library(TSA)
data(lynx)
plot(log(lynx))
pacf(log(lynx))
arma.lynx=arima(log(lynx),order=c(3,0,0))
arma.lynx
# R-squared
1-.2669/1.653
data(sunspots)
?sunspots
plot(sunspots)
?aggregate
frequency(sunspots)
sunspots.y=aggregate(sunspots,nfrequency=1)
frequency(sunspots.y)
plot(sunspots.y)
sunspots.y1=aggregate(sunspots,nfrequency=1,FUN=median)*12
lines(sunspots.y1,col='brown')
hist(sunspots.y)
boxcox=BoxCox.ar(sunspots.y+min(sunspots.y[sunspots.y!=0]))
boxcox
# MLE suggest square root transformation
plot(sqrt(sunspots.y))
acf(sqrt(sunspots.y),lag.max=60)
pacf(sqrt(sunspots.y),lag.max=60)
eacf(sqrt(sunspots.y))
arima.s=arima(sqrt(sunspots.y),order=c(3,0,0))
polyroot(c(1,-arima.s$coef[-4]))
Mod(polyroot(c(1,-arima.s$coef[-4])))
# stationary
Arg(polyroot(c(1,-arima.s$coef[-4])))
theta from the Arg = theta=0.5698923
period=2*pi/theta
period