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11. For this exercise use data set visitors ,the monthly Australian short-term overseas visitors data, May 1985April 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 naive 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? RStudio File Edit Code View Plots Session Build Debug Profile Tools Window Help . 1 2 Q 9 0 Thu May 23 1:10 PM ... RStudio + - OR -| | Go to file/function 1 89 - Addins . R Project: (None) - H R data sets x HW4.Rmd x HW2.Rmd x Econ144Project2.Rmd x Environment History Connections Financial, Econ... R - Daily data a... O Knit on Save ABC Knit - 3. *0 - 1 3 Run . . H. 37 MiB - Source Visual Outline R . Global Environment . O visitors split Next Prev All Replace Replace All In selection Match case Whole word Regex Wrap 195 - ## Question 6 196 For this exercise use data set visitors, the monthly Australian short-term overseas visitors data, May 1985-April 2005. 197 198 *a)* Make a time plot of your data and describe the main features of the series. 199 200 - "{} 201 data("visitors") 202 visitors ECON 144 > Homework Assignments ... 207 plot(visitors_decomp) Name Size 208 - L .. 214:9 # Question 6 + R Markdown 144 Homework 2.pdf 449. 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Rmd) O Execution halted R HW.R 3.1 F Residual from statsm zoom Ps WD 4 2RStudio File Edit Code View Plots Session Build Debug Profile Tools Window Help . 1 2 Q 9 0 Thu May 23 1:11 PM ... RStudio + . OR - | |Go to file/function 1 89 . Addins . R Project: (None) - H R data sets x HW4.Rmd* x HW2.Rmd x Econ144Project2.Rmd x Environment History Connections Financial, Econ... R - Daily data a.. Knit on Save ABC Knit - 3 *0 -1 8 Run . . - 36 MiB - Source Visual Outline R - Global Environment . O visitors train Next Prev All Replace Replace All In selection Match case Whole word Regex Wrap 214 \ ewpage 215 216 *b)* Split your data into a training set and a test set comprising the last two 217 years of available data. Forecast the test set using Holt-Winters' 218 multiplicative method 219 220 - ""{} 221 train = visitors[: '2003-04-30'] 222 test = visitors['2003-05-01':] 223 224 model = ExponentialSmoothing(train, seasonal='mul', trend='add', seasonal_periods=12). fit() Files Plots Packages Help View 225 forecast = model . forecast(len(test)) 226 ( ECON 144 > Homework Assignments ... 227 plt. plot(train, label='Training Data') Name Size 228 plt. plot(test, label='Test Data')| - - -1 1 - 1- 7 111-71 mist L .. 228:34 C Chunk 9 R Markdown 144 Homework 2.pdf 449. Console Terminal x Render x Background Jobs 0 144hm2.Rmd 16.6 .../Homework Assignments/ HW4.Rmd 144HW1.Rmd 5.31 1 . . I 4% [unnamed-chunk-1] CEU4200000001.CSV 18.5 processing file: HW4. 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