AUT University School of Engineering, Computer and Mathematical Sciences STAT603: Forecasting Assignment 1 The purpose of this assignment is to assess your analytical and computing skills on the material covered. Total Possible Marks: 30 marks, which contribute 15% towards your final grade in this paper. Deadline: 11:59pm, Friday, April 16, 2021 Submission: The assignment must be submitted as a soft copy in a single .pdf file on Blackboard. Your filename must include 1) your lastname, 2) your firstname, and 3) your student id, e.g., if John White submits his as- signment, his .pdf file must be named ”White John 123456789”. Report/Assignment: Your assignment must be self-contained, i.e., you need to embed your R code in your answers. See example in the box below: Page Limit: Maximum number of pages is 10 including graphs and R code. 1 Data: • Quarterly total beer available for consumption (million litres) in New Zealand from Quarter 1, 2010 to Quarter 4, 2019 (Filename: NZ_TotalBeer_Quarterly.xlsx) • Quarterly average nation-wide temperature (degrees celcius) in New Zealand from Quarter 1, 2010 to Quarter 4, 2019 (Filename: NZ_AvgTemp_Quarterly.xlsx) • Quarterly real national disposable income (Billion NZ dollars) in New Zealand from Quarter 1, 2010 to Quarter 3, 2019 (Filename: NZ_DispIncome_Quarterly.xlsx) Note: All data should be converted into time series using ts function in R. R: All computing tasks must be done using R or RStudio. Plagiarism: If this is the case for your assignment, your case will be referred to an appropriate university’s office. Tasks/Questions: 1. Use the quarterly total beer available for consumption data. (17 marks) (a) Plot the series and discuss the main features of the data. (2 marks) (b) Discuss whether a transformation is needed. If yes, do so and describe the effect. (3 marks) (c) Find and discuss whether the autocorrelation exists in this time series. (2 marks) (d) Compute two years of forecasts (i.e. holding the last two years of data out as the test set) using the four methods: (1) mean, (2) naive, (3) seasonal naive, and (4) drift. Plot the series and the forecasts, and discuss the results. (8 marks) (e) Compare the root mean squared error (RMSE) of forecasts from the four methods in (d). Which method do you think is best for this time series? (2 marks) 2 2. Time series regression models (13 marks) (a) Fit a regression model to the quarterly total beer available for con- sumption data with a linear trend and seasonal dummies. Discuss the results. (2 marks) (b) Plot the quarterly total beer available for consumption data with the quarterly average nation-wide temperature and real national disposable income data. Perform the correlation analysis and dis- cuss the results. (3 marks) (c) Fit a regression model to the quarterly total beer available for consumption data with the quarterly average nation-wide temper- ature and real national disposable income data as the explanatory variables. Discuss the results. (2 marks) (d) Do we need to include the linear trend and seasonal dummies in the regression model in (c)? Perform a relevant analysis and discuss the results. (3 marks) (e) Compute two year of forecasts for the regression models in (a) and (c). Evaluate the forecast accuracy and compare with those in Question 1 parts (d)-(e). (3 marks) 3


































































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