#  In this program we are going to use the function "ts.sim" to simulate 200 observations of
#  some simple ARMA models, plot them and then plot their sample ACF's and sample PACF's.
#  Note that, due to sampling variation, the sample ACF's and sample PACF's will not exactly
#  coincide with their theoretical (population) ACF's and PACF's even though this would be
#  the case as the sample size goes to infinity.  Again, you can adjust this program slightly
#  by choosing different ar and ma parameter values as long as they satisfy the stationary and
#  invertibility conditions.  

# Here we simulate an AR(1) model with ar1 = 0.7

ts.sim.1<-arima.sim(list(order=c(1,0,1), ar=0.7, ma=0.0), n=200)
ts.plot(ts.sim.1)
windows()
par(mfrow=c(1,2))
acf(ts.sim.1)
pacf(ts.sim.1)

# Here we simulate a MA(1) model with ma1 = 0.6

ts.sim.2<-arima.sim(list(order=c(1,0,1), ar=0.0, ma=0.6), n=200)
windows()
par(mfrow=c(1,1))
ts.plot(ts.sim.2)
windows()
par(mfrow=c(1,2))
acf(ts.sim.2)
pacf(ts.sim.2)

# Here we simulate an ARMA(1,1) model with ar1 = 0.7 and ma1 = 0.6

ts.sim.3<-arima.sim(list(order=c(1,0,1), ar=0.7, ma=0.6), n=200)
windows()
par(mfrow=c(1,1))
ts.plot(ts.sim.3)
windows()
par(mfrow=c(1,2))
acf(ts.sim.3)
pacf(ts.sim.3)