##monthly feb 1978-aug 1995
auemp<-ts(scan("unemploy.dat", skip=1))
dauemp<-ts(diff(auemp))


#temp<-spec.pgram(reslauemp, taper=0, log="no")
#freq=temp$freq[temp$spec>0.005]
#periods=1/temp$freq[temp$spec>0.005]


pdf("au.pdf")

plot(auemp)

lauemp<-log(auemp)
smoothlauemp<-filter(lauemp,rep(1,12)/12)
plot(smoothlauemp)
reslauemp<-smoothlauemp-lauemp
reslauemp<-reslauemp[!is.na(reslauemp)]
t<-1:length(reslauemp)
c1<-cos(2*pi*t/12)
s1<-sin(2*pi*t/12)
c2<-cos(2*pi*t/6)
s2<-sin(2*pi*t/6)
c3<-cos(2*pi*t/4)
s3<-sin(2*pi*t/4)
c4<-cos(2*pi*t/3)
s4<-sin(2*pi*t/3)
c5<-cos(2*pi*t/2.4)
s5<-sin(2*pi*t/2.4)
plot(ts(reslauemp))
acf(reslauemp)
spec.pgram(reslauemp,taper=0, log="no",na.action = na.pass)
fit1<-lm(reslauemp~c1+s1+c2+s2+c3+s3+c4+s4+c5+s5)
plot(ts(residuals(fit1)))
acf(residuals(fit1))
spec.pgram(residuals(fit1),taper=0, log="no")



t<-1:length(auemp)
t2<-t^2
t3<-t^3
c1<-cos(2*pi*t/12)
s1<-sin(2*pi*t/12)
c2<-cos(2*pi*t/6)
s2<-sin(2*pi*t/6)
c3<-cos(2*pi*t/4)
s3<-sin(2*pi*t/4)
c4<-cos(2*pi*t/3)
s4<-sin(2*pi*t/3)
c5<-cos(2*pi*t/2.4)
s5<-sin(2*pi*t/2.4)



lauemp<-log(auemp)
smoothlauemp<-ts(supsmu(1:length(auemp),lauemp,span=0.1)$y)
plot(smoothlauemp)
reslauemp<-smoothlauemp-lauemp
plot(reslauemp)
acf(reslauemp)
spec.pgram(reslauemp,taper=0, log="no")
fit1<-lm(reslauemp~c1+s1+c2+s2+c3+s3+c4+s4+c5+s5)
plot(ts(residuals(fit1)))
acf(residuals(fit1))
spec.pgram(residuals(fit1),taper=0, log="no")

lauemp<-log(auemp)
smoothlauemp<-ts(supsmu(1:length(auemp),lauemp,span=0.03)$y)
plot(smoothlauemp)
reslauemp<-smoothlauemp-lauemp
plot(reslauemp)
acf(reslauemp)
spec.pgram(reslauemp,taper=0, log="no")
fit1<-lm(reslauemp~c1+s1+c2+s2+c3+s3+c4+s4+c5+s5)
plot(ts(residuals(fit1)))
acf(residuals(fit1))
spec.pgram(residuals(fit1),taper=0, log="no")


lauemp<-log(auemp)
smoothlauemp<-ts(ksmooth(1:length(auemp),lauemp,"normal",bandwidth=15)$y)
plot(smoothlauemp)
reslauemp<-smoothlauemp-lauemp
plot(reslauemp)
acf(reslauemp)
spec.pgram(reslauemp,taper=0, log="no")
fit1<-lm(reslauemp~c1+s1+c2+s2+c3+s3+c4+s4+c5+s5)
plot(ts(residuals(fit1)))
acf(residuals(fit1))
spec.pgram(residuals(fit1),taper=0, log="no")


lauemp<-log(auemp)
smoothlauemp<-ts(ksmooth(1:length(auemp),lauemp,"normal",bandwidth=2)$y)
plot(smoothlauemp)
reslauemp<-smoothlauemp-lauemp
plot(reslauemp)
acf(reslauemp)
spec.pgram(reslauemp,taper=0, log="no")
fit1<-lm(reslauemp~c1+s1+c2+s2+c3+s3+c4+s4+c5+s5)
plot(ts(residuals(fit1)))
acf(residuals(fit1))
spec.pgram(residuals(fit1),taper=0, log="no")



dlauemp<-diff(lauemp)
plot(dlauemp)
acf(dlauemp)
spec.pgram(dlauemp,taper=0, log="no")
fit1<-lm(reslauemp~c1+s1+c2+s2+c3+s3+c4+s4+c5+s5)
plot(ts(residuals(fit1)))
acf(residuals(fit1))
spec.pgram(residuals(fit1),taper=0, log="no")


dev.off()