Using the data below, what is the simple exponential smoothing forecast for the 4th week where...

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