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:

  1. 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.
  2. The sample ACF of the residuals should look like that of white noise. Examine the ACF for departures from this behavior.
  3. Normality is an essential assumption when fitting ARMA models. Examine the Q-Q plot for departures from normality and to identify outliers.
  4. 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.