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4What is the MAPE for the three-period weighted moving average forecast as of period 15?
A local restaurant has recorded the demand for bottled water in each of the last 15 months of business. Use the recorded demand data below to develop three-period and four-period moving- average forecasts for bottles of water. Round off all calculations to two decimal places. Maintaining two decimal places is required for all calculations. (Weights are t=0.5, t=1-0.4 and t=2-0.1) What is the MAD for the three-period weighted moving-average forecast as of period 15?
Expert Answer
The three-period weighted moving-average forecast is given as follows:
Ft+1 = (wt)(Dt) + (wt-1)(Dt-1) + (wt-2)(Dt-2)
Ft+1 = (0.5)(Dt) + (0.4)(Dt-1) + (0.1)(Dt-2)
For period 4, F4 = (0.5)(D3) + (0.4)(D2) + (0.1)(D1)
F4 = (0.5)(905) + (0.4)(910) + (0.1)(925)
F4 = 909.00
MAD = Mean Absolute Deviation = (Σ(|Demand – Forecast|))/number of periods
MAPE = Mean absolute percentage Error = (Σ(Absolute deviation/Demand) x 100)/number of periods
| Period | Demand | Forecast | Absolute Deviation | Absolute % error |
| t | D | F | AD = |D – F| | APE = AD/D x 100 |
| 1 | 925 | |||
| 2 | 910 | |||
| 3 | 905 | |||
| 4 | 850 | 909.00 | |850-909|=59 | (59/850) x 100 = 6.94% |
| 5 | 860 | 878.00 | 18 | 2.09% |
| 6 | 890 | 860.50 | 29.5 | 3.31% |
| 7 | 960 | 874.00 | 86 | 8.96% |
| 8 | 895 | 922.00 | 27 | 3.02% |
| 9 | 910 | 920.50 | 10.5 | 1.15% |
| 10 | 905 | 909.00 | 4 | 0.44% |
| 11 | 870 | 906.00 | 36 | 4.14% |
| 12 | 860 | 888.00 | 28 | 3.26% |
| 13 | 900 | 868.50 | 31.5 | 3.50% |
| 14 | 920 | 881.00 | 39 | 4.24% |
| 15 | 950 | 906.00 | 44 | 4.63% |
| Total | 412.5 | 45.68% | ||
| Average | 34.375 | 3.81% | ||
MAD = 34.375
MAPE = 3.81%
