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 4.12 Table B.2 contains data on pharmaceutical product sales. TABLE B.2 Pharmaceutical Product Sales Sales (in thousands) Sales (in thousands) Sales (in thousands) Sales (in thousands) Week Week Week 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

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...

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 4.12
Table B.2 contains data on pharmaceutical product sales.

TABLE B.2 Pharmaceutical Product Sales

	Sales (in thousands)		Sales (in thousands)		Sales (in thousands)		Sales (in thousands)
Week	Week	Week	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

May 25, 2022

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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...

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