For this exercise use data set visitors , the monthly Australian short-term overseas visitors data, May 1985–April 2005.
a. Make a time plot of your data and describe the main features of the series.
b. Split your data into a training set and a test set comprising the last two years of available data. Forecast the test set using 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 Box-Cox transformed series;
iii. a seasonal naïve method;
iv. an STL decomposition applied to the Box-Cox transformed data followed by an ETS model applied to the seasonally adjusted (transformed) data.
e. Which method gives the best forecasts? Does it pass the residual tests?
f. Compare the same four methods using time series cross-validation with the tsCV() function instead of using a training and test set. Do you come to the same conclusions?