1) 4 year Exponential Moving Average forecast | year | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Sales | 20 | 21 | 23 | 22 | 25 | 24 | 27 | 26 | 28 | 30 |
Calculate 4 year Exponential Moving Average forecast
Solution:
`alpha=2/(n+1)=2/(4+1)=0.4`
(1)
year | (2)
Sales | (3)
Exponential Smoothing
`(alpha=0.4)` |
| 1 | 20 | 20 |
| 2 | 21 | `0.4*20+0.6*20=20` |
| 3 | 23 | `0.4*21+0.6*20=20.4` |
| 4 | 22 | `0.4*23+0.6*20.4=21.44` |
| 5 | 25 | `0.4*22+0.6*21.44=21.664` |
| 6 | 24 | `0.4*25+0.6*21.664=22.9984` |
| 7 | 27 | `0.4*24+0.6*22.9984=23.399` |
| 8 | 26 | `0.4*27+0.6*23.399=24.8394` |
| 9 | 28 | `0.4*26+0.6*24.8394=25.3037` |
| 10 | 30 | `0.4*28+0.6*25.3037=26.3822` |
| 11 | | `0.4*30+0.6*26.3822=27.8293` |
(1)
year | (2)
Sales | (3)
Exponential Smoothing | (4)
Error | (5)
|Error| | (6)
`"Error"^2` | (7)
`|%"Error"|` |
| 1 | 20 | 20 | | | | |
| 2 | 21 | 20 | | | | |
| 3 | 23 | 20.4 | | | | |
| 4 | 22 | 21.44 | | | | |
| 5 | 25 | 21.664 | `25-21.664=3.336` | `3.336` | `11.1289` | `13.34%` |
| 6 | 24 | 22.9984 | `24-22.9984=1.0016` | `1.0016` | `1.0032` | `4.17%` |
| 7 | 27 | 23.399 | `27-23.399=3.601` | `3.601` | `12.9669` | `13.34%` |
| 8 | 26 | 24.8394 | `26-24.8394=1.1606` | `1.1606` | `1.3469` | `4.46%` |
| 9 | 28 | 25.3037 | `28-25.3037=2.6963` | `2.6963` | `7.2703` | `9.63%` |
| 10 | 30 | 26.3822 | `30-26.3822=3.6178` | `3.6178` | `13.0885` | `12.06%` |
| 11 | | 27.8293 | Total | `15.4133` | `46.8048` | `57.01%` |
Forecasting errors
1. Mean absolute error (MAE), also called mean absolute deviation (MAD)
MAE`=1/n sum |e_i|=15.4133/6=2.5689`
2. Mean squared error (MSE)
MSE`=1/n sum |e_i^2|=46.8048/6=7.8008`
3. Root mean squared error (RMSE)
RMSE`=sqrt(MSE)=sqrt(7.8008)=2.793`
4. Mean absolute percentage error (MAPE)
MAPE`=1/n sum |e_i/y_i|=57.01/6=9.5`
This material is intended as a summary. Use your textbook for detail explanation.
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