1) 4 year Single Exponential Smoothing 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 Single Exponential Smoothing forecast
Solution:
(1)
year | (2)
Sales | (3)
Exponential Smoothing
`(alpha=0.1)` |
| 1 | 20 | 20 |
| 2 | 21 | `0.1*20+0.9*20=20` |
| 3 | 23 | `0.1*21+0.9*20=20.1` |
| 4 | 22 | `0.1*23+0.9*20.1=20.39` |
| 5 | 25 | `0.1*22+0.9*20.39=20.551` |
| 6 | 24 | `0.1*25+0.9*20.551=20.9959` |
| 7 | 27 | `0.1*24+0.9*20.9959=21.2963` |
| 8 | 26 | `0.1*27+0.9*21.2963=21.8667` |
| 9 | 28 | `0.1*26+0.9*21.8667=22.28` |
| 10 | 30 | `0.1*28+0.9*22.28=22.852` |
| 11 | | `0.1*30+0.9*22.852=23.5668` |
(1)
year | (2)
Sales | (3)
Exponential Smoothing | (4)
Error | (5)
|Error| | (6)
`"Error"^2` | (7)
`|%"Error"|` |
| 1 | 20 | 20 | | | | |
| 2 | 21 | 20 | | | | |
| 3 | 23 | 20.1 | | | | |
| 4 | 22 | 20.39 | | | | |
| 5 | 25 | 20.551 | `25-20.551=4.449` | `4.449` | `19.7936` | `17.8%` |
| 6 | 24 | 20.9959 | `24-20.9959=3.0041` | `3.0041` | `9.0246` | `12.52%` |
| 7 | 27 | 21.2963 | `27-21.2963=5.7037` | `5.7037` | `32.5321` | `21.12%` |
| 8 | 26 | 21.8667 | `26-21.8667=4.1333` | `4.1333` | `17.0843` | `15.9%` |
| 9 | 28 | 22.28 | `28-22.28=5.72` | `5.72` | `32.7183` | `20.43%` |
| 10 | 30 | 22.852 | `30-22.852=7.148` | `7.148` | `51.0938` | `23.83%` |
| 11 | | 23.5668 | Total | `30.1581` | `162.2467` | `111.59%` |
Forecasting errors
1. Mean absolute error (MAE), also called mean absolute deviation (MAD)
MAE`=1/n sum |e_i|=30.1581/6=5.0263`
2. Mean squared error (MSE)
MSE`=1/n sum |e_i^2|=162.2467/6=27.0411`
3. Root mean squared error (RMSE)
RMSE`=sqrt(MSE)=sqrt(27.0411)=5.2001`
4. Mean absolute percentage error (MAPE)
MAPE`=1/n sum |e_i/y_i|=111.59/6=18.6`
This material is intended as a summary. Use your textbook for detail explanation.
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