Question

The accompanying data file contains 20 observations for t and y_t.

The data are plotted below.

t	1	2	3	4	5	6	7	8	9	10
yt	10.8	14.1	10.3	10.9	11.3	13.5	10.7	9.2	8.8	12
t	11	12	13	14	15	16	17	18	19	20
yt	9.8	11	15.1	12.5	12.9	12.3	9	14.9	10.1	11.9

***I Really only need an answer for t=21 but I included the rest for context.

b-1. Use the exponential smoothing method to make forecasts with α = 0.2. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

t	yt	yˆty^t
1	10.8	?
2	14.1	?
3	10.3	?
19	10.1	?
20	11.9	?
21	???	???

c-1. Use the exponential smoothing method to make forecasts with α = 0.4. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

t	yt	yˆty^t
1	10.8	?
2	14.1	?
3	10.3	?
19	10.1	?
20	11.9	?
21???????

Answer 1

b-1)

t	yt	yhatt
1	10.8
2	14.1	10.80
3	10.3	11.46
4	10.9	11.23
5	11.3	11.16
6	13.5	11.19
7	10.7	11.65
8	9.2	11.46
9	8.8	11.01
10	12	10.57
11	9.8	10.85
12	11	10.64
13	15.1	10.71
14	12.5	11.59
15	12.9	11.77
16	12.3	12.00
17	9	12.06
18	14.9	11.45
19	10.1	12.14
20	11.9	11.73
21		11.76

c-1)

t	yt	yhatt
1	10.8
2	14.1	10.80
3	10.3	12.12
4	10.9	11.39
5	11.3	11.20
6	13.5	11.24
7	10.7	12.14
8	9.2	11.57
9	8.8	10.62
10	12	9.89
11	9.8	10.73
12	11	10.36
13	15.1	10.62
14	12.5	12.41
15	12.9	12.45
16	12.3	12.63
17	9	12.50
18	14.9	11.10
19	10.1	12.62
20	11.9	11.61
		11.73