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# Fourier Analysis of IMS (IMS Health Holdings, Inc. Commo)

IMS (IMS Health Holdings, Inc. Commo) appears to have interesting cyclic behaviour every 14 weeks (.3909*sine), 15 weeks (.3156*sine), and 7 weeks (.2242*cosine).

IMS (IMS Health Holdings, Inc. Commo) has an average price of 27.62 (topmost row, frequency = 0).

Click on the checkboxes shown on the right to see how the various frequencies contribute to the graph. Look for large magnitude coefficients (sine or cosine), as these are associated with frequencies which contribute most to the associated stock plot. If you find a large magnitude coefficient which dramatically changes the graph, look at the associated "Period" in weeks, as you may have found a significant recurring cycle for the stock of interest.

## Fourier Analysis

Using data from 4/4/2014 to 2/27/2017 for IMS (IMS Health Holdings, Inc. Commo), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
027.6249   0
1-.06205 -.65172 (1*2π)/153153 weeks
21.34431 -2.39902 (2*2π)/15377 weeks
3-1.33472 -.15165 (3*2π)/15351 weeks
4-.36995 -.96089 (4*2π)/15338 weeks
5-.44251 -.3667 (5*2π)/15331 weeks
6.16046 -.50993 (6*2π)/15326 weeks
7.1486 -.92528 (7*2π)/15322 weeks
8-.10653 .03091 (8*2π)/15319 weeks
9.19073 -.03587 (9*2π)/15317 weeks
10-.18108 -.31557 (10*2π)/15315 weeks
11-.21487 -.3909 (11*2π)/15314 weeks
12-.00211 -.24938 (12*2π)/15313 weeks
13-.11474 -.06216 (13*2π)/15312 weeks
14.1795 .0178 (14*2π)/15311 weeks
15-.08547 -.27207 (15*2π)/15310 weeks
16-.15101 -.09175 (16*2π)/15310 weeks
17-.21515 -.19529 (17*2π)/1539 weeks
18-.12216 -.08829 (18*2π)/1539 weeks
19-.01827 -.18318 (19*2π)/1538 weeks
20.13075 -.16134 (20*2π)/1538 weeks
21-.22424 -.16208 (21*2π)/1537 weeks
22.01095 -.02449 (22*2π)/1537 weeks
23.05128 -.05932 (23*2π)/1537 weeks
24-.14826 -.13731 (24*2π)/1536 weeks
25-.12086 .0198 (25*2π)/1536 weeks
26-.1176 -.17222 (26*2π)/1536 weeks
27.04003 .02606 (27*2π)/1536 weeks
28-.16998 -.24387 (28*2π)/1535 weeks
29-.07282 .03868 (29*2π)/1535 weeks
30.00693 -.18491 (30*2π)/1535 weeks
31-.11625 -.01347 (31*2π)/1535 weeks
32-.10465 -.20077 (32*2π)/1535 weeks
33-.07121 -.01569 (33*2π)/1535 weeks
34.11753 .01525 (34*2π)/1535 weeks
35-.18589 -.14847 (35*2π)/1534 weeks
36-.00546 -.13211 (36*2π)/1534 weeks
37-.1024 -.06365 (37*2π)/1534 weeks
38.00058 -.0097 (38*2π)/1534 weeks
39-.02628 -.03983 (39*2π)/1534 weeks
40.02559 -.03342 (40*2π)/1534 weeks
41-.08121 -.05633 (41*2π)/1534 weeks
42-.08217 .00613 (42*2π)/1534 weeks
43-.13233 -.00821 (43*2π)/1534 weeks
44.00466 -.09031 (44*2π)/1533 weeks
45-.09017 -.06099 (45*2π)/1533 weeks
46-.06089 .00448 (46*2π)/1533 weeks
47-.04215 -.03128 (47*2π)/1533 weeks
48.00102 -.10564 (48*2π)/1533 weeks
49-.09706 .00046 (49*2π)/1533 weeks
50-.06561 .02838 (50*2π)/1533 weeks
51-.03216 -.04324 (51*2π)/1533 weeks
52-.09994 -.01352 (52*2π)/1533 weeks
53-.00343 .0055 (53*2π)/1533 weeks
54-.14601 -.00622 (54*2π)/1533 weeks
55-.09279 -.10812 (55*2π)/1533 weeks
56-.08491 .00895 (56*2π)/1533 weeks
57-.04518 -.06798 (57*2π)/1533 weeks
58-.02229 -.0832 (58*2π)/1533 weeks
59-.0423 .04248 (59*2π)/1533 weeks
60-.0908 -.11823 (60*2π)/1533 weeks
61-.02056 .06043 (61*2π)/1533 weeks
62.00528 -.08302 (62*2π)/1532 weeks
63-.12645 .02197 (63*2π)/1532 weeks
