Question
In: Statistics and Probability
Consider the following times-series where the data is recorded weekly Data collected over 36 weeks t...
Consider the following times-series where the data is recorded weekly
Data collected over 36 weeks
|
t |
X |
t |
X |
t |
X |
t |
X |
t |
X |
t |
X |
|
1 |
9.8 |
7 |
36.4 |
13 |
53.4 |
19 |
99.2 |
25 |
105.3 |
31 |
141.3 |
|
2 |
9.0 |
8 |
51.0 |
14 |
66.6 |
20 |
90.4 |
26 |
116.7 |
32 |
151.8 |
|
3 |
10.5 |
9 |
51.1 |
15 |
70.6 |
21 |
91.2 |
27 |
113.2 |
33 |
151.1 |
|
4 |
20.6 |
10 |
46.9 |
16 |
76.4 |
22 |
94.9 |
28 |
120.5 |
34 |
156.4 |
|
5 |
28.1 |
11 |
50.5 |
17 |
88.4 |
23 |
94.2 |
29 |
124.2 |
35 |
155.9 |
|
6 |
28.3 |
12 |
58.5 |
18 |
98.6 |
24 |
104.1 |
30 |
130.2 |
36 |
160.0 |
Provide an estimate of the value of the time-series at week 37
Solutions
Expert Solution
| Estimated Parameters of Exponential Smoothing | |
| Parameter | Value |
| alpha | 0.999951954484354 |
| beta | FALSE |
| gamma | FALSE |
| Interpolation Forecasts of Exponential Smoothing | |||
| t | Observed | Fitted | Residuals |
| 2 | 9 | 9.8 | -0.800000000000001 |
| 3 | 10.5 | 9.00003843641252 | 1.49996156358748 |
| 4 | 20.6 | 10.4999279335732 | 10.1000720664268 |
| 5 | 28.1 | 20.5995147368295 | 7.5004852631705 |
| 6 | 28.3 | 28.0996396353179 | 0.200360364682066 |
| 7 | 36.4 | 28.299990373583 | 8.10000962641703 |
| 8 | 51 | 36.3996108308608 | 14.6003891691392 |
| 9 | 51.1 | 50.9992985167737 | 0.10070148322626 |
| 10 | 46.9 | 51.0999951617453 | -4.19999516174531 |
| 11 | 50.5 | 46.9002017909333 | 3.59979820906674 |
| 12 | 58.5 | 50.4998270458388 | 8.00017295416118 |
| 13 | 53.4 | 58.4996156275652 | -5.09961562756516 |
| 14 | 66.6 | 53.4002450136624 | 13.1997549863376 |
| 15 | 70.6 | 66.5993658109653 | 4.00063418903471 |
| 16 | 76.4 | 70.5998077874675 | 5.80019221253254 |
| 17 | 88.4 | 76.3997213267743 | 12.0002786732257 |
| 18 | 98.6 | 88.3994234404232 | 10.2005765595767 |
| 19 | 99.2 | 98.5995099080393 | 0.600490091960694 |
| 20 | 90.4 | 99.1999711491439 | -8.79997114914389 |
| 21 | 91.2 | 90.4004227991515 | 0.799577200848475 |
| 22 | 94.9 | 91.1999615839011 | 3.70003841609892 |
| 23 | 94.2 | 94.8998222297464 | -0.699822229746388 |
| 24 | 104.1 | 94.2000336233199 | 9.8999663766801 |
| 25 | 105.3 | 104.099524351011 | 1.20047564898945 |
| 26 | 116.7 | 105.299942322528 | 11.4000576774716 |
| 27 | 113.2 | 116.69945227835 | -3.49945227835049 |
| 28 | 120.5 | 113.200168132989 | 7.29983186701079 |
| 29 | 124.2 | 120.499649275814 | 3.70035072418618 |
| 30 | 130.2 | 124.199822214741 | 6.0001777852586 |
| 31 | 141.3 | 130.199711718364 | 11.1002882816357 |
| 32 | 151.8 | 141.299466680926 | 10.5005333190743 |
| 33 | 151.1 | 151.799495496462 | -0.699495496462134 |
| 34 | 156.4 | 151.100033607622 | 5.2999663923782 |
| 35 | 155.9 | 156.399745360382 | -0.49974536038178 |
| 36 | 160 | 155.900024010524 | 4.09997598947646 |
| Extrapolation Forecasts of Exponential Smoothing | |||
| t | Forecast | 95% Lower Bound | 95% Upper Bound |
| 37 | 159.999803014539 | 148.82993000964 | 171.169676019439 |
orchestra answered 2 years agoRelated Solutions
Consider the following times-series where the data is recorded weekly Data collected over 36 weeks t...
Consider the following times-series where the data is recorded
weekly
Data collected over 36 weeks
t
X
t
X
t
X
t
X
t
X
t
X
1
9.8
7
36.4
13
53.4
19
99.2
25
105.3
31
141.3
2
9.0
8
51.0
14
66.6
20
90.4
26
116.7
32
151.8
3
10.5
9
51.1
15
70.6
21
91.2
27
113.2
33
151.1
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20.6
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46.9
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76.4
22
94.9
28
120.5
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156.4
5
28.1
11
50.5
17...
Consider the following times-series where the data is recorded weekly Data collected over 36 weeks t...
Consider the following times-series where the data is recorded
weekly
Data collected over 36 weeks
t
X
t
X
t
X
t
X
t
X
t
X
1
9.8
7
36.4
13
53.4
19
99.2
25
105.3
31
141.3
2
9.0
8
51.0
14
66.6
20
90.4
26
116.7
32
151.8
3
10.5
9
51.1
15
70.6
21
91.2
27
113.2
33
151.1
4
20.6
10
46.9
16
76.4
22
94.9
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120.5
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28.1
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Consider the following times-series where the data is recorded weekly Data collected over 36 weeks t...
Consider the following times-series where the data is recorded
weekly
Data collected over 36 weeks
t
X
t
X
t
X
t
X
t
X
t
X
1
9.8
7
36.4
13
53.4
19
99.2
25
105.3
31
141.3
2
9.0
8
51.0
14
66.6
20
90.4
26
116.7
32
151.8
3
10.5
9
51.1
15
70.6
21
91.2
27
113.2
33
151.1
4
20.6
10
46.9
16
76.4
22
94.9
28
120.5
34
156.4
5
28.1
11
50.5
17...
Consider the following times-series where the data is recorded weekly Data collected over 36 week t...
Consider the following times-series where the data is recorded
weekly
Data collected over 36 week
t
X
t
X
t
X
t
X
t
X
t
X
1
9.8
7
36.4
13
53.4
19
99.2
25
105.3
31
141.3
2
9.0
8
51.0
14
66.6
20
90.4
26
116.7
32
151.8
3
10.5
9
51.1
15
70.6
21
91.2
27
113.2
33
151.1
4
20.6
10
46.9
16
76.4
22
94.9
28
120.5
34
156.4
5
28.1
11
50.5
17...
We consider data on weekly sales for coffee. Data has n = 18 weeks of coffee...
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with 15% price reduction), and advertisement (A = 1 with
advertisement, = 0 otherwise)
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estimate by OLS -> log(Q) = 0.701 (0.415) + 0.756D (0.091) +
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We consider data on weekly sales for coffee. Data has n = 18 weeks of coffee...
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price, = 1.05 in weeks with 5% price reduction, and = 1.15 in weeks
with 15% price reduction), and advertisement (A = 1 with
advertisement, = 0 otherwise)
Model = log(Q) = B0 + B1D + B2A + u
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