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# Fourier Analysis of IMS (IMS Health Holdings)

IMS (IMS Health Holdings) appears to have interesting cyclic behaviour every 13 weeks (1.2688*sine), 14 weeks (1.154*sine), and 11 weeks (.9168*cosine).

IMS (IMS Health Holdings) has an average price of 23.71 (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 4/3/2014 to 2/26/2018 for IMS (IMS Health Holdings), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
023.70662   0
1-6.96495 2.40366 (1*2π)/152152 weeks
2-3.2543 2.7819 (2*2π)/15276 weeks
3-3.17237 5.56581 (3*2π)/15251 weeks
4.12984 3.97349 (4*2π)/15238 weeