sun.ts<-ts(round(sunspot.year[71:171]))
sun.ts

ts.plot(sun.ts,xlab="Year",ylab="Sunspot Activity")

acf(sun.ts,lag.max=20,type="correlation")

newsun<-sun.ts[12:100]-sun.ts[1:89]
ts.plot(newsun,xlab="Time",ylab="11 year differences")
abline(h=0)
acf(newsun,lag.max=20)

sun.ar<-ar.yw(newsun)
sun.ar

ts.plot(sun.ar$aic,xlab="Order of series",ylab="Akaike criterion")
ts.plot(sun.ar$resid,xlab="Year",ylab="Residuals from ar model")
abline(h=0)

acf(na.omit(sun.ar$resid),lag.max=20)