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

3. 5 year Weighted Moving Average forecast Example


1) 5 year Weighted Moving Average forecast
year123456789101112
Sales5.24.95.54.95.25.75.45.85.965.24.8
Calculate 5 year Weighted Moving Average forecast with weight=1,2,1,2,1

Solution:
The value of table for `x` and `y`

x123456789101112
y5.24.95.54.95.25.75.45.85.965.24.8

The weights of the 5 years are respectively 1,2,1,2,1 and their sum is 7
Calculation of 5 year moving averages of the data
(1)
year		(2)
Sales		(3)
5 year weighted moving total		(4)
5 year weighted moving average
`(3)-:7`
15.2
24.9
35.5`1xx5.2+2xx4.9+1xx5.5+2xx4.9+1xx5.2=35.5``35.5-:7=5.0714`
44.9`1xx4.9+2xx5.5+1xx4.9+2xx5.2+1xx5.7=36.9``36.9-:7=5.2714`
55.2`1xx5.5+2xx4.9+1xx5.2+2xx5.7+1xx5.4=37.3``37.3-:7=5.3286`
65.7`1xx4.9+2xx5.2+1xx5.7+2xx5.4+1xx5.8=37.6``37.6-:7=5.3714`
75.4`1xx5.2+2xx5.7+1xx5.4+2xx5.8+1xx5.9=39.5``39.5-:7=5.6429`
85.8`1xx5.7+2xx5.4+1xx5.8+2xx5.9+1xx6=40.1``40.1-:7=5.7286`
95.9`1xx5.4+2xx5.8+1xx5.9+2xx6+1xx5.2=40.1``40.1-:7=5.7286`
106`1xx5.8+2xx5.9+1xx6+2xx5.2+1xx4.8=38.8``38.8-:7=5.5429`
115.2
124.8


(1)
year		(2)
Sales		(3)
5 year weighted moving average		(4)
Error		(5)
|Error|		(6)
`"Error"^2`		(7)
`|%"Error"|`
15.2
24.9
35.5
44.9
55.2
65.75.0714`5.7-5.0714=0.6286``0.6286``0.3951``11.03%`
75.45.2714`5.4-5.2714=0.1286``0.1286``0.0165``2.38%`
85.85.3286`5.8-5.3286=0.4714``0.4714``0.2222``8.13%`
95.95.3714`5.9-5.3714=0.5286``0.5286``0.2794``8.96%`
1065.6429`6-5.6429=0.3571``0.3571``0.1276``5.95%`
115.25.7286`5.2-5.7286=-0.5286``0.5286``0.2794``10.16%`
124.85.7286`4.8-5.7286=-0.9286``0.9286``0.8622``19.35%`
135.5429Total`3.5714``2.1824``65.96%`


Forecasting errors

1. Mean absolute error (MAE), also called mean absolute deviation (MAD)
MAE`=1/n sum |e_i|=3.5714/7=0.5102`


2. Mean squared error (MSE)
MSE`=1/n sum |e_i^2|=2.1824/7=0.3118`


3. Root mean squared error (RMSE)
RMSE`=sqrt(MSE)=sqrt(0.3118)=0.5584`


4. Mean absolute percentage error (MAPE)
MAPE`=1/n sum |e_i/y_i|=65.96/7=9.42`

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


2. 4 year Weighted Moving Average forecast Example
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