Develop the three-week moving average forecasts for this time series. Compute MSE and a forecast for week 7 (to 2 decimals if necessary).Week Time Series ForecastValue 1 18 2 15 3 16 4 13 5 17 6 16MSE: The forecast for week 7:
Use = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for week 7.Week Time Series Forecast
Value
1 18
2 15
3 16
4 13
5 17
6 16MSE:
The forecast for week 7:
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?

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.

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