Problem 1 [4 marks ]: Forecast the Chinese GDP from the global_economy data set using an ETS model . Experiment with the various options in the ETS () function to see how much the forecasts change with damped trend, or with a Box-Cox transformation. Try to develop an intuition of what each is doing to the forecasts . Discuss your results . [Hint: use h=20 when forecasting, so you can clearly see the differences between the various options when plotting the forecasts .] Problem 2 [6 marks ]: Use the quarterly number of arrivals to Australia from New Zealand, 1981 Q1 - 2012 Q3, from data set aus_arrivals a. Make a time plot of your data and describe the main features of the series . b. Create a training set that withholds the last two years of available data. Forecast the test set using an appropriate model for Holt - Winters ' multiplicative method c. Why is multiplicative seasonality necessary here? d. Forecast the two-year test set using each of the following methods: i) an ETS model; ii) an additive ETS model applied to a log transformed series ; iii ) a seasonal naive method