# March 23 2001
# Script for periodogram examples for spectral density course

library(ts)      # need ts
data(sunspots)   # attach the sunspot data

euler_-0.577216
var.log.exp_pi^2/6
var.exp_1

sunspot.pgram_pgram(sunspots)


f.hat.plt.eg2_function(m=15,x.pgram,bands=T){
 par(oma=c(0,0,4,0))
 txt_paste( c("Daniell Smooth, m = ",m),collapse="")
 k.daniell_kernel("daniell",m=m)
# f.hat_kernapply(x.pgram$pgram/(2*pi),k.daniell)
 freq_x.pgram$freq[m:(length(x.pgram$pgram)-(m+1))]
 log.f.hat_kernapply(log(x.pgram$pgram/(2*pi)),k.daniell)
if(bands==T){
 log.f.ci.up_log.f.hat+2*sqrt(var.log.exp/(2*m+1))
 log.f.ci.low_log.f.hat-2*sqrt(var.log.exp/(2*m+1))
 ylim_c(min(log.f.hat,log.f.ci.low), max(log.f.hat,log.f.ci.up))
 plot(freq,log.f.hat,type="l",main=txt,ylim=ylim)
 lines(freq,log.f.ci.up,lty=2)
 lines(freq,log.f.ci.low,lty=2)
}
else{
 plot(freq,log.f.hat,type="l",main=txt)
}

 mtext("Monthly Sunspot Smoothed Log Periodogram", outer=T,side=3,line=3,cex=1.5)
}



f.hat.plt.eg2(15,sunspot.pgram,bands=T)
f.hat.plt.eg2(25,sunspot.pgram,bands=T)