Question
In: Statistics and Probability
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 | 16 | 11 | 17 | 14 |
a. Use a smoothing constant of a = 0.4 to compute the MSE (to 2 decimals).
(___)
2.Consider the following time series data.
| Week | 1 | 2 | 3 | 4 | 5 | 6 |
| Value | 19 | 13 | 17 | 12 | 17 | 15 |
b. Develop the three-week moving average forecasts for this time series. Compute MSE and a forecast for week 7 (to 2 decimals if necessary).
| MSE | (___) |
| The forecast for week 7 | (___) |
c. Use a = 0.2 to compute the exponential smoothing forecasts for the time series. Compute MSE and a forecast for week 7 (to 2 decimals).
| MSE | (___) |
| The forecast for week 7 | (___) |
e. Use a smoothing constant of a = 0.4 to compute the MSE (to 2 decimals).
(___)
Solutions
Expert Solution
1)
a)
| Period | Data | ES(0.4) Forecasts |
| 1 | 18 | 18 |
| 2 | 13 | 18+0.4⋅(18−18)=18 |
| 3 | 16 | 18+0.4⋅(13−18)=16 |
| 4 | 11 | 16+0.4⋅(16−16)=16 |
| 5 | 17 | 16+0.4⋅(11−16)=144 |
| 6 | 14 | 14+0.4⋅(17−14)=15.2 |
| 7 | - | 15.2+0.4⋅(14−15.2)=14.72 |
2)
b)
| Period | Data | MA(3) Forecasts |
| 1 | 19 | - |
| 2 | 13 | - |
| 3 | 17 | - |
| 4 | 12 | (19 + 13 + 17)/3 = 16.3333 |
| 5 | 17 | (13 + 17 + 12)/3 = 14 |
| 6 | 15 | (17 + 12 + 17)/3 = 15.3333 |
| 7 | - | (12 + 17 + 15)/3 = 14.6667 |
fore cast for week 7 = 14.6667
the mean square error is MSE=9.3
c)
| MSE | 11.88 |
| The forecast for week 7 | 16.2877 |
e)
orchestra answered 1 year agoRelated Solutions
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