Table B.2 contains data on pharmaceutical product sales.
a. Fit an ARIMA model to this time series, excluding the last 10 observations. Investigate model adequacy. Explain how this model would be used for forecasting.
b. Forecast the last 10 observations.
c. In Exercise 4.12, you were asked to use simple exponential smoothing with λ = 0.1 to smooth the data, and to forecast the last 10 observations. Compare the ARIMA and exponential smoothing forecasts. Which forecasting method do you prefer?
d. How would prediction intervals be obtained for the ARIMA forecasts?
Exercise 4.12Table B.2 contains data on pharmaceutical product sales.
TABLE B.2 Pharmaceutical Product Sales
Sales
(in thousands)
Week
10618.1
31
10334.5
61
10538.2
91
10375.4
2
10537.9
32
10480.1
62
10286.2
92
10123.4
3
10209.3
33
10387.6
63
10171.3
93
10462.7
4
10553.0
34
10202.6
64
10393.1
94
10205.5
5
9934.9
35
10219.3
65
10162.3
95
10522.7
6
10534.5
36
10382.7
66
10164.5
96
10253.2
7
10196.5
37
10820.5
67
10327.0
97
10428.7
8
10511.8
38
10358.7
68
10365.1
98
10615.8
9
10089.6
39
10494.6
69
10755.9
99
10417.3
10
10371.2
40
10497.6
70
10463.6
100
10445.4
11
10239.4
41
10431.5
71
10080.5
101
10690.6
12
10472.4
42
10447.8
72
10479.6
102
10271.8
13
10827.2
43
10684.4
73
9980.9
103
10524.8
14
10640.8
44
10176.5
74
10039.2
104
9815.0
15
10517.8
45
10616.0
75
10246.1
105
10398.5
16
10154.2
46
10627.7
76
10368.0
106
10553.1
17
9969.2
47
10684.0
77
10446.3
107
10655.8
18
10260.4
48
10246.7
78
10535.3
108
10199.1
19
10737.0
49
10265.0
79
10786.9
109
10416.6
20
10430.0
50
10090.4
80
9975.8
110
10391.3
21
10689.0
51
9881.1
81
10160.9
111
10210.1
22
10430.4
52
10449.7
82
10422.1
112
10352.5
23
10002.4
53
10276.3
83
10757.2
113
10423.8
24
10135.7
54
10175.2
84
10463.8
114
10519.3
25
10096.2
55
10212.5
85
10307.0
115
10596.7
26
10288.7
56
10395.5
86
10134.7
116
10650.0
27
10289.1
57
10545.9
87
10207.7
117
10741.6
28
10589.9
58
10635.7
88
10488.0
118
10246.0
29
10551.9
59
10265.2
89
10262.3
119
10354.4
30
10208.3
60
10551.6
90
10785.9
120
10155.4
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