Problem 15-05 (Algorithmic) Consider the following time series data. Week 1 2 3 4 5 6 Value 16 12 14 13 15 14 a. Choose the correct time series plot. (i) 20. Time Series Value 20 Time Series Value Week(t) Week(t) (iv) 20. Time Series Value 20. Time Series Value Week(t) Week(t) W Plot (1) pattern exists in the data? Plot (ii) Plot (iii) ree-week moving average for this time series. Compute MSE and a forecast for week 7. Round your answers to two decimal places. b. De plot (iv) Problem 15-05 (Algorithmic) Consider the following time series data. Week 1 2 3 4 5 6 Value 16 12 14 13 15 14 a. Choose the correct time series plot. 20. Time Series Value 20 Time Series Value Week(t) 6 Week(t) 3 4 5 (iii) (iv) 20. Time Series Value 20. Time Series Value Week(t) Week(t) What type of pattern exists in the data? Horizontal Pattern week moving average for this time series. Compute MSE and a forecast for week 7. Round your answers to two decimal places. Trend Pattern JlForecast b. Develop a three-week moving average for this time series. Compute MSE and a forecast for week 7. Round your answers to two decimal places. Time Series Forecast Value 1 16 12 14 21 5 6 15 14 C Week Forecast MSE: The forecast for week 7: c. Use a = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for week 7. Round your answers to two decimal places. Time Series Value | 1 16 | 2 | 12 | 3 14 1 13 I 5 15 C 61 14 MSE: The forecast for week 7: 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? Explain. The input in the box below will not be graded, but may be reviewed and considered by your instructor. e. Use trial and error to find a value of the exponential smoothing coefficient a that results in a smaller MSE than what you calculated for a = 0.2. Find a value of a for the smallest MSE. Round your answer to three decimal places