A manufacturer has sold the following number of refrigerators over recent years: Year 2018 2019 2020 2021 Sales (000s) 10.6 11.5 12.9 14.0 It is proposed to use Holt’s method to forecast future sales: y^+m = + mb (m = number of periods ahead to forecast) = y + (1 − )(−1 + −1 ) (0 < < 1) (Smoothed level) = ( − −1 ) + (1 − )−1 (0 < < 1) (Smoothed trend) a) The manufacturer uses Holt’s linear exponential smoothing method with values of α=0.1 and β=0.2 for the smoothing constants. In 2017, the level is 9.9 and the trend is 1.0. Calculate the one-year-ahead forecasts (to three decimal places) for each of the years 2018, 2019, 2020 and 2021 using the latest data that would have been available at the end of the preceding years, 2017, 2018, 2019 and 2020. (10 marks) A different forecasting method produced the following forecasts of refrigerator sales for 2018 to 2021: Year 2018 2019 2020 2021 Sales (000s) 10.4 11.5 13.1 14.5 b) Compare the accuracy of this method with the method used in part (a) on the basis of the Mean Absolute Error and the Mean Square Error for these four years (with calculations to three decimal places). What conclusions do you draw? (6 marks) c) It has been suggested that the Holt-Winters method should be used instead of Holt’s method. Explain why Holt-Winters is not appropriate for this data. (2 marks) d) If the forecasts start to lag behind changes in the trend, what change should be made to the parameter β and why? (3 marks) e) When starting to use Holt’s method, a "simple approach" is to initialise the level at the first observation and initialise the trend to be zero. Describe an alternative approach and explain its advantages over the "simple approach".