#Smoothing the periodogram: spec.pgram as last week
#regulate the amount of smoothing with the argument span

# Ocean wave data (From Percival and Walden)
ocw <- ts(scan(url("http://stat.ethz.ch/Teaching/Datasets/ocwave.dat")),
          frequency=4)
ocw <- ts(scan("Ocwave.sapa"),frequency=4)
plot(ocw)
acf(ocw,lag.max=100)
spec.pgram(ocw,taper=0,demean=TRUE,detrend=FALSE)
spec.pgram(ocw,demean=TRUE,detrend=FALSE,add=TRUE,col=2)
#notice again the advantage of tapering (taper has default value 0.1)
par(mfrow=c(3,1)) #smoothing the periodogram
spec.pgram(ocw,demean=TRUE,detrend=FALSE)
spec.pgram(ocw,spans=c(5,5))
spec.pgram(ocw,spans=c(11,11))
spec.ar(ar.mle(ocw)) #ar spectrum for comparison
spec.ar(ar.burg(ocw))


# To understand the argument span: Show the weights used for smoothing
sp  <- spec.pgram(ocw,spans=11,plot=FALSE)
sp$kernel
sp  <- spec.pgram(ocw,spans=c(11,11),plot=FALSE)
sp$kernel


#Lynx data
par(mfrow=c(3,1))
spec.pgram(log(lynx),demean=TRUE,detrend=FALSE)
spec.pgram(log(lynx),spans=c(3,3),demean=TRUE,detrend=FALSE)
spec.ar(ar.mle(log(lynx)))

#simulated AR(4), as used last week
ar.coef <- c(2.7607,-3.8106,2.6535,-0.9238)
x <- arima.sim(n=1024,model=list(ar=ar.coef))
par(mfrow=c(3,1))
spec.pgram(x,demean=TRUE,detrend=FALSE)
spec.pgram(x,spans=c(11,11),demean=TRUE,detrend=FALSE)
spec.ar(ar.mle(x,order.max=4))