Exercise 2 - Application (10 marks)

For the purposes of this report, only consider the data from July 2012 to June 2021 as the sample of data that is available to you - that is, ignore any recent observations. This means that the first actual observation in your Excel file is from July 2012 and your last actual observation in your Excel file is from June 2021.

For the Original data for the Total number of dwelling units (Series ID: A418427K) available in Table 6: Forecast the out-of-sample values for every month in the period July 2021 - June 2022 (both months inclusive) using Winter's Exponential Smoothing (Multiplicative) with the following parameters: alpha = 0.35, beta = 0.35, and gamma = 0.35. For the seeds of the level, trend, and seasonal components - use the methods described and discussed in class.

Before you begin Exercise 2, let's check that you have the right data! The average should be 9756.2!

Once you perform Winters Exponential Smoothing with alpha, beta and gamma, what are the following numerical values: 11. The seasonal component for May 2021. 12. The within-sample forecast for March 2021.

13. The out-of-sample forecast for June 2022. 14. The MAE. 15. The MSE.

Critically think for a way to optimise alpha, beta, and gamma via the MSE, and report the following values after your optimisation: 16. Alpha 17. Gamma

18. The MSE 19. The within-sample forecast for March 2021. 20. The out-of-sample forecast for June 2022.