1) 4 year Weighted 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 Weighted Moving Average forecast with weight=1,2,2,1
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 |
|---|
The weights of the 4 years are respectively 1,2,2,1 and their sum is 6
Calculation of 4 year moving averages of the data
(1)
year | (2)
Sales | (3)
4 year weighted moving total | (4)
4 year weighted moving average
`(3)-:6` | (5)
2 item moving total of
column (4) | (6)
4 year centered weighted moving average
`(5)-:2` |
| 1 | 20 | | | | |
| | | | | |
| 2 | 21 | | | | |
| | `1xx20+2xx21+2xx23+1xx22=130` | `130-:6=21.6667` | | |
| 3 | 23 | | | `21.6667+22.6667=44.3333` | `44.3333-:2=22.1667` |
| | `1xx21+2xx23+2xx22+1xx25=136` | `136-:6=22.6667` | | |
| 4 | 22 | | | `22.6667+23.5=46.1667` | `46.1667-:2=23.0833` |
| | `1xx23+2xx22+2xx25+1xx24=141` | `141-:6=23.5` | | |
| 5 | 25 | | | `23.5+24.5=48` | `48-:2=24` |
| | `1xx22+2xx25+2xx24+1xx27=147` | `147-:6=24.5` | | |
| 6 | 24 | | | `24.5+25.5=50` | `50-:2=25` |
| | `1xx25+2xx24+2xx27+1xx26=153` | `153-:6=25.5` | | |
| 7 | 27 | | | `25.5+26.3333=51.8333` | `51.8333-:2=25.9167` |
| | `1xx24+2xx27+2xx26+1xx28=158` | `158-:6=26.3333` | | |
| 8 | 26 | | | `26.3333+27.5=53.8333` | `53.8333-:2=26.9167` |
| | `1xx27+2xx26+2xx28+1xx30=165` | `165-:6=27.5` | | |
| 9 | 28 | | | | |
| | | | | |
| 10 | 30 | | | | |
(1)
year | (2)
Sales | (3)
4 year weighted moving average | (4)
Error | (5)
|Error| | (6)
`"Error"^2` | (7)
`|%"Error"|` |
| 1 | 20 | | | | | |
| 2 | 21 | | | | | |
| 3 | 23 | | | | | |
| 4 | 22 | | | | | |
| 5 | 25 | 22.1667 | `25-22.1667=2.8333` | `2.8333` | `8.0278` | `11.33%` |
| 6 | 24 | 23.0833 | `24-23.0833=0.9167` | `0.9167` | `0.8403` | `3.82%` |
| 7 | 27 | 24 | `27-24=3` | `3` | `9` | `11.11%` |
| 8 | 26 | 25 | `26-25=1` | `1` | `1` | `3.85%` |
| 9 | 28 | 25.9167 | `28-25.9167=2.0833` | `2.0833` | `4.3403` | `7.44%` |
| 10 | 30 | 26.9167 | `30-26.9167=3.0833` | `3.0833` | `9.5069` | `10.28%` |
| 11 | | 0 | Total | `12.9167` | `32.7153` | `47.83%` |
Forecasting errors
1. Mean absolute error (MAE), also called mean absolute deviation (MAD)
MAE`=1/n sum |e_i|=12.9167/6=2.1528`
2. Mean squared error (MSE)
MSE`=1/n sum |e_i^2|=32.7153/6=5.4525`
3. Root mean squared error (RMSE)
RMSE`=sqrt(MSE)=sqrt(5.4525)=2.3351`
4. Mean absolute percentage error (MAPE)
MAPE`=1/n sum |e_i/y_i|=47.83/6=7.97`
This material is intended as a summary. Use your textbook for detail explanation.
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