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Home > Statistical Methods calculators > Exponential Moving Average forecast example
7. Simple Moving Average forecast example ( Enter your problem )
( Enter your problem )
  1. Formula & 3 year Exponential Moving Average forecast Example
  2. 4 year Exponential Moving Average forecast Example
  3. 5 year Exponential Moving Average forecast Example
 		Other related methods
  1. Simple Moving Average
  2. Weighted Moving Average
  3. Exponential Moving Average
  4. Single Exponential Smoothing
  5. Simple Moving Average forecast
  6. Weighted Moving Average forecast
  7. Exponential Moving Average forecast
  8. Single Exponential Smoothing forecast
6. Weighted Moving Average forecast
(Previous method)		2. 4 year Exponential Moving Average forecast Example
(Next example)

1. Formula & 3 year Exponential Moving Average forecast Example


Formula
Examples
1) 3 year Exponential Moving Average forecast
year123456789101112
Sales5.24.95.54.95.25.75.45.85.965.24.8
Calculate 3 year Exponential Moving Average forecast

Solution:
`alpha=2/(n+1)=2/(3+1)=0.5`

(1)
year		(2)
Sales		(3)
Exponential Smoothing
`(alpha=0.5)`
15.25.2
24.9`0.5*5.2+0.5*5.2=5.2`
35.5`0.5*4.9+0.5*5.2=5.05`
44.9`0.5*5.5+0.5*5.05=5.275`
55.2`0.5*4.9+0.5*5.275=5.0875`
65.7`0.5*5.2+0.5*5.0875=5.1438`
75.4`0.5*5.7+0.5*5.1438=5.4219`
85.8`0.5*5.4+0.5*5.4219=5.4109`
95.9`0.5*5.8+0.5*5.4109=5.6055`
106`0.5*5.9+0.5*5.6055=5.7527`
115.2`0.5*6+0.5*5.7527=5.8764`
124.8`0.5*5.2+0.5*5.8764=5.5382`
13`0.5*4.8+0.5*5.5382=5.1691`


(1)
year		(2)
Sales		(3)
Exponential Smoothing		(4)
Error		(5)
|Error|		(6)
`"Error"^2`		(7)
`|%"Error"|`
15.25.2
24.95.2
35.55.05
44.95.275`4.9-5.275=-0.375``0.375``0.1406``7.65%`
55.25.0875`5.2-5.0875=0.1125``0.1125``0.0127``2.16%`
65.75.1438`5.7-5.1438=0.5562``0.5562``0.3094``9.76%`
75.45.4219`5.4-5.4219=-0.0219``0.0219``0.0005``0.41%`
85.85.4109`5.8-5.4109=0.3891``0.3891``0.1514``6.71%`
95.95.6055`5.9-5.6055=0.2945``0.2945``0.0867``4.99%`
1065.7527`6-5.7527=0.2473``0.2473``0.0611``4.12%`
115.25.8764`5.2-5.8764=-0.6764``0.6764``0.4575``13.01%`
124.85.5382`4.8-5.5382=-0.7382``0.7382``0.5449``15.38%`
135.1691Total`3.411``1.7648``64.19%`


Forecasting errors

1. Mean absolute error (MAE), also called mean absolute deviation (MAD)
MAE`=1/n sum |e_i|=3.411/9=0.379`


2. Mean squared error (MSE)
MSE`=1/n sum |e_i^2|=1.7648/9=0.1961`


3. Root mean squared error (RMSE)
RMSE`=sqrt(MSE)=sqrt(0.1961)=0.4428`


4. Mean absolute percentage error (MAPE)
MAPE`=1/n sum |e_i/y_i|=64.19/9=7.13`

2) 3 year Exponential Moving Average forecast
year12345678910
Sales30253525203035403045
Calculate 3 year Exponential Moving Average forecast

Solution:
`alpha=2/(n+1)=2/(3+1)=0.5`

(1)
year		(2)
Sales		(3)
Exponential Smoothing
`(alpha=0.5)`
13030
225`0.5*30+0.5*30=30`
335`0.5*25+0.5*30=27.5`
425`0.5*35+0.5*27.5=31.25`
520`0.5*25+0.5*31.25=28.125`
630`0.5*20+0.5*28.125=24.0625`
735`0.5*30+0.5*24.0625=27.0312`
840`0.5*35+0.5*27.0312=31.0156`
930`0.5*40+0.5*31.0156=35.5078`
1045`0.5*30+0.5*35.5078=32.7539`
11`0.5*45+0.5*32.7539=38.877`


(1)
year		(2)
Sales		(3)
Exponential Smoothing		(4)
Error		(5)
|Error|		(6)
`"Error"^2`		(7)
`|%"Error"|`
13030
22530
33527.5
42531.25`25-31.25=-6.25``6.25``39.0625``25%`
52028.125`20-28.125=-8.125``8.125``66.0156``40.62%`
63024.0625`30-24.0625=5.9375``5.9375``35.2539``19.79%`
73527.0312`35-27.0312=7.9688``7.9688``63.501``22.77%`
84031.0156`40-31.0156=8.9844``8.9844``80.719``22.46%`
93035.5078`30-35.5078=-5.5078``5.5078``30.336``18.36%`
104532.7539`45-32.7539=12.2461``12.2461``149.9668``27.21%`
1138.877Total`55.0195``464.8548``176.22%`


Forecasting errors

1. Mean absolute error (MAE), also called mean absolute deviation (MAD)
MAE`=1/n sum |e_i|=55.0195/7=7.8599`


2. Mean squared error (MSE)
MSE`=1/n sum |e_i^2|=464.8548/7=66.4078`


3. Root mean squared error (RMSE)
RMSE`=sqrt(MSE)=sqrt(66.4078)=8.1491`


4. Mean absolute percentage error (MAPE)
MAPE`=1/n sum |e_i/y_i|=176.22/7=25.17`

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


6. Weighted Moving Average forecast
(Previous method)		2. 4 year Exponential Moving Average forecast Example
(Next example)


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