7.5 For this exercise, use the monthly Australian short-term overseas visitors data, May 1985-April 2005. (Data set:

visitors.)

(a) Make a time plot of your data and describe the main features of the series.

(b) Forecast the next two years using Holt-Winters'

multiplicative method.

(c) Why is multiplicative seasonality necessary here?

(d) Experiment with making the trend exponential and/or damped.

(e) Compare the RMSE of the one-step forecasts from the various methods. Which do you prefer?

(f) Now fit each of the following models to the same data:

(i) a multiplicative Holt-Winters' method;

(ii) an ETS model;

(iii) an additive ETS model applied to a Box-Cox transformed series;

(iv) a seasonal naive method applied to the Box-Cox transformed series;

(v) an STL decomposition applied to the Box-Cox transformed data followed by an ETS model applied to the seasonally adjusted (transformed)

data.

(g) For each model, look at the residual diagnostics and compare the forecasts for the next two years. Which do you prefer