1) 5 year Exponential Moving Average forecast | year | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| Sales | 5.2 | 4.9 | 5.5 | 4.9 | 5.2 | 5.7 | 5.4 | 5.8 | 5.9 | 6 | 5.2 | 4.8 |
Calculate 5 year Exponential Moving Average forecast
Solution:
`alpha=2/(n+1)=2/(5+1)=0.3333`
(1)
year | (2)
Sales | (3)
Exponential Smoothing
`(alpha=0.3333)` |
| 1 | 5.2 | 5.2 |
| 2 | 4.9 | `0.3333*5.2+0.6667*5.2=5.2` |
| 3 | 5.5 | `0.3333*4.9+0.6667*5.2=5.1` |
| 4 | 4.9 | `0.3333*5.5+0.6667*5.1=5.2333` |
| 5 | 5.2 | `0.3333*4.9+0.6667*5.2333=5.1222` |
| 6 | 5.7 | `0.3333*5.2+0.6667*5.1222=5.1482` |
| 7 | 5.4 | `0.3333*5.7+0.6667*5.1482=5.3321` |
| 8 | 5.8 | `0.3333*5.4+0.6667*5.3321=5.3547` |
| 9 | 5.9 | `0.3333*5.8+0.6667*5.3547=5.5031` |
| 10 | 6 | `0.3333*5.9+0.6667*5.5031=5.6354` |
| 11 | 5.2 | `0.3333*6+0.6667*5.6354=5.7569` |
| 12 | 4.8 | `0.3333*5.2+0.6667*5.7569=5.5713` |
| 13 | | `0.3333*4.8+0.6667*5.5713=5.3142` |
(1)
year | (2)
Sales | (3)
Exponential Smoothing | (4)
Error | (5)
|Error| | (6)
`"Error"^2` | (7)
`|%"Error"|` |
| 1 | 5.2 | 5.2 | | | | |
| 2 | 4.9 | 5.2 | | | | |
| 3 | 5.5 | 5.1 | | | | |
| 4 | 4.9 | 5.2333 | | | | |
| 5 | 5.2 | 5.1222 | | | | |
| 6 | 5.7 | 5.1482 | `5.7-5.1482=0.5518` | `0.5518` | `0.3045` | `9.68%` |
| 7 | 5.4 | 5.3321 | `5.4-5.3321=0.0679` | `0.0679` | `0.0046` | `1.26%` |
| 8 | 5.8 | 5.3547 | `5.8-5.3547=0.4453` | `0.4453` | `0.1983` | `7.68%` |
| 9 | 5.9 | 5.5031 | `5.9-5.5031=0.3969` | `0.3969` | `0.1575` | `6.73%` |
| 10 | 6 | 5.6354 | `6-5.6354=0.3646` | `0.3646` | `0.1329` | `6.08%` |
| 11 | 5.2 | 5.7569 | `5.2-5.7569=-0.5569` | `0.5569` | `0.3102` | `10.71%` |
| 12 | 4.8 | 5.5713 | `4.8-5.5713=-0.7713` | `0.7713` | `0.5949` | `16.07%` |
| 13 | | 5.3142 | Total | `3.1547` | `1.7029` | `58.2%` |
Forecasting errors
1. Mean absolute error (MAE), also called mean absolute deviation (MAD)
MAE`=1/n sum |e_i|=3.1547/7=0.4507`
2. Mean squared error (MSE)
MSE`=1/n sum |e_i^2|=1.7029/7=0.2433`
3. Root mean squared error (RMSE)
RMSE`=sqrt(MSE)=sqrt(0.2433)=0.4932`
4. Mean absolute percentage error (MAPE)
MAPE`=1/n sum |e_i/y_i|=58.2/7=8.31`
This material is intended as a summary. Use your textbook for detail explanation.
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