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`

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