Consider the following time series data.
Week 1 2 3 4 5 6
Value 18 13 15 13 15 15
(b) | Develop a three-week moving average for this time series. Compute MSE and a forecast for week 7. |
If required, round your answers to two decimal places. |
(c) Use α = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for week 7. | |
If required, round your answers to two decimal places. |
(d) Use trial and error to find a value of the exponential smoothing coefficient α that results in a smaller MSE than what you calculated for α = 0.20. Use a two-decimal digit precision.
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 | 15 | |||
4 | 13 | 15.33 | 2.33 | 5.44 |
5 | 15 | 13.67 | 1.33 | 1.78 |
6 | 15 | 14.33 | 0.67 | 0.44 |
Total | 4.33 | 7.67 | ||
Average | 1.44 | 2.56 | ||
MAD | MSE |
MSE =2.56
forecast =14.33
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 | 15 | 17.00 | 2.00 | 4.00 |
4 | 13 | 16.60 | 3.60 | 12.96 |
5 | 15 | 15.88 | 0.88 | 0.77 |
6 | 15 | 15.70 | 0.70 | 0.50 |
Total | 12.18 | 43.23 | ||
Average | 2.44 | 8.65 | ||
MAD | MSE |
MSE =8.65
forecast =15.56
d)value of alpha =0.62
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