Question

The following time series shows the sales of a particular product over the past 12 months.

Month	Sales
1	105
2	135
3	120
4	105
5	90
6	120
7	145
8	140
9	100
10	80
11	100
12	110

(b)

Use α = 0.4 to compute the exponential smoothing forecasts for the time series. (Round your answers to two decimal places.)

Month t	Time Series Value Yt	Forecast Ft
1	105
2	135
3	120
4	105
5	90
6	120
7	145
8	140
9	100
10	80
11	100
12	110

(c)

Use a smoothing constant of α = 0.6 to compute the exponential smoothing forecasts. (Round your answers to two decimal places.)

Month t	Time Series Value Yt	Forecast Ft
1	105
2	135
3	120
4	105
5	90
6	120
7	145
8	140
9	100
10	80
11	100
12	110

Answer 1

b) At α = 0.4

Month	Sales, A(t)	Forecast, Ft = Ft-1 + α(At-1 - Ft-1)
1	105	-	-
2	135	105	105
3	120	105 + 0.4(135 - 105)	117
4	105	117 + 0.4(120 - 117)	118.2
5	90	118.2 + 0.4(105 - 118.2)	112.92
6	120	112.92 + 0.4(90 - 112.92)	103.75
7	145	103.75 + 0.4(120 - 103.75)	110.25
8	140	110.25 + 0.4(145 - 110.25)	124.15
9	100	124.15 + 0.4(140 - 124.15)	130.49
10	80	130.49 + 0.4(100 - 130.49)	118.29
11	100	118.29 + 0.4(80 - 118.29)	102.98
12	110	102.98 + 0.4(100 - 102.98)	101.79

c) At α = 0.6

Month	Sales	Forecast, Ft= Ft-1+ α(At-1- Ft-1)
1	105	-	-
2	135	105	105
3	120	105 + 0.6(135 - 105)	123
4	105	123 + 0.6(120 - 123)	121.2
5	90	121.2 + 0.6(105 - 121.2)	111.48
6	120	111.48 + 0.6(90 - 111.48)	98.59
7	145	98.59 + 0.6(120 - 98.59)	111.44
8	140	111.44 + 0.6(145 - 111.44)	131.57
9	100	131.57 + 0.6(140 - 131.57)	136.63
10	80	136.63 + 0.6(100 - 136.63)	114.65
11	100	114.65 + 0.6(80 - 114.65)	93.86
12	110	93.86 + 0.6(100 - 93.86)	97.54