sdf: Spectral Density Functions for Long-Memory Processes In waveslim: Basic wavelet routines for one-, two- and three-dimensional signal processing

Description

Draws the spectral density functions (SDFs) for standard long-memory processes including fractional difference (FD), seasonal persistent (SP), and seasonal fractional difference (SFD) processes.

Usage

 ```1 2 3 4``` ```fdp.sdf(freq, d, sigma2 = 1) spp.sdf(freq, d, fG, sigma2 = 1) spp2.sdf(freq, d1, f1, d2, f2, sigma2 = 1) sfd.sdf(freq, s, d, sigma2 = 1) ```

Arguments

 `freq` vector of frequencies, normally from 0 to 0.5 `d,d1,d2` fractional difference parameter `fG,f1,f2` Gegenbauer frequency `s` seasonal parameter `sigma2` innovations variance

Value

The power spectrum from an FD, SP or SFD process.

Author(s)

Brandon Whitcher

`fdp.mle`, `spp.mle`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```dB <- function(x) 10 * log10(x) fdp.main <- expression(paste("FD", group("(",d==0.4,")"))) sfd.main <- expression(paste("SFD", group("(",list(s==12, d==0.4),")"))) spp.main <- expression(paste("SPP", group("(",list(delta==0.4, f[G]==1/12),")"))) freq <- 0:512/1024 par(mfrow=c(2,2), mar=c(5-1,4,4-1,2), col.main="darkred") plot(freq, dB(fdp.sdf(freq, .4)), type="l", xlab="frequency", ylab="spectrum (dB)", main=fdp.main) plot(freq, dB(spp.sdf(freq, .4, 1/12)), type="l", xlab="frequency", ylab="spectrum (dB)", font.main=1, main=spp.main) plot(freq, dB(sfd.sdf(freq, 12, .4)), type="l", xlab="frequency", ylab="spectrum (dB)", main=sfd.main) ```