(a) Find an ARIMA model that provides a good fit to the variable unemp in the USMacroG data set in the AER package.
(b) Now perform a small model-based bootstrap to see how well auto. arima can select the true model. To do this, simulate eight data sets from the ARIMA model selected in part (a) of this problem. Apply auto.arima with BIC to each of these data sets. How often is the "correct" amount of di®erencing selected, that is, d and D are correctly selected? How often is the "correct" model selected? "Correct" means in agreement with the simulation model. "Correct model" means both the correct amount of differencing and the correct orders for all the seasonal and nonseasonal AR and MA components.