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)")