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`

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