/*  This data set comes from the book by Stephen A. DeLurgio 
     "Forecasting Principles and Applications" (Irwin, 1998), p. 531.
     Henry Machler's Hideaway Orchids.  Use this data to model the
     interventions associated with Mother's Day sales (days 38, 39, 40).
     Also the model is used to forecast 10 days in advance.  */

data orchids;
  input DAY	DATE SALES;
  datalines;
1	40181	112.41
2	40281	188.24
3	40381	162.91
4	40481	326.25
5	40581	316.4
6	40681	157.34
7	40781	168.01
8	40881	99.12
9	40981	216.66
10	41081	209.14
11	41181	482.7
12	41281	358.34
13	41381	184.13
14	41481	126.35
15	41581	141.5
16	41681	267.33
17	41781	332.13
18	41881	475.52
19	41981	383.44
20	42081	274.23
21	42181	87.41
22	42281	234.22
23	42381	293.52
24	42481	260.67
25	42581	237.17
26	42681	220.4
27	42781	197.88
28	42881	123.87
29	42981	264.24
30	43081	230.22
31	50181	164.94
32	50281	237.85
33	50381	222.69
34	50481	116.79
35	50581	189.41
36	50681	295.77
37	50781	129.47
38	50881	742.6
39	50981	1057.96
40	51081	402.77
41	51181	94.68
42	51281	152.65
43	51381	239.45
44	51481	132.9
45	51581	79.13
46	51681	476.48
47	51781	155.92
48	51881	166.06
49	51981	100.85
50	52081	96.3
51	52181	131.53
52	52281	136.83
53	52381	559.31
54	52481	183.84
55	52581	237.67
56	52681	139.08
57	52781	119.21
58	52881	131.74
59	52981	199.46
60	53081	418.7
61	53181	230.41
62	60181	191.66
63	60281	100.25
64	60381	154.68
65	60481	259.4
66	60581	121.98
67	60681	277.62
68	60781	234.29
69	60881	162.54
70	60981	50.58
71	61081	98.86
72	61181	193.48
73	61281	94.61
74	61381	379.06
75	61481	244.44
76	61581	134.68
77	61681	39.82
78	61781	77.56
79	61881	95.76
80	61981	102.13
81	62081	355.86
82	62181	163.32
83	62281	56.84
84	62381	125.48
85	62481	239.45
86	62581	132.9
87	62681	79.13
88	62781	476.48
89	62881	155.92
90	62981	166.06
91	63081	100.85
92	70181	214.24
93	70281	102.46
94	70381	85.69
95	70481	415.19
96	70581	234.37
97	70681	136.52
98	70781	252.57
99	70881	299.92
100	70981	181.15
101	71081	85.02
102	71181	504.08
103	71281	228.59
104	71381	126.61
105	71481	277.23
106	71581	283.9
107	71681	167.73
108	71781	119.43
109	71881	510.22
110	71981	319.52
111	72081	37.61
112	72181	300.53
113	72281	263
114	72381	186.94
115	72481	126.42
116	72581	508.94
117	72681	370.61
118	72781	74.04
119	72881	229.73
120	72981	164.41
121	73081	278.9
122	73181	145.96
123	80181	481.83
124	80281	431.9
125	80381	76.56
126	80481	200.61
127	80581	172.04
128	80681	246.33
129	80781	178.73
130	80881	397.09
131	80981	410.99
132	81081	162.69
133	81181	123.29
134	81281	254.95
135	81381	239.77
136	81481	106.71
137	81581	506.05
138	81681	402.9
139	81781	250.49
140	81881	37.07
;

run;

/* Use the post-intervention data (obs. 41 - 140) to determine the Box-Jenkins model
   for the noise of this data.  The autocorrelaton function produced here is even more
   suggestive of the "gap" AR(7) model: y(t) = phi0 + phi1*y(t-7) + a(t).  When using
   all of the data, including the Mother's day intervention at obs. 38, 39, and 40
   the autocorrelation function gets somewhat "distorted" (contaminated) by the
   inclusion of the 3-day intervention.  */  

data orchids2;
  set orchids;
  if _n_ > 40;

  run;

proc arima data = orchids2;
  identify var = sales;

run;