R: Spectral Density Functions for Long-Memory Processes

Spectral Density Functions {waveslim} | R Documentation

## Spectral Density Functions for Long-Memory Processes

### 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

    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

### See Also

`fdp.mle`, `spp.mle`.

### Examples

    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)

[Package waveslim version 1.8.3 Index]