options(windowsBuffered=FALSE)
y=scan('F:/Math355/SPIRITS.txt',skip=2,nline=4)
yts=ts(log(y))
plot(yts,main="Log Quarterly Sales of Alcoholic Spirits",type='b',col=2)

n=length(y)
time=seq(1:n)
quarter=c(rep(seq(1:4),10))
quarter
fquarter=as.factor(quarter)

ymod1=lm(yts~time+fquarter)
summary(ymod1)
yfit1=ymod1$fitted
lines(yfit1,col=3)

yres1=ymod1$res
plot(yres1)

ymod2=lm(y~time+cos(2*pi*time/4)+sin(2*pi*time/4))
summary(ymod2)
yfit2=ymod2$fitted
plot(yts,main="Quarterly Sales of Alcoholic Spirits in Log Transcations",type='p',col=2)
lines(yfit2,col=4)

ymod3=lm(y~time+cos(2*pi*time/4)+sin(2*pi*time/4)+cos(2*pi*time/2)+sin(2*pi*time/2))
summary(ymod3)
yfit3=ymod3$fitted
plot(yts,main="Quarterly Sales of Alcoholic Spirits in Log Transcations",type='p',col=2)
lines(yfit2,col=4)

ymod3=lm(y~time+cos(2*pi*time/4)+sin(2*pi*time/4)+cos(2*pi*time/1)+sin(2*pi*time/1))
summary(ymod3)
yfit3=ymod3$fitted
plot(yts,main="Quarterly Sales of Alcoholic Spirits in Log Transcations",type='p',col=2)
lines(yfit2,col=4)

yspec=spec.pgram(yts,pad=4,detrend=TRUE)
plot(yspec$freq,yspec$spec,type='l',col=5)

resspec=spec.pgram(ymod3$res,pad=4,detrend=FALSE)
plot(resspec$freq,resspec$spec,type='l',col=5)

acf(ymod3$res,lag.max=20,col=6)
pacf(ymod3$res,lag.max=20,col=6)