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3. Consider data set ukcars, the quarterly UK passenger vehicle production data from 1977 Q1 to 2005 Q1. Use only observations from 1977 to 2002 as the training data to fit any model below, and the rest as the test data when it is necessary. a. [2 marks] Plot the data and describe the main features of the series. b. [2 marks] Decompose the series using STL with fixed seasonality with command st1 (t.window=21,s.window='periodic', robust = T) in R. Plot the seasonally adjusted data and the original series together. c. [4 marks] Apply Holt's linear trend method to produce forecasts of the seasonally adjusted data. Then, obtain forecasts for the next two years of the production series. d. [4 marks] Repeat part c using the damped trend method. e. [4 marks] For both methods in parts c and d, compute both in-sample and out- sample RMSE for the training data and the test data, respectively. [Hint: use Metrics::rmse () function.] f. [4 marks] Now use ets () to choose a seasonal model for the production data. What is it? g. [4 marks] Which of the above three methods/models give the best forecast accuracy in terms of RMSE?