1) 3 year Single Exponential Smoothing forecast | year | 1 | 2 | 3 | 4 | 5 | 6 |
| Sales | 650 | 700 | 810 | 800 | 900 | 700 |
Calculate 3 year Single Exponential Smoothing forecastSolution:(1)
year | (2)
Sales | (3)
Exponential Smoothing
`(alpha=0.1)` |
| 1 | 650 | 650 |
| 2 | 700 | `0.1*650+0.9*650=650` |
| 3 | 810 | `0.1*700+0.9*650=655` |
| 4 | 800 | `0.1*810+0.9*655=670.5` |
| 5 | 900 | `0.1*800+0.9*670.5=683.45` |
| 6 | 700 | `0.1*900+0.9*683.45=705.105` |
| 7 | | `0.1*700+0.9*705.105=704.5945` |
(1)
year | (2)
Sales | (3)
Exponential Smoothing | (4)
Error | (5)
|Error| | (6)
`"Error"^2` | (7)
`|%"Error"|` |
| 1 | 650 | 650 | | | | |
| 2 | 700 | 650 | | | | |
| 3 | 810 | 655 | | | | |
| 4 | 800 | 670.5 | `800-670.5=129.5` | `129.5` | `16770.25` | `16.19%` |
| 5 | 900 | 683.45 | `900-683.45=216.55` | `216.55` | `46893.9025` | `24.06%` |
| 6 | 700 | 705.105 | `700-705.105=-5.105` | `5.105` | `26.061` | `0.73%` |
| 7 | | 704.5945 | Total | `351.155` | `63690.2135` | `40.98%` |
Forecasting errors1. Mean absolute error (MAE), also called mean absolute deviation (MAD)MAE`=1/n sum |e_i|=351.155/3=117.0517`
2. Mean squared error (MSE)MSE`=1/n sum |e_i^2|=63690.2135/3=21230.0712`
3. Root mean squared error (RMSE)RMSE`=sqrt(MSE)=sqrt(21230.0712)=145.7054`
4. Mean absolute percentage error (MAPE)MAPE`=1/n sum |e_i/y_i|=40.98/3=13.66`
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