\\\\(
\nonumber
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\\\\)
This exercise should be done in groups of 2 or 3 students.
The following R-code simulates random arma models of a specified order (AR order equal to p and MA order equal to q), and prints out the parameters and makes a plot of the ACF and PACF of 5000 simulations steps
p <- 1 # AR order
q <- 1 # MA order
n <- 5000
theta <- runif(p,-1/p,1/p)
phi <- runif(q,-1/q,1/q)
Y <- arima.sim(list(ar=theta,ma=phi),n)
par(mfrow=c(1,2))
acf(Y,main="ACF")
pacf(Y,main="PACF")
cat("AR parameters:",round(theta,3))
cat("MA parameters:",round(phi,3))
- Run the code a few times for varying values of p and q and look at the ACF and PACF plots.
- Use the golden table for ARMA identification to describe why the figures (hopefully) make sense.
- Take turns where one group member:
- Chooses a model order at secret
- Runs the script to generate the ACF and PACF plots
- Asks the rest of the group members to guess ARMA order based on the plots
- The difficulty can be increased by reducing the amount of simulated observations (i.e. reducing n).