Question

In: Math

Consider the following time series data. Week 1 2 3 4 5 6 Value 18 13...

Consider the following time series data. Week 1 2 3 4 5 6 Value 18 13 17 12 17 15 a. Which of the following is a correct time series plot for this data? What type of pattern exists in the data? b. Develop the three-week moving average forecasts for this time series. Compute MSE and a forecast for week (to 2 decimals if necessary). MSE The forecast for week c. Use to compute the exponential smoothing forecasts for the time series. Compute MSE and a forecast for week (to 2 decimals). MSE The forecast for week d. Compare the three-week moving average approach with the exponential smoothing approach using . Which appears to provide more accurate forecasts based on MSE? e. Use a smoothing constant of to compute the MSE (to 2 decimals). Does a smoothing constant of or appear to provide more accurate forecasts based on MSE? The exponential smoothing forecast using provides a forecast than the exponential smoothing forecast using since it has a smaller MSE.

Solutions

Expert Solution

a)

type of pattern: Horizontal

b)

3 week
Time period Actual Value(A) Moving avg. Forecast(F) Forecast error E=|A-F| Squared Forecast Error
1 18
2 13
3 17
4 12 16.00 4.00 16.00
5 17 14.00 3.00 9.00
6 15 15.33 0.33 0.11
Total 7.33 25.11
Average 2.44 8.37
MAD MSE

  MSE =8.37

forecast =14.67

c)

Time period Actual Value(A) Forecast(F) Forecast error E=A-F Squared Forecast Error
1 18
2 13 18.00 5.00 25.00
3 17 17.00 0.00 0.00
4 12 17.00 5.00 25.00
5 17 16.00 1.00 1.00
6 15 16.20 1.20 1.44
Total 12.20 52.44
Average 2.44 10.49
MAD MSE

  MSE =10.49

forecast =15.96

d)

three-week moving average  appears to provide more accurate forecasts because of smaller MSE

e)

MSE =10.25
The exponential smoothing forecast using 0.4 provides a better forecast than the exponential smoothing forecast using 0.2 since it has a smaller MSE.


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