Exercise

# Diagnostics - simulated overfitting

One way to check an analysis is to overfit the model by adding an extra parameter to see if it makes a difference in the results. If adding parameters changes the results drastically, then you should rethink your model. If, however, the results do not change by much, you can be confident that your fit is correct.

We generated 250 observations from an ARIMA(0,1,1) model with MA parameter .9. First, you will fit the model to the data using established techniques.

Then, you can check a model by overfitting (adding a parameter) to see if it makes a difference. In this case, you will add an additional MA parameter to see that it is not needed.

As usual, the astsa package is preloaded and the generated data in `x`

are plotted in your workspace. The differenced data `diff(x)`

are also plotted. Note that it looks stationary.

Instructions

**100 XP**

- Plot the sample ACF and PACF of the differenced data using
`acf2()`

and note that the model is easily identified. - Fit an ARIMA(0,1,1) model to the simulated data using
`sarima()`

. Compare the MA parameter estimate to the actual value of .9, and examine the residual plots. - Overfit the model by adding an additional MA parameter. That is, fit an ARIMA(0,1,2) to the data and compare it to the ARIMA(0,1,1) run.