Problem 2 [6 marks]: Use the quarterly number of arrivals to Australia from New Zealand, 1981 Q1 - 2012 Q3 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 th 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