Fitting an ARMA model
You are now ready to merge the AR model and the MA model into the ARMA model. We generated data from the ARMA(2,1) model, $$X_t = X_{t-1} - .9 X_{t-2} + W_t + .8 W_{t-1}, $$ x <- arima.sim(model = list(order = c(2, 0, 1), ar = c(1, -.9), ma = .8), n = 250)
. Look at the simulated data and the sample ACF and PACF pair to determine a possible model.
Recall that for ARMA(\(p, q\)) models, both the theoretical ACF and PACF tail off. In this case, the orders are difficult to discern from data and it may not be clear if either the sample ACF or sample PACF is cutting off or tailing off. In this case, you know the actual model orders, so fit an ARMA(2,1) to the generated data. General modeling strategies will be discussed further in the course.
This exercise is part of the course
ARIMA Models in R
Exercise instructions
- The package astsa is preloaded. 250 ARMA(2,1) observations are in
x
. - As in the previous exercises, use
plot()
to plot the generated data inx
and useacf2()
to view the sample ACF and PACF pairs. - Use
sarima()
to fit an ARMA(2,1) to the generated data. Examine the t-table and compare the estimates to the true values.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# astsa is preloaded
# Plot x
# Plot the sample P/ACF of x
# Fit an ARMA(2,1) to the data and examine the t-table