Formula

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Examples
1) 3 year Simple 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 3 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	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

Calculation of 3 year moving averages of the data

(1) year	(2) Sales	(3) 3 year moving total	(4) 3 year moving average `(3)-:3`
1	5.2
2	4.9	`5.2+4.9+5.5=15.6`	`15.6-:3=5.2`
3	5.5	`4.9+5.5+4.9=15.3`	`15.3-:3=5.1`
4	4.9	`5.5+4.9+5.2=15.6`	`15.6-:3=5.2`
5	5.2	`4.9+5.2+5.7=15.8`	`15.8-:3=5.2667`
6	5.7	`5.2+5.7+5.4=16.3`	`16.3-:3=5.4333`
7	5.4	`5.7+5.4+5.8=16.9`	`16.9-:3=5.6333`
8	5.8	`5.4+5.8+5.9=17.1`	`17.1-:3=5.7`
9	5.9	`5.8+5.9+6=17.7`	`17.7-:3=5.9`
10	6	`5.9+6+5.2=17.1`	`17.1-:3=5.7`
11	5.2	`6+5.2+4.8=16`	`16-:3=5.3333`
12	4.8

(1) year	(2) Sales	(3) 3 year moving average	(4) Error	(5) |Error|	(6) `"Error"^2`	(7) `|%"Error"|`
1	5.2
2	4.9
3	5.5
4	4.9	5.2	`4.9-5.2=-0.3`	`0.3`	`0.09`	`6.12%`
5	5.2	5.1	`5.2-5.1=0.1`	`0.1`	`0.01`	`1.92%`
6	5.7	5.2	`5.7-5.2=0.5`	`0.5`	`0.25`	`8.77%`
7	5.4	5.2667	`5.4-5.2667=0.1333`	`0.1333`	`0.0178`	`2.47%`
8	5.8	5.4333	`5.8-5.4333=0.3667`	`0.3667`	`0.1344`	`6.32%`
9	5.9	5.6333	`5.9-5.6333=0.2667`	`0.2667`	`0.0711`	`4.52%`
10	6	5.7	`6-5.7=0.3`	`0.3`	`0.09`	`5%`
11	5.2	5.9	`5.2-5.9=-0.7`	`0.7`	`0.49`	`13.46%`
12	4.8	5.7	`4.8-5.7=-0.9`	`0.9`	`0.81`	`18.75%`
13		5.3333	Total	`3.5667`	`1.9633`	`67.34%`

Forecasting errors

1. Mean absolute error (MAE), also called mean absolute deviation (MAD)
MAE`=1/n sum |e_i|=3.5667/9=0.3963`


2. Mean squared error (MSE)
MSE`=1/n sum |e_i^2|=1.9633/9=0.2181`


3. Root mean squared error (RMSE)
RMSE`=sqrt(MSE)=sqrt(0.2181)=0.4671`


4. Mean absolute percentage error (MAPE)
MAPE`=1/n sum |e_i/y_i|=67.34/9=7.48`

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2) 3 year Simple Moving Average forecast

year	1	2	3	4	5	6	7	8	9	10
Sales	30	25	35	25	20	30	35	40	30	45

Calculate 3 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	30	25	35	25	20	30	35	40	30	45

Calculation of 3 year moving averages of the data

(1) year	(2) Sales	(3) 3 year moving total	(4) 3 year moving average `(3)-:3`
1	30
2	25	`30+25+35=90`	`90-:3=30`
3	35	`25+35+25=85`	`85-:3=28.3333`
4	25	`35+25+20=80`	`80-:3=26.6667`
5	20	`25+20+30=75`	`75-:3=25`
6	30	`20+30+35=85`	`85-:3=28.3333`
7	35	`30+35+40=105`	`105-:3=35`
8	40	`35+40+30=105`	`105-:3=35`
9	30	`40+30+45=115`	`115-:3=38.3333`
10	45

(1) year	(2) Sales	(3) 3 year moving average	(4) Error	(5) |Error|	(6) `"Error"^2`	(7) `|%"Error"|`
1	30
2	25
3	35
4	25	30	`25-30=-5`	`5`	`25`	`20%`
5	20	28.3333	`20-28.3333=-8.3333`	`8.3333`	`69.4444`	`41.67%`
6	30	26.6667	`30-26.6667=3.3333`	`3.3333`	`11.1111`	`11.11%`
7	35	25	`35-25=10`	`10`	`100`	`28.57%`
8	40	28.3333	`40-28.3333=11.6667`	`11.6667`	`136.1111`	`29.17%`
9	30	35	`30-35=-5`	`5`	`25`	`16.67%`
10	45	35	`45-35=10`	`10`	`100`	`22.22%`
11		38.3333	Total	`53.3333`	`466.6667`	`169.4%`

Forecasting errors

1. Mean absolute error (MAE), also called mean absolute deviation (MAD)
MAE`=1/n sum |e_i|=53.3333/7=7.619`


2. Mean squared error (MSE)
MSE`=1/n sum |e_i^2|=466.6667/7=66.6667`


3. Root mean squared error (RMSE)
RMSE`=sqrt(MSE)=sqrt(66.6667)=8.165`


4. Mean absolute percentage error (MAPE)
MAPE`=1/n sum |e_i/y_i|=169.4/7=24.2`

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