11.7 Exercises

  1. Write out the \(\bm{S}\) matrices for the Australian tourism hierarchy and the Australian prison grouped structure. Use the smatrix command to verify your answers.

  2. Consider the PBS data which has aggregation structure ATC1/ATC2 * Concession * Type.

    1. Produce plots of the aggregated data by Concession, Type and ATC1.
    2. Forecast the PBS data using ETS, ARIMA and SNAIVE models, applied to all but the last three years of data.
    3. Reconcile each of the forecasts using MinT.
    4. Which type of model works best on the test set?
    5. Does the reconciliation improve the forecast accuracy?
    6. Why doesn’t the reconciliation make any difference to the SNAIVE forecasts?
  3. Repeat the tourism example from Section 11.4, but also evaluate the forecast distribution accuracy using CRPS skill scores. Which method does best on this measure?

  4. Repeat the prison example from Section 11.6, but using a bootstrap to generate the forecast distributions rather than assuming normality. Does it make much difference to the CRPS skill scores?