In: Math
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.
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.