# fit recruits

library(ts)

#rec <- scan("E:\\Stat207\\Class\\Examples\\Ch2\\recruit.dat")

rec <- scan("http://www.sci.csueastbay.edu/~esuess/Statistics_6871/Handouts/Handout6/recruit.dat")

x <- ts(rec)   # x is the time series object
par(mfrow=c(3,1))
ts.plot(x, gpars=list(main="Recruits (x)"))
acf(x)
acf(x,type="partial")

#indicates AR(2) fit  but we'll also fit an ARMA(1,1)
rec.ar2 <- ar(x, order.max = 10)
# type 
help(ar) #to see what you get, e.g.
rec.ar2$ar  #gives parameters
rec.ar2$aic # gives AIC from lag 0 to order.max
# NOTE arima DOES FIT A CONSTANT 
rec.ar2 <- arima0(x, order=c(2,0,0))
# some results
rec.ar2$var.coef
rec.ar2$aic
rec.ar2$sigma2

# now the ARMA(1,1) fit
rec.arma <- arima0(x, order=c(1,0,1))
rec.arma$var.coef
rec.arma$aic

# Forecast 12 time units ahead for AR(2) model
rec.ar2.fore <- predict(rec.arma,n.ahead=12)
cbind(rec.ar2.fore$pred,rec.ar2.fore$se)
par(mfrow=c(1,1))
ts.plot(x,rec.ar2.fore$pred,rec.ar2.fore$pred+2*rec.ar2.fore$se,
	rec.ar2.fore$pred-2*rec.ar2.fore$se)