1) 4 year Simple Moving Average forecast | year | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Sales | 20 | 21 | 23 | 22 | 25 | 24 | 27 | 26 | 28 | 30 |
Calculate 4 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 | 20 | 21 | 23 | 22 | 25 | 24 | 27 | 26 | 28 | 30 |
|---|
Calculation of 4 year moving averages of the data
(1)
year | (2)
Sales | (3)
4 year moving total | (4)
4 year moving average
`(3)-:4` | (5)
2 item moving total of
column (4) | (6)
4 year centered moving average
`(5)-:2` |
| 1 | 20 | | | | |
| | | | | |
| 2 | 21 | | | | |
| | `20+21+23+22=86` | `86-:4=21.5` | | |
| 3 | 23 | | | `21.5+22.75=44.25` | `44.25-:2=22.125` |
| | `21+23+22+25=91` | `91-:4=22.75` | | |
| 4 | 22 | | | `22.75+23.5=46.25` | `46.25-:2=23.125` |
| | `23+22+25+24=94` | `94-:4=23.5` | | |
| 5 | 25 | | | `23.5+24.5=48` | `48-:2=24` |
| | `22+25+24+27=98` | `98-:4=24.5` | | |
| 6 | 24 | | | `24.5+25.5=50` | `50-:2=25` |
| | `25+24+27+26=102` | `102-:4=25.5` | | |
| 7 | 27 | | | `25.5+26.25=51.75` | `51.75-:2=25.875` |
| | `24+27+26+28=105` | `105-:4=26.25` | | |
| 8 | 26 | | | `26.25+27.75=54` | `54-:2=27` |
| | `27+26+28+30=111` | `111-:4=27.75` | | |
| 9 | 28 | | | | |
| | | | | |
| 10 | 30 | | | | |
(1)
year | (2)
Sales | (3)
4 year moving average | (4)
Error | (5)
|Error| | (6)
`"Error"^2` | (7)
`|%"Error"|` |
| 1 | 20 | | | | | |
| 2 | 21 | | | | | |
| 3 | 23 | | | | | |
| 4 | 22 | | | | | |
| 5 | 25 | 22.125 | `25-22.125=2.875` | `2.875` | `8.2656` | `11.5%` |
| 6 | 24 | 23.125 | `24-23.125=0.875` | `0.875` | `0.7656` | `3.65%` |
| 7 | 27 | 24 | `27-24=3` | `3` | `9` | `11.11%` |
| 8 | 26 | 25 | `26-25=1` | `1` | `1` | `3.85%` |
| 9 | 28 | 25.875 | `28-25.875=2.125` | `2.125` | `4.5156` | `7.59%` |
| 10 | 30 | 27 | `30-27=3` | `3` | `9` | `10%` |
| 11 | | 0 | Total | `12.875` | `32.5469` | `47.69%` |
Forecasting errors
1. Mean absolute error (MAE), also called mean absolute deviation (MAD)
MAE`=1/n sum |e_i|=12.875/6=2.1458`
2. Mean squared error (MSE)
MSE`=1/n sum |e_i^2|=32.5469/6=5.4245`
3. Root mean squared error (RMSE)
RMSE`=sqrt(MSE)=sqrt(5.4245)=2.3291`
4. Mean absolute percentage error (MAPE)
MAPE`=1/n sum |e_i/y_i|=47.69/6=7.95`
This material is intended as a summary. Use your textbook for detail explanation.
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