Answer:
a. We have:
MSE: 63.03
The forecast for week 7: 15.33
b. We have:
MSE: 47.49
The forecast for week 7: 16.35
c. The exponential smoothing forecast using = 0.2. appears to provide the better forecast based on MSE.
Explanation:
a. Develop the three-week moving average forecasts for this time series. Compute MSE and a forecast for week 7 (to 2 decimals if necessary).
Note: See Part a of the attached excel file for the Calculations of Forecast, Error, and Error^2.
From the attached excel file, we can have:
MSE = Mean squared error = Total of Error^2 / Number of observation under the Error^2 = 252.11 / 4 = 63.03
The forecast for week 7 = 15.33
b. Use = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for week 7.
Note: See Part b of the attached excel file for the Calculations of Forecast, Error, and Error^2.
From the attached excel file, we can have:
MSE = Mean squared error = Total of Error^2 / Number of observation under the Error^2 = 284.96 / 6 = 47.49
The forecast for week 7 = 16.35
Note that under exponential smoothing, forecast for week 2 has to be the Time Series Value for week 1.
b. Compare the three-week moving average forecast with the exponential smoothing forecast using = 0.2. Which appears to provide the better forecast based on MSE?
Since 47.49 MSE of the exponential smoothing forecast using = 0.2 is less than 63.03 MSE of the three-week moving average forecast, it implies that the exponential smoothing forecast using = 0.2. appears to provide the better forecast based on MSE.
