The following time series shows the sales of a particularproduct over the past 12 months.
| Month | Sales |
|---|
| 1 | 105 |
| 2 | 135 |
| 3 | 120 |
| 4 | 105 |
| 5 | 90 |
| 6 | 120 |
| 7 | 145 |
| 8 | 140 |
| 9 | 100 |
| 10 | 80 |
| 11 | 100 |
| 12 | 110 |
Use α = 0.5 to compute the exponential smoothingforecasts for the time series. (Round your answers to two decimalplaces.)
| Month t | Time Series Value Yt | Forecast Ft |
|---|
| 1 | 105 | |
| 2 | 135 | |
| 3 | 120 | |
| 4 | 105 | |
| 5 | 90 | |
| 6 | 120 | |
| 7 | 145 | |
| 8 | 140 | |
| 9 | 100 | |
| 10 | 80 | |
| 11 | 100 | |
| 12 | 110 | |
Use a smoothing constant of α = 0.7 to compute theexponential smoothing forecasts. (Round your answers to two decimalplaces.)
| Month t | Time Series Value Yt | Forecast Ft |
|---|
| 1 | 105 | |
| 2 | 135 | |
| 3 | 120 | |
| 4 | 105 | |
| 5 | 90 | |
| 6 | 120 | |
| 7 | 145 | |
| 8 | 140 | |
| 9 | 100 | |
| 10 | 80 | |
| 11 | 100 | |
| 12 | 110 | |
| Week | Sales (1,000s
of gallons) |
|---|
| 1 | 17 |
| 2 | 22 |
| 3 | 19 |
| 4 | 24 |
| 5 | 19 |
| 6 | 16 |
| 7 | 21 |
| 8 | 19 |
| 9 | 23 |
| 10 | 20 |
| 11 | 16 |
| 12 | 22 |
(a) Compute four-week and five-week moving averages for the timeseries.
| Week | Time Series
Value | 4-Week
Moving
Average
Forecast | 5-Week
Moving
Average
Forecast |
|---|
| 1 | 17 | | |
| 2 | 22 | | |
| 3 | 19 | | |
| 4 | 24 | | |
| 5 | 19 | | |
| 6 | 16 | | |
| 7 | 21 | | |
| 8 | 19 | | |
| 9 | 23 | | |
| 10 | 20 | | |
| 11 | 16 | | |
| 12 | 22 | | |
Compute the MSE for the four-week moving average forecasts.(Round your answer to two decimal places.)
Compute the MSE for the five-week moving average forecasts.(Round your answer to two decimal places.)
