1. Consider the data series, austourists, (available in fpp2 package, you can type help(austourists) to see the description of this data)

(a) Plot the series. Do you observe any pattern (Trend/Seasonal/Cyclic) in this series?

(b) Plot the two seasonal plots. Use the plots to support your answer in part (a).

(c) Plot the autocorrelation plot of the series. Use the plot to support your answer in part (a).

2. Consider the data series, auscafe, (available in fpp2 package, you can type help(auscafe) to see the description of this data)

(a) Plot the series. Discuss why applying Box-Cox transformation on this series is appropriate.

(b) Using R to find the optimal λ value for Box-Cox transformation. Plot the transformed series. What is the main difference between the transformed series and the original series?

(c) Apply Box-Cox transformation to drift method forecasting. Plot both simple back transformation forecast and bias adjusted forecast. Do you find any difference? (Hint: Set larger h will be helpful to see the difference, e.g. h = 30) What do these two different forecasts capture?

3. Consider the usmelec data series, (available in fpp2 package, you can type help(usmelec) to see the description of this data)

(a) Applying seasonal naive method and drift method to forecast the data series. Check the residuals from these two methods. Do you find these two methods satisfy the assumptions? (You need to report all the results from check residuals function and explain each of them.)

(b) Split the data into a training set and a test set, where the training set ends at December 1999. And test set starts at January 2000. Using seasonal naive method and drift method with training data and forecast the test data. Which method provides smaller RMSE?

(c) Now use Cross-validation to compare seasonal naive method and drift method. Which method provides smaller RMSE?

1. Consider the data series, austourists, (available in fpp2 packag...