### Simulate arima models


# Simulate ARMA(1,1) ... generates a time series object
y <- arima.sim(n=100, model=list(ar=c(1,0.5), ma=c(0.5,0.2)), rand.gen=rnorm)

polyroot(c(1,-1,-0.5))   # one in, one out

polyroot(c(1,-1.5,0.75)) # complex pair, outside



y <- arima.sim(n=200, model=list(ar=c(1.5,-0.75), ma=c(0.5,0.2)), rand.gen=rnorm)
plot(y)

y <- arima.sim(n= 200, model=list(ar=c(1.6,-0.8), ma=c(0.5,0.2)), rand.gen=rnorm)
plot(y)

y <- arima.sim(n= 200, model=list(ar=c(1.8,-0.9), ma=c(0.5,0.2)), rand.gen=rnorm)
plot(y)

y <- arima.sim(n= 200, model=list(ar=c(1.8,-0.9)), rand.gen=rnorm)
plot(y)

y <- arima.sim(n= 200, model=list(ar=c(1.9,-0.95)), rand.gen=rnorm)
plot(y)


# --- representations of the process
# get code from S&S

load("http://www-stat.wharton.upenn.edu/~stine/stat910/rcode/tsa3.rda")
source("http://www-stat.wharton.upenn.edu/~stine/stat910/rcode/tsa3.rda")

ls()

spec.arma(ar=c(1.9,-0.95))

ARMAacf(ar=c(1.9,-0.95))
ARMAacf(ar=c(1.9,-0.95), pacf=TRUE)


ARMAtoMA(ar=c(1.9,-0.95), ma=1, 40)


# estimation routine
arima(y, order=c(2,0,0))