Formula
Examples
1) 3 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 3 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 3 year moving averages of the data
(1)
year | (2)
Sales | (3)
3 year moving total | (4)
3 year moving average
`(3)-:3` |
| 1 | 5.2 | | |
| 2 | 4.9 | `5.2+4.9+5.5=15.6` | `15.6-:3=5.2` |
| 3 | 5.5 | `4.9+5.5+4.9=15.3` | `15.3-:3=5.1` |
| 4 | 4.9 | `5.5+4.9+5.2=15.6` | `15.6-:3=5.2` |
| 5 | 5.2 | `4.9+5.2+5.7=15.8` | `15.8-:3=5.2667` |
| 6 | 5.7 | `5.2+5.7+5.4=16.3` | `16.3-:3=5.4333` |
| 7 | 5.4 | `5.7+5.4+5.8=16.9` | `16.9-:3=5.6333` |
| 8 | 5.8 | `5.4+5.8+5.9=17.1` | `17.1-:3=5.7` |
| 9 | 5.9 | `5.8+5.9+6=17.7` | `17.7-:3=5.9` |
| 10 | 6 | `5.9+6+5.2=17.1` | `17.1-:3=5.7` |
| 11 | 5.2 | `6+5.2+4.8=16` | `16-:3=5.3333` |
| 12 | 4.8 | | |
(1)
year | (2)
Sales | (3)
3 year moving average | (4)
Error | (5)
|Error| | (6)
`"Error"^2` | (7)
`|%"Error"|` |
| 1 | 5.2 | | | | | |
| 2 | 4.9 | | | | | |
| 3 | 5.5 | | | | | |
| 4 | 4.9 | 5.2 | `4.9-5.2=-0.3` | `0.3` | `0.09` | `6.12%` |
| 5 | 5.2 | 5.1 | `5.2-5.1=0.1` | `0.1` | `0.01` | `1.92%` |
| 6 | 5.7 | 5.2 | `5.7-5.2=0.5` | `0.5` | `0.25` | `8.77%` |
| 7 | 5.4 | 5.2667 | `5.4-5.2667=0.1333` | `0.1333` | `0.0178` | `2.47%` |
| 8 | 5.8 | 5.4333 | `5.8-5.4333=0.3667` | `0.3667` | `0.1344` | `6.32%` |
| 9 | 5.9 | 5.6333 | `5.9-5.6333=0.2667` | `0.2667` | `0.0711` | `4.52%` |
| 10 | 6 | 5.7 | `6-5.7=0.3` | `0.3` | `0.09` | `5%` |
| 11 | 5.2 | 5.9 | `5.2-5.9=-0.7` | `0.7` | `0.49` | `13.46%` |
| 12 | 4.8 | 5.7 | `4.8-5.7=-0.9` | `0.9` | `0.81` | `18.75%` |
| 13 | | 5.3333 | Total | `3.5667` | `1.9633` | `67.34%` |
Forecasting errors
1. Mean absolute error (MAE), also called mean absolute deviation (MAD)
MAE`=1/n sum |e_i|=3.5667/9=0.3963`
2. Mean squared error (MSE)
MSE`=1/n sum |e_i^2|=1.9633/9=0.2181`
3. Root mean squared error (RMSE)
RMSE`=sqrt(MSE)=sqrt(0.2181)=0.4671`
4. Mean absolute percentage error (MAPE)
MAPE`=1/n sum |e_i/y_i|=67.34/9=7.48`
2) 3 year Simple 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 Simple Moving Average forecast
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 |
|---|
Calculation of 3 year moving averages of the data
(1)
year | (2)
Sales | (3)
3 year moving total | (4)
3 year moving average
`(3)-:3` |
| 1 | 30 | | |
| 2 | 25 | `30+25+35=90` | `90-:3=30` |
| 3 | 35 | `25+35+25=85` | `85-:3=28.3333` |
| 4 | 25 | `35+25+20=80` | `80-:3=26.6667` |
| 5 | 20 | `25+20+30=75` | `75-:3=25` |
| 6 | 30 | `20+30+35=85` | `85-:3=28.3333` |
| 7 | 35 | `30+35+40=105` | `105-:3=35` |
| 8 | 40 | `35+40+30=105` | `105-:3=35` |
| 9 | 30 | `40+30+45=115` | `115-:3=38.3333` |
| 10 | 45 | | |
(1)
year | (2)
Sales | (3)
3 year moving average | (4)
Error | (5)
|Error| | (6)
`"Error"^2` | (7)
`|%"Error"|` |
| 1 | 30 | | | | | |
| 2 | 25 | | | | | |
| 3 | 35 | | | | | |
| 4 | 25 | 30 | `25-30=-5` | `5` | `25` | `20%` |
| 5 | 20 | 28.3333 | `20-28.3333=-8.3333` | `8.3333` | `69.4444` | `41.67%` |
| 6 | 30 | 26.6667 | `30-26.6667=3.3333` | `3.3333` | `11.1111` | `11.11%` |
| 7 | 35 | 25 | `35-25=10` | `10` | `100` | `28.57%` |
| 8 | 40 | 28.3333 | `40-28.3333=11.6667` | `11.6667` | `136.1111` | `29.17%` |
| 9 | 30 | 35 | `30-35=-5` | `5` | `25` | `16.67%` |
| 10 | 45 | 35 | `45-35=10` | `10` | `100` | `22.22%` |
| 11 | | 38.3333 | Total | `53.3333` | `466.6667` | `169.4%` |
Forecasting errors
1. Mean absolute error (MAE), also called mean absolute deviation (MAD)
MAE`=1/n sum |e_i|=53.3333/7=7.619`
2. Mean squared error (MSE)
MSE`=1/n sum |e_i^2|=466.6667/7=66.6667`
3. Root mean squared error (RMSE)
RMSE`=sqrt(MSE)=sqrt(66.6667)=8.165`
4. Mean absolute percentage error (MAPE)
MAPE`=1/n sum |e_i/y_i|=169.4/7=24.2`
This material is intended as a summary. Use your textbook for detail explanation.
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