Question

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

t	1	2	3	4	5	6	7	8	9	10
yt	12.1	12.2	9.3	12.8	8.6	9.3	14.3	12.1	11.5	15.1
t	11	12	13	14	15	16	17	18	19	20
yt	13.5	9.8	9.6	14.5	14.9	12.4	11.2	8.8	11.8	10

a. Discuss the presence of random variations.

• The smoother appearance of the graph suggests the presence of random variations.

• The smoother appearance of the graph suggests the absence of random variations.

• The jagged appearance of the graph suggests the presence of random variations.

• The jagged appearance of the graph suggests the absence of random variations.

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	yˆt
1	12.1
2	12.2
3	9.3
⋮	⋮	⋮
19	11.8
20	10.0
21

b-2. Compute the resulting MSE and MAD. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

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	yˆt
1	12.1
2	12.2
3	9.3
⋮	⋮	⋮
19	11.8
20	10.0
21

c-2. Compute the resulting MSE and MAD. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

d. Use the appropriate value of α to make a forecast for period 21. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

yˆt

Answer 1

a The jagged appearance of the graph suggests the presence of random variations.

b-1)

t	yt	yhatt
1	12.1
2	12.2	12.10
3	9.3	12.12
4	12.8	11.56
5	8.6	11.80
6	9.3	11.16
7	14.3	10.79
8	12.1	11.49
9	11.5	11.61
10	15.1	11.59
11	13.5	12.29
12	9.8	12.53
13	9.6	11.99
14	14.5	11.51
15	14.9	12.11
16	12.4	12.67
17	11.2	12.61
18	8.8	12.33
19	11.8	11.62
20	10	11.66
21		11.33

b-2)

MSE=5.10

MAD=1.90

c-1)

t	yt	yhatt
1	12.1
2	12.2	12.10
3	9.3	12.14
4	12.8	11.00
5	8.6	11.72
6	9.3	10.47
7	14.3	10.00
8	12.1	11.72
9	11.5	11.87
10	15.1	11.72
11	13.5	13.07
12	9.8	13.24
13	9.6	11.87
14	14.5	10.96
15	14.9	12.38
16	12.4	13.39
17	11.2	12.99
18	8.8	12.27
19	11.8	10.88
20	10	11.25
21		10.75

c-2)

MSE=5.65

MAD=2.00

d)

yˆt =11.33