Exercise

# Fitting an MA(1) model

In this exercise, we generated data from an MA(1) model, $$X_t = W_t - .8 W_{t-1} ,$$ `x <- arima.sim(model = list(order = c(0, 0, 1), ma = -.8), n = 100)`

. Look at the simulated data and the sample ACF and PACF to determine the order based on the table given in the first exercise. Then fit the model.

Recall that for pure MA(q) models, the theoretical ACF will cut off at lag q while the PACF will tail off.

Instructions

**100 XP**

- The package astsa is preloaded. 100 MA(1) observations are available in your workspace as
`x`

. - Use
`plot()`

to plot the generated data in`x`

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

from the`astsa`

package. - Use
`sarima()`

from`astsa`

to fit an MA(1) to the previously generated data. Examine the t-table and compare the estimates to the true values.