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Develop an exponential smoothing forecast
(alphaαequals=0.30.3)
for February 2016 through January 2017. Assume that your forecast for January 2016 was
100100.
Calculate the MFE, MAD, and MAPE values for February through December 2016.
Find an exponential smoothing forecast for each period and fill-in the table below (enter your responses rounded to one decimal place).
Month,Demand
January 2016,119
February,72
March,113
April,82
May,82
June,131
July,111
August,116
September,89
October,95
November,88
December,90
Expert Answer
Exponential moving average (EMA) for February = (Demand for January – EMA for January)*α + EMA for January
MFE = Mean of the sum of the forecasting errors
MAD = Mean of the sum of the absolute forecasting errors
MAPE = Mean of the sum of the absolute % of errors
EMA with alpha = .3
| Period | Month (2016) | Demand | Exponential moving average (α = .3) |
| 1 | January | 119 | 100.00 |
| 2 | February | 72 | 105.70 |
| 3 | March | 113 | 95.59 |
| 4 | April | 82 | 100.81 |
| 5 | May | 82 | 95.17 |
| 6 | June | 131 | 91.22 |
| 7 | July | 111 | 103.15 |
| 8 | August | 116 | 105.51 |
| 9 | September | 89 | 108.65 |
| 10 | October | 95 | 102.76 |
| 11 | November | 88 | 100.43 |
| 12 | December | 90 | 96.70 |
| 13 | January (2017) | 94.69 |
MFE:
| Period | Month (2016) | Demand | Exponential moving average (α = .3) | Forecasting Error | Cumulative Forecasting error | MFE |
| 1 | January | 119 | 100.00 | 19.00 | 19.00 | 19 |
| 2 | February | 72 | 105.70 | -33.70 | -14.70 | -7.35 |
| 3 | March | 113 | 95.59 | 17.41 | 2.71 | 0.90 |
| 4 | April | 82 | 100.81 | -18.81 | -16.10 | -4.03 |
| 5 | May | 82 | 95.17 | -13.17 | -29.27 | -5.85 |
| 6 | June | 131 | 91.22 | 39.78 | 10.51 | 1.75 |
| 7 | July | 111 | 103.15 | 7.85 | 18.36 | 2.62 |
| 8 | August | 116 | 105.51 | 10.49 | 28.85 | 3.61 |
| 9 | September | 89 | 108.65 | -19.65 | 9.19 | 1.02 |
| 10 | October | 95 | 102.76 | -7.76 | 1.44 | 0.14 |
| 11 | November | 88 | 100.43 | -12.43 | -10.99 | -1.00 |
| 12 | December | 90 | 96.70 | -6.70 | -17.70 | -1.47 |
| 13 | January (2017) | 94.69 |
MAD:
| Period | Month (2016) | Demand | Exponential moving average (α = .3) | Absolute error | Cumulative of absolute Forecasting error | MAD |
| 1 | January | 119 | 100.00 | 19.00 | 19.00 | 19.00 |
| 2 | February | 72 | 105.70 | 33.70 | 52.70 | 26.35 |
| 3 | March | 113 | 95.59 | 17.41 | 70.11 | 23.37 |
| 4 | April | 82 | 100.81 | 18.81 | 88.92 | 22.23 |
| 5 | May | 82 | 95.17 | 13.17 | 102.09 | 20.42 |
| 6 | June | 131 | 91.22 | 39.78 | 141.87 | 23.65 |
| 7 | July | 111 | 103.15 | 7.85 | 149.72 | 21.39 |
| 8 | August | 116 | 105.51 | 10.49 | 160.21 | 20.03 |
| 9 | September | 89 | 108.65 | 19.65 | 179.87 | 19.99 |
| 10 | October | 95 | 102.76 | 7.76 | 187.63 | 18.76 |
| 11 | November | 88 | 100.43 | 12.43 | 200.06 | 18.19 |
| 12 | December | 90 | 96.70 | 6.70 | 206.76 | 17.23 |
| 13 | January (2017) | 94.69 |
MAPE:
| Period | Month (2016) | Demand | Exponential moving average (α = .3) | % of absolute error | Cumulative % of absolute error | MAPE |
| 1 | January | 119 | 100.00 | 15.97% | 15.97% | 15.97% |
| 2 | February | 72 | 105.70 | 46.81% | 62.77% | 31.39% |
| 3 | March | 113 | 95.59 | 15.41% | 78.18% | 26.06% |
| 4 | April | 82 | 100.81 | 22.94% | 101.12% | 25.28% |
| 5 | May | 82 | 95.17 | 16.06% | 117.18% | 23.44% |
| 6 | June | 131 | 91.22 | 30.37% | 147.55% | 24.59% |
| 7 | July | 111 | 103.15 | 7.07% | 154.62% | 22.09% |
| 8 | August | 116 | 105.51 | 9.05% | 163.66% | 20.46% |
| 9 | September | 89 | 108.65 | 22.08% | 185.75% | 20.64% |
| 10 | October | 95 | 102.76 | 8.17% | 193.92% | 19.39% |
| 11 | November | 88 | 100.43 | 14.13% | 208.04% | 18.91% |
| 12 | December | 90 | 96.70 | 7.45% | 215.49% | 17.96% |
| 13 | January (2017) | 94.69 |
