Exercise

# Residual analysis - I

As you saw in the video, an `sarima()`

run includes a residual analysis graphic. Specifically, the output shows (1) the standardized residuals, (2) the sample ACF of the residuals, (3) a normal Q-Q plot, and (4) the p-values corresponding to the Box-Ljung-Pierce Q-statistic.

In each run, check the four residual plots as follows:

- The standardized residuals should behave as a white noise sequence with mean zero and variance one. Examine the residual plot for departures from this behavior.
- The sample ACF of the residuals should look like that of white noise. Examine the ACF for departures from this behavior.
- Normality is an essential assumption when fitting ARMA models. Examine the Q-Q plot for departures from normality and to identify outliers.
- Use the Q-statistic plot to help test for departures from whiteness of the residuals.

As in the previous exercise, `dl_varve <- diff(log(varve))`

, which is plotted below a plot of `varve`

. The astsa package is preloaded.

Instructions

**100 XP**

- Use
`sarima()`

to fit an MA(1) to`dl_varve`

and do a complete residual analysis as prescribed above. Make a note of what you see for the next exercise. - Use another call to
`sarima()`

to fit an ARMA(1,1) to`dl_varve`

and do a complete residual analysis as prescribed above. Again, make a note of what you see for the next exercise.