Single Exponential Smoothing forecast 4 year Single Exponential Smoothing forecast Example

1) 4 year Single Exponential Smoothing 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 Single Exponential Smoothing forecast

Solution:

(1) year	(2) Sales	(3) Exponential Smoothing `(alpha=0.1)`
1	20	20
2	21	`0.120+0.920=20`
3	23	`0.121+0.920=20.1`
4	22	`0.123+0.920.1=20.39`
5	25	`0.122+0.920.39=20.551`
6	24	`0.125+0.920.551=20.9959`
7	27	`0.124+0.920.9959=21.2963`
8	26	`0.127+0.921.2963=21.8667`
9	28	`0.126+0.921.8667=22.28`
10	30	`0.128+0.922.28=22.852`
11		`0.130+0.922.852=23.5668`

(1) year	(2) Sales	(3) Exponential Smoothing	(4) Error	(5) \|Error\|	(6) `"Error"^2`	(7) `\|%"Error"\|`
1	20	20
2	21	20
3	23	20.1
4	22	20.39
5	25	20.551	`25-20.551=4.449`	`4.449`	`19.7936`	`17.8%`
6	24	20.9959	`24-20.9959=3.0041`	`3.0041`	`9.0246`	`12.52%`
7	27	21.2963	`27-21.2963=5.7037`	`5.7037`	`32.5321`	`21.12%`
8	26	21.8667	`26-21.8667=4.1333`	`4.1333`	`17.0843`	`15.9%`
9	28	22.28	`28-22.28=5.72`	`5.72`	`32.7183`	`20.43%`
10	30	22.852	`30-22.852=7.148`	`7.148`	`51.0938`	`23.83%`
11		23.5668	Total	`30.1581`	`162.2467`	`111.59%`

Forecasting errors

1. Mean absolute error (MAE), also called mean absolute deviation (MAD)
MAE`=1/n sum |e_i|=30.1581/6=5.0263`

2. Mean squared error (MSE)
MSE`=1/n sum |e_i^2|=162.2467/6=27.0411`

3. Root mean squared error (RMSE)
RMSE`=sqrt(MSE)=sqrt(27.0411)=5.2001`

4. Mean absolute percentage error (MAPE)
MAPE`=1/n sum |e_i/y_i|=111.59/6=18.6`

This material is intended as a summary. Use your textbook for detail explanation.
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2. 4 year Single Exponential Smoothing forecast Example