Simple Moving Average forecast 5 year Exponential Moving Average forecast Example

1) 5 year Exponential 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 Exponential Moving Average forecast

Solution:
`alpha=2/(n+1)=2/(5+1)=0.3333`

(1) year	(2) Sales	(3) Exponential Smoothing `(alpha=0.3333)`
1	5.2	5.2
2	4.9	`0.33335.2+0.66675.2=5.2`
3	5.5	`0.33334.9+0.66675.2=5.1`
4	4.9	`0.33335.5+0.66675.1=5.2333`
5	5.2	`0.33334.9+0.66675.2333=5.1222`
6	5.7	`0.33335.2+0.66675.1222=5.1482`
7	5.4	`0.33335.7+0.66675.1482=5.3321`
8	5.8	`0.33335.4+0.66675.3321=5.3547`
9	5.9	`0.33335.8+0.66675.3547=5.5031`
10	6	`0.33335.9+0.66675.5031=5.6354`
11	5.2	`0.33336+0.66675.6354=5.7569`
12	4.8	`0.33335.2+0.66675.7569=5.5713`
13		`0.33334.8+0.66675.5713=5.3142`

(1) year	(2) Sales	(3) Exponential Smoothing	(4) Error	(5) \|Error\|	(6) `"Error"^2`	(7) `\|%"Error"\|`
1	5.2	5.2
2	4.9	5.2
3	5.5	5.1
4	4.9	5.2333
5	5.2	5.1222
6	5.7	5.1482	`5.7-5.1482=0.5518`	`0.5518`	`0.3045`	`9.68%`
7	5.4	5.3321	`5.4-5.3321=0.0679`	`0.0679`	`0.0046`	`1.26%`
8	5.8	5.3547	`5.8-5.3547=0.4453`	`0.4453`	`0.1983`	`7.68%`
9	5.9	5.5031	`5.9-5.5031=0.3969`	`0.3969`	`0.1575`	`6.73%`
10	6	5.6354	`6-5.6354=0.3646`	`0.3646`	`0.1329`	`6.08%`
11	5.2	5.7569	`5.2-5.7569=-0.5569`	`0.5569`	`0.3102`	`10.71%`
12	4.8	5.5713	`4.8-5.5713=-0.7713`	`0.7713`	`0.5949`	`16.07%`
13		5.3142	Total	`3.1547`	`1.7029`	`58.2%`

Forecasting errors

1. Mean absolute error (MAE), also called mean absolute deviation (MAD)
MAE`=1/n sum |e_i|=3.1547/7=0.4507`

2. Mean squared error (MSE)
MSE`=1/n sum |e_i^2|=1.7029/7=0.2433`

3. Root mean squared error (RMSE)
RMSE`=sqrt(MSE)=sqrt(0.2433)=0.4932`

4. Mean absolute percentage error (MAPE)
MAPE`=1/n sum |e_i/y_i|=58.2/7=8.31`

This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then Submit Here

3. 5 year Exponential Moving Average forecast Example