64.00792 -.06611 (64*2π)/1532 weeks
65-.05472 .06738 (65*2π)/1532 weeks
66-.01287 -.0671 (66*2π)/1532 weeks
67-.0684 .0597 (67*2π)/1532 weeks
68-.0963 -.02143 (68*2π)/1532 weeks
69-.00237 -.03669 (69*2π)/1532 weeks
70-.04632 .03565 (70*2π)/1532 weeks
71-.05976 .03046 (71*2π)/1532 weeks
72-.08874 .05407 (72*2π)/1532 weeks
73-.04975 -.06626 (73*2π)/1532 weeks
74-.14479 .06711 (74*2π)/1532 weeks
75-.02058 -.10038 (75*2π)/1532 weeks
76-.0615 .07482 (76*2π)/1532 weeks
77-.0615 -.07482 (77*2π)/1532 weeks
78-.02058 .10038 (78*2π)/1532 weeks
79-.14479 -.06711 (79*2π)/1532 weeks
80-.04975 .06626 (80*2π)/1532 weeks
81-.08874 -.05407 (81*2π)/1532 weeks
82-.05976 -.03046 (82*2π)/1532 weeks
83-.04632 -.03565 (83*2π)/1532 weeks
84-.00237 .03669 (84*2π)/1532 weeks
85-.0963 .02143 (85*2π)/1532 weeks
86-.0684 -.0597 (86*2π)/1532 weeks
87-.01287 .0671 (87*2π)/1532 weeks
88-.05472 -.06738 (88*2π)/1532 weeks
89.00792 .06611 (89*2π)/1532 weeks
90-.12645 -.02197 (90*2π)/1532 weeks
91.00528 .08302 (91*2π)/1532 weeks
92-.02056 -.06043 (92*2π)/1532 weeks
93-.0908 .11823 (93*2π)/1532 weeks
94-.0423 -.04248 (94*2π)/1532 weeks
95-.02229 .0832 (95*2π)/1532 weeks
96-.04518 .06798 (96*2π)/1532 weeks
97-.08491 -.00895 (97*2π)/1532 weeks
98-.09279 .10812 (98*2π)/1532 weeks
99-.14601 .00622 (99*2π)/1532 weeks
100-.00343 -.0055 (100*2π)/1532 weeks
101-.09994 .01352 (101*2π)/1532 weeks
102-.03216 .04324 (102*2π)/1532 weeks
103-.06561 -.02838 (103*2π)/1531 weeks
104-.09706 -.00046 (104*2π)/1531 weeks
105.00102 .10564 (105*2π)/1531 weeks
106-.04215 .03128 (106*2π)/1531 weeks
107-.06089 -.00448 (107*2π)/1531 weeks
108-.09017 .06099 (108*2π)/1531 weeks
109.00466 .09031 (109*2π)/1531 weeks
110-.13233 .00821 (110*2π)/1531 weeks
111-.08217 -.00613 (111*2π)/1531 weeks
112-.08121 .05633 (112*2π)/1531 weeks
113.02559 .03342 (113*2π)/1531 weeks
114-.02628 .03983 (114*2π)/1531 weeks
115.00058 .0097 (115*2π)/1531 weeks
116-.1024 .06365 (116*2π)/1531 weeks
117-.00546 .13211 (117*2π)/1531 weeks
118-.18589 .14847 (118*2π)/1531 weeks
119.11753 -.01525 (119*2π)/1531 weeks
120-.07121 .01569 (120*2π)/1531 weeks
121-.10465 .20077 (121*2π)/1531 weeks
122-.11625 .01347 (122*2π)/1531 weeks
123.00693 .18491 (123*2π)/1531 weeks
124-.07282 -.03868 (124*2π)/1531 weeks
125-.16998 .24387 (125*2π)/1531 weeks
126.04003 -.02606 (126*2π)/1531 weeks
127-.1176 .17222 (127*2π)/1531 weeks
128-.12086 -.0198 (128*2π)/1531 weeks
129-.14826 .13731 (129*2π)/1531 weeks
130.05128 .05932 (130*2π)/1531 weeks
131.01095 .02449 (131*2π)/1531 weeks
132-.22424 .16208 (132*2π)/1531 weeks
133.13075 .16134 (133*2π)/1531 weeks
134-.01827 .18318 (134*2π)/1531 weeks
135-.12216 .08829 (135*2π)/1531 weeks
136-.21515 .19529 (136*2π)/1531 weeks
137-.15101 .09175 (137*2π)/1531 weeks
138-.08547 .27207 (138*2π)/1531 weeks
139.1795 -.0178 (139*2π)/1531 weeks
140-.11474 .06216 (140*2π)/1531 weeks
141-.00211 .24938 (141*2π)/1531 weeks
142-.21487 .3909 (142*2π)/1531 weeks
143-.18108 .31557 (143*2π)/1531 weeks
144.19073 .03587 (144*2π)/1531 weeks
145-.10653 -.03091 (145*2π)/1531 weeks
146.1486 .92528 (146*2π)/1531 weeks
147.16046 .50993 (147*2π)/1531 weeks
148-.44251 .3667 (148*2π)/1531 weeks
149-.36995 .96089 (149*2π)/1531 weeks
150-1.33472 .15165 (150*2π)/1531 weeks
1511.34431 2.39902 (151*2π)/1531 weeks