This exercise concerns as accommodation: the total quarterly takings from accommodation and the room occupancy level for hotels, motels, and guest houses in Australia, between January 1998 and June 2016. Total quarterly takings are in millions of Australian dollars.

(a) Compute the CPI-adjusted takings and plot the result for each state

(b) Select three states and for each of them, fit a dynamic regression model of CPI-adjusted takings with seasonal dummy variables, a piecewise linear time trend with one knot at 2008 Q1, and ARIMA errors.

(c) Check that the residuals of the model look like white noise.

(d) Forecast the takings for each of the selected states to the end of 2017. (Hint: You will need to produce forecasts of the CPI first.)

(e) What sources of uncertainty have not been taken into account in the prediction intervals?