1) 5 year Weighted 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 Weighted Moving Average forecast with weight=1,2,1,2,1
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 |
|---|
The weights of the 5 years are respectively 1,2,1,2,1 and their sum is 7
Calculation of 5 year moving averages of the data
(1)
year | (2)
Sales | (3)
5 year weighted moving total | (4)
5 year weighted moving average
`(3)-:7` |
| 1 | 5.2 | | |
| 2 | 4.9 | | |
| 3 | 5.5 | `1xx5.2+2xx4.9+1xx5.5+2xx4.9+1xx5.2=35.5` | `35.5-:7=5.0714` |
| 4 | 4.9 | `1xx4.9+2xx5.5+1xx4.9+2xx5.2+1xx5.7=36.9` | `36.9-:7=5.2714` |
| 5 | 5.2 | `1xx5.5+2xx4.9+1xx5.2+2xx5.7+1xx5.4=37.3` | `37.3-:7=5.3286` |
| 6 | 5.7 | `1xx4.9+2xx5.2+1xx5.7+2xx5.4+1xx5.8=37.6` | `37.6-:7=5.3714` |
| 7 | 5.4 | `1xx5.2+2xx5.7+1xx5.4+2xx5.8+1xx5.9=39.5` | `39.5-:7=5.6429` |
| 8 | 5.8 | `1xx5.7+2xx5.4+1xx5.8+2xx5.9+1xx6=40.1` | `40.1-:7=5.7286` |
| 9 | 5.9 | `1xx5.4+2xx5.8+1xx5.9+2xx6+1xx5.2=40.1` | `40.1-:7=5.7286` |
| 10 | 6 | `1xx5.8+2xx5.9+1xx6+2xx5.2+1xx4.8=38.8` | `38.8-:7=5.5429` |
| 11 | 5.2 | | |
| 12 | 4.8 | | |
(1)
year | (2)
Sales | (3)
5 year weighted 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 | 5.0714 | `5.7-5.0714=0.6286` | `0.6286` | `0.3951` | `11.03%` |
| 7 | 5.4 | 5.2714 | `5.4-5.2714=0.1286` | `0.1286` | `0.0165` | `2.38%` |
| 8 | 5.8 | 5.3286 | `5.8-5.3286=0.4714` | `0.4714` | `0.2222` | `8.13%` |
| 9 | 5.9 | 5.3714 | `5.9-5.3714=0.5286` | `0.5286` | `0.2794` | `8.96%` |
| 10 | 6 | 5.6429 | `6-5.6429=0.3571` | `0.3571` | `0.1276` | `5.95%` |
| 11 | 5.2 | 5.7286 | `5.2-5.7286=-0.5286` | `0.5286` | `0.2794` | `10.16%` |
| 12 | 4.8 | 5.7286 | `4.8-5.7286=-0.9286` | `0.9286` | `0.8622` | `19.35%` |
| 13 | | 5.5429 | Total | `3.5714` | `2.1824` | `65.96%` |
Forecasting errors
1. Mean absolute error (MAE), also called mean absolute deviation (MAD)
MAE`=1/n sum |e_i|=3.5714/7=0.5102`
2. Mean squared error (MSE)
MSE`=1/n sum |e_i^2|=2.1824/7=0.3118`
3. Root mean squared error (RMSE)
RMSE`=sqrt(MSE)=sqrt(0.3118)=0.5584`
4. Mean absolute percentage error (MAPE)
MAPE`=1/n sum |e_i/y_i|=65.96/7=9.42`
This material is intended as a summary. Use your textbook for detail explanation.
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