### Examples of Spectra of ARMA models

# --- Read code from S&S
source("http://www.stat.pitt.edu/stoffer/tsa2/Rcode/itall.R")

# --- Key routine for spectra plots is spec.arma  (from S&S)

spec.arma(ar=c(0.9), var.noise=1)
spec.arma(ar=c(-0.9), var.noise=1)

spec.arma(ar=c(1.2,-0.8))

r<-polyroot(c(1,-1.2,0.8))
abline(v=Arg(r[1])/(2*pi))

spec.arma(ar=c(1.2,-0.8), ma=c(0.5,0.3,0.7,0.6))
abline(v=Arg(r[1])/(2*pi))

# --- compare to estimates from data  (y-axis in plot on log scale)

spec.arma(ar=c(1.2,-0.8))
xt.256 <- arima.sim(model=list(ar=c(1.2,-0.8)), n=256, rand.gen=rnorm)
pg <- spec.pgram(xt.256, taper=0.1, detrend=FALSE, plot=FALSE)
points(pg$freq, pg$spec, col="darkgray")


spec.arma(ar=c(1.2,-0.8))
xt.512 <- arima.sim(model=list(ar=c(1.2,-0.8)), n=512, rand.gen=rnorm)
pg <- spec.pgram(xt.512, taper=0.1, detrend=FALSE, plot=FALSE)
points(pg$freq, pg$spec, col="lightblue")


spec.arma(ar=c(1.2,-0.8))
xt <- arima.sim(model=list(ar=c(1.2,-0.8)), n=1024, rand.gen=rnorm)
pg <- spec.pgram(xt, taper=0.1, detrend=FALSE, plot=FALSE)
points(pg$freq, pg$spec, col="darkgray")

# --- origin of smoothing...
pg <- spec.pgram(xt.256, taper=0.25, detrend=FALSE, plot=FALSE, kernel("modified.daniell", c(5,7)))
points(pg$freq, pg$spec, col="red")


# --- AR spectral estimate
spec.arma(ar=c(1.2,-0.8))
pg <- spec.pgram(xt.256, taper=0.1, detrend=FALSE, plot=FALSE)
points(pg$freq, pg$spec, col="darkgray")
ar <- spec.ar(xt.256, n.freq=128, plot=FALSE)
points(ar$freq, ar$spec, col="blue")