Exercise

# 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.

Instructions

**100 XP**

- The package astsa is preloaded.
`x`

contains the 200 AR(2) observations. - Use
`plot()`

to plot the generated data in`x`

. - Plot the sample ACF and PACF pair using
`acf2()`

from the`astsa`

package. - Use
`sarima()`

to fit an AR(2) to the previously generated data in`x`

. Examine the t-table and compare the estimates to the true values.