Consider the following time series data. Week 1 2 3 4 5 6 Value 18 13 16 11 17 14 (a) Choose the correct time series plot. (i) (ii) Time Series Value 20 18 16 14 12 10 Time Series Value 20 18 16 14 12 10 2 3 4 2 3 4 Week (1) Week (t) (iii) (iv) Time Series Value 20 18 16 14 12 10 8 6 4 Time Series Value 20 18 16 14 12 10 6 4 0 0 2 3 4 2 3 4 5 Week (0) Week (0) Plot (ii) What type of pattern exists in the data? Horizontal Pattern (b) Develop a three-week moving average for this time series. Compute MSE and a forecast for week 7. Do not round intermediate calculations. If required, round your answers to two decimal places. Week Value Forecast 1 18 2 13 3 16 4 11 15.67 5 17 13.33 6 14 14.67 MSE: 11.89 The forecast for week 7: 14 (c) Use a = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for week 7. Do not round intermediate calculations. If required, round your answers to two decimal places. Week Value Forecast 1 18 N 13 18.00 3 16 17.00 4 11 16.80 5 17 15.64 6 14 15.91 MSE: 13.03 The forecast for week 7: C 15.53 (d) Compare the three-week moving average forecast with the exponential smoothing forecast using a = 0.2. Which appears to provide the better forecast based on MSE? Three-week moving average Explain. Using this approach results in a smaller MSE (e) Use trial and error to find a value of the exponential smoothing coefficient a that yields the minimum MSE. Do not round intermediate calculations. Use a two-decimal digit precision for the exponential smoothing coefficient. alpha: 12.20 Consider the following time series data. Week 1 2 3 4 5 6 Value 18 13 16 11 17 14 (a) Choose the correct time series plot. (i) (ii) Time Series Value 20 18 16 14 12 10 Time Series Value 20 18 16 14 12 10 2 3 4 2 3 4 Week (1) Week (t) (iii) (iv) Time Series Value 20 18 16 14 12 10 8 6 4 Time Series Value 20 18 16 14 12 10 6 4 0 0 2 3 4 2 3 4 5 Week (0) Week (0) Plot (ii) What type of pattern exists in the data? Horizontal Pattern (b) Develop a three-week moving average for this time series. Compute MSE and a forecast for week 7. Do not round intermediate calculations. If required, round your answers to two decimal places. Week Value Forecast 1 18 2 13 3 16 4 11 15.67 5 17 13.33 6 14 14.67 MSE: 11.89 The forecast for week 7: 14 (c) Use a = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for week 7. Do not round intermediate calculations. If required, round your answers to two decimal places. Week Value Forecast 1 18 N 13 18.00 3 16 17.00 4 11 16.80 5 17 15.64 6 14 15.91 MSE: 13.03 The forecast for week 7: C 15.53 (d) Compare the three-week moving average forecast with the exponential smoothing forecast using a = 0.2. Which appears to provide the better forecast based on MSE? Three-week moving average Explain. Using this approach results in a smaller MSE (e) Use trial and error to find a value of the exponential smoothing coefficient a that yields the minimum MSE. Do not round intermediate calculations. Use a two-decimal digit precision for the exponential smoothing coefficient. alpha: 12.20