Answer 3:-
The exponential smoothing forecast with smoothing constant α=0.4 for the 4th week is computed using the following formula :-
Note*= here is two different methods to solve the sum .
First method= Fn =Ft+α (At-Ft)
Week | Time series value | SES forecast |
1 | 6.00 | F1 =A =6.00 |
2 | 4.00 | F2= F1+α (A1-F1) = 6+0.4(6-6) =6 |
3 | 3.00 | F3 = F2+α (A2-F2) = 6 +0.4(4-6) = 5.2 |
4 | 3.00 | F4 = F3+α (A3-F3) = 5.2+0.4(3-5.2)= 4.32 |
Second method :- α (previous period actual) + (1-α) previous forecast
Week | Time series value | SES forecast |
1 | 6.00 | 6.00 |
2 | 4.00 | 0.4(6)+(1-0.4)*6 = 6 |
3 | 3.00 | 0.4(4) + (1-0.4)*6 = 5.2 |
4 | 3.00 | 0.4(3) + (1-0.4)*5.2 = 4.32 |
So 4th week forecast is :-
Week | Time series value | SES forecast |
1 | 6.00 | 6.00 |
2 | 4.00 | 6 |
3 | 3.00 | 5.2 |
4 | 3.00 | 4.32 |
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