Formula
Examples
1) 3 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 3 year Weighted Moving Average forecast with weight=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 3 years are respectively 1,2,1 and their sum is 4
Calculation of 3 year moving averages of the data
(1)
year | (2)
Sales | (3)
3 year weighted moving total | (4)
3 year weighted moving average
`(3)-:4` |
| 1 | 5.2 | | |
| 2 | 4.9 | `1xx5.2+2xx4.9+1xx5.5=20.5` | `20.5-:4=5.125` |
| 3 | 5.5 | `1xx4.9+2xx5.5+1xx4.9=20.8` | `20.8-:4=5.2` |
| 4 | 4.9 | `1xx5.5+2xx4.9+1xx5.2=20.5` | `20.5-:4=5.125` |
| 5 | 5.2 | `1xx4.9+2xx5.2+1xx5.7=21` | `21-:4=5.25` |
| 6 | 5.7 | `1xx5.2+2xx5.7+1xx5.4=22` | `22-:4=5.5` |
| 7 | 5.4 | `1xx5.7+2xx5.4+1xx5.8=22.3` | `22.3-:4=5.575` |
| 8 | 5.8 | `1xx5.4+2xx5.8+1xx5.9=22.9` | `22.9-:4=5.725` |
| 9 | 5.9 | `1xx5.8+2xx5.9+1xx6=23.6` | `23.6-:4=5.9` |
| 10 | 6 | `1xx5.9+2xx6+1xx5.2=23.1` | `23.1-:4=5.775` |
| 11 | 5.2 | `1xx6+2xx5.2+1xx4.8=21.2` | `21.2-:4=5.3` |
| 12 | 4.8 | | |
(1)
year | (2)
Sales | (3)
3 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 | 5.125 | `4.9-5.125=-0.225` | `0.225` | `0.0506` | `4.59%` |
| 5 | 5.2 | 5.2 | `5.2-5.2=0` | `0` | `0` | `0%` |
| 6 | 5.7 | 5.125 | `5.7-5.125=0.575` | `0.575` | `0.3306` | `10.09%` |
| 7 | 5.4 | 5.25 | `5.4-5.25=0.15` | `0.15` | `0.0225` | `2.78%` |
| 8 | 5.8 | 5.5 | `5.8-5.5=0.3` | `0.3` | `0.09` | `5.17%` |
| 9 | 5.9 | 5.575 | `5.9-5.575=0.325` | `0.325` | `0.1056` | `5.51%` |
| 10 | 6 | 5.725 | `6-5.725=0.275` | `0.275` | `0.0756` | `4.58%` |
| 11 | 5.2 | 5.9 | `5.2-5.9=-0.7` | `0.7` | `0.49` | `13.46%` |
| 12 | 4.8 | 5.775 | `4.8-5.775=-0.975` | `0.975` | `0.9506` | `20.31%` |
| 13 | | 5.3 | Total | `3.525` | `2.1156` | `66.5%` |
Forecasting errors
1. Mean absolute error (MAE), also called mean absolute deviation (MAD)
MAE`=1/n sum |e_i|=3.525/9=0.3917`
2. Mean squared error (MSE)
MSE`=1/n sum |e_i^2|=2.1156/9=0.2351`
3. Root mean squared error (RMSE)
RMSE`=sqrt(MSE)=sqrt(0.2351)=0.4848`
4. Mean absolute percentage error (MAPE)
MAPE`=1/n sum |e_i/y_i|=66.5/9=7.39`
2) 3 year Weighted Moving Average forecast | year | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Sales | 30 | 25 | 35 | 25 | 20 | 30 | 35 | 40 | 30 | 45 |
Calculate 3 year Weighted Moving Average forecast with weight=1,2,1
Solution:
The value of table for `x` and `y`
| x | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|
| y | 30 | 25 | 35 | 25 | 20 | 30 | 35 | 40 | 30 | 45 |
|---|
The weights of the 3 years are respectively 1,2,1 and their sum is 4
Calculation of 3 year moving averages of the data
(1)
year | (2)
Sales | (3)
3 year weighted moving total | (4)
3 year weighted moving average
`(3)-:4` |
| 1 | 30 | | |
| 2 | 25 | `1xx30+2xx25+1xx35=115` | `115-:4=28.75` |
| 3 | 35 | `1xx25+2xx35+1xx25=120` | `120-:4=30` |
| 4 | 25 | `1xx35+2xx25+1xx20=105` | `105-:4=26.25` |
| 5 | 20 | `1xx25+2xx20+1xx30=95` | `95-:4=23.75` |
| 6 | 30 | `1xx20+2xx30+1xx35=115` | `115-:4=28.75` |
| 7 | 35 | `1xx30+2xx35+1xx40=140` | `140-:4=35` |
| 8 | 40 | `1xx35+2xx40+1xx30=145` | `145-:4=36.25` |
| 9 | 30 | `1xx40+2xx30+1xx45=145` | `145-:4=36.25` |
| 10 | 45 | | |
(1)
year | (2)
Sales | (3)
3 year weighted moving average | (4)
Error | (5)
|Error| | (6)
`"Error"^2` | (7)
`|%"Error"|` |
| 1 | 30 | | | | | |
| 2 | 25 | | | | | |
| 3 | 35 | | | | | |
| 4 | 25 | 28.75 | `25-28.75=-3.75` | `3.75` | `14.0625` | `15%` |
| 5 | 20 | 30 | `20-30=-10` | `10` | `100` | `50%` |
| 6 | 30 | 26.25 | `30-26.25=3.75` | `3.75` | `14.0625` | `12.5%` |
| 7 | 35 | 23.75 | `35-23.75=11.25` | `11.25` | `126.5625` | `32.14%` |
| 8 | 40 | 28.75 | `40-28.75=11.25` | `11.25` | `126.5625` | `28.12%` |
| 9 | 30 | 35 | `30-35=-5` | `5` | `25` | `16.67%` |
| 10 | 45 | 36.25 | `45-36.25=8.75` | `8.75` | `76.5625` | `19.44%` |
| 11 | | 36.25 | Total | `53.75` | `482.8125` | `173.88%` |
Forecasting errors
1. Mean absolute error (MAE), also called mean absolute deviation (MAD)
MAE`=1/n sum |e_i|=53.75/7=7.6786`
2. Mean squared error (MSE)
MSE`=1/n sum |e_i^2|=482.8125/7=68.9732`
3. Root mean squared error (RMSE)
RMSE`=sqrt(MSE)=sqrt(68.9732)=8.305`
4. Mean absolute percentage error (MAPE)
MAPE`=1/n sum |e_i/y_i|=173.88/7=24.84`
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
