridge University Press, 2000.
SEE ALSO:
,
,
.
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)")