1) 5 year Simple 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 Simple Moving Average forecast
Solution:
The value of table for `x` and `y`
| x | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|
| y | 5.2 | 4.9 | 5.5 | 4.9 | 5.2 | 5.7 | 5.4 | 5.8 | 5.9 | 6 | 5.2 | 4.8 |
|---|
Calculation of 5 year moving averages of the data
(1)
year | (2)
Sales | (3)
5 year moving total | (4)
5 year moving average
`(3)-:5` |
| 1 | 5.2 | | |
| 2 | 4.9 | | |
| 3 | 5.5 | `5.2+4.9+5.5+4.9+5.2=25.7` | `25.7-:5=5.14` |
| 4 | 4.9 | `4.9+5.5+4.9+5.2+5.7=26.2` | `26.2-:5=5.24` |
| 5 | 5.2 | `5.5+4.9+5.2+5.7+5.4=26.7` | `26.7-:5=5.34` |
| 6 | 5.7 | `4.9+5.2+5.7+5.4+5.8=27` | `27-:5=5.4` |
| 7 | 5.4 | `5.2+5.7+5.4+5.8+5.9=28` | `28-:5=5.6` |
| 8 | 5.8 | `5.7+5.4+5.8+5.9+6=28.8` | `28.8-:5=5.76` |
| 9 | 5.9 | `5.4+5.8+5.9+6+5.2=28.3` | `28.3-:5=5.66` |
| 10 | 6 | `5.8+5.9+6+5.2+4.8=27.7` | `27.7-:5=5.54` |
| 11 | 5.2 | | |
| 12 | 4.8 | | |
(1)
year | (2)
Sales | (3)
5 year moving average | (4)
Error | (5)
|Error| | (6)
`"Error"^2` | (7)
`|%"Error"|` |
| 1 | 5.2 | | | | | |
| 2 | 4.9 | | | | | |
| 3 | 5.5 | | | | | |
| 4 | 4.9 | | | | | |
| 5 | 5.2 | | | | | |
| 6 | 5.7 | 5.14 | `5.7-5.14=0.56` | `0.56` | `0.3136` | `9.82%` |
| 7 | 5.4 | 5.24 | `5.4-5.24=0.16` | `0.16` | `0.0256` | `2.96%` |
| 8 | 5.8 | 5.34 | `5.8-5.34=0.46` | `0.46` | `0.2116` | `7.93%` |
| 9 | 5.9 | 5.4 | `5.9-5.4=0.5` | `0.5` | `0.25` | `8.47%` |
| 10 | 6 | 5.6 | `6-5.6=0.4` | `0.4` | `0.16` | `6.67%` |
| 11 | 5.2 | 5.76 | `5.2-5.76=-0.56` | `0.56` | `0.3136` | `10.77%` |
| 12 | 4.8 | 5.66 | `4.8-5.66=-0.86` | `0.86` | `0.7396` | `17.92%` |
| 13 | | 5.54 | Total | `3.5` | `2.014` | `64.55%` |
Forecasting errors
1. Mean absolute error (MAE), also called mean absolute deviation (MAD)
MAE`=1/n sum |e_i|=3.5/7=0.5`
2. Mean squared error (MSE)
MSE`=1/n sum |e_i^2|=2.014/7=0.2877`
3. Root mean squared error (RMSE)
RMSE`=sqrt(MSE)=sqrt(0.2877)=0.5364`
4. Mean absolute percentage error (MAPE)
MAPE`=1/n sum |e_i/y_i|=64.55/7=9.22`
This material is intended as a summary. Use your textbook for detail explanation.
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