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`

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