library(TSA) ?spectrum t <- 1:100 cos1 <- cos(2*pi*t*5/100) cos2 <- cos(2*pi*t*15/100 + 0.2) plot(t,cos1,type="l",lty=1,lwd=2,'ylab'="cosines") lines(t,cos2,lty=2,lwd=2) y<-2*cos1 + 3*cos2 plot(t,y,type='o') periodogram(y) cbind(periodogram(y)$freq,periodogram(y)$spec) t<- 1:100 cos1<-cos(2*pi*5.5/100) cos1<-cos(2*pi*t*5.5/100) cos2<-cos(2*pi*t*15.3/100 + 0.2) plot(t,cos1,type='l',lty=1,lwd=2,'ylab'="cosines") lines(t,cos2,lty=2) y<-2*cos1 + 3*cos2 plot(t,y,type='o') periodogram(y) cbind(periodogram(y)$freq, periodogram(y)$spec) spectrum(y,log="no",pad=2) ?ARMAspec plot(arima.sim(model=list(ma=0.9),n=100)) ARMAspec(model=list(ma=0.9)) plot(arima.sim(model=list(ma=-0.9),n=100)) ARMAspec(model=list(ma=-0.9)) plot(arima.sim(model=list(ar=0.9),n=100)) ARMAspec(model=list(ar=0.9)) plot(arima.sim(model=list(ar=-0.6),n=100)) ARMAspec(model=list(ar=-0.6)) plot(arima.sim(model=list(ma = -0.8, ar=0.5),n=100)) ARMAspec(model=list(ma = -0.8, ar=0.5)) x <- rnorm(1000) sp <- spectrum(x, log="no") lines(sp$freq, spectrum(x, log="no",span=21,plot=FALSE)$spec, lwd=3) lines(sp$freq, spectrum(x, log="no",span= c(21,21),plot=FALSE)$spec, lwd=3) lines(sp$freq, spectrum(x, log="no",span= c(21,21,21),plot=FALSE)$spec, lwd=3) x <- arima.sim(model=list(ar=-0.5),n=200) sp<-spectrum(x,log="no") lines(sp$freq,ARMAspec(model=list(ar=-0.5),freq=sp$freq,plot=F)$spec,lwd=3) x <- arima.sim(model=list(ar=-0.5),n=1000) sp<-spectrum(x,log="no", span = 60) lines(sp$freq,ARMAspec(model=list(ar=-0.5),freq=sp$freq,plot=F)$spec,lwd=3) #AIr PASSENGER data(AirPassengers) AP <- AirPassengers plot(AP) boxplot(AP~cycle(AP)) x <- diff(log(AP)) plot(x) spectrum(as.matrix(x),log="no") axis(1,at=c(1*12/length(x)))