Formula
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 forecastSolution:The value of table for
x and
yx | 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) Error2 | (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 errors1. Mean absolute error (MAE), also called mean absolute deviation (MAD)MAE
=1n∑|ei|=3.56679=0.39632. Mean squared error (MSE)MSE
=1n∑|e2i|=1.96339=0.21813. Root mean squared error (RMSE)RMSE
=√MSE=√0.2181=0.46714. Mean absolute percentage error (MAPE)MAPE
=1n∑|eiyi|=67.349=7.48
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 forecastSolution:The value of table for
x and
yx | 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) Error2 | (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 errors1. Mean absolute error (MAE), also called mean absolute deviation (MAD)MAE
=1n∑|ei|=53.33337=7.6192. Mean squared error (MSE)MSE
=1n∑|e2i|=466.66677=66.66673. Root mean squared error (RMSE)RMSE
=√MSE=√66.6667=8.1654. Mean absolute percentage error (MAPE)MAPE
=1n∑|eiyi|=169.47=24.2
This material is intended as a summary. Use your textbook for detail explanation.
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