Fitting an AR(2) model
For this exercise, we generated data from the AR(2) model, $$X_t = 1.5 X_{t-1} - .75 X_{t-2} + W_t,$$ using x <- arima.sim(model = list(order = c(2, 0, 0), ar = c(1.5, -.75)), n = 200). Look at the simulated data and the sample ACF and PACF pair to determine the model order. Then fit the model and compare the estimated parameters to the true parameters.
This is a part of the course
“ARIMA Models in R”
Exercise instructions
- The package astsa is preloaded.
xcontains the 200 AR(2) observations. - Use
plot()to plot the generated data inx. - Plot the sample ACF and PACF pair using
acf2()from theastsapackage. - Use
sarima()to fit an AR(2) to the previously generated data inx. 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 AR(2) to the data and examine the t-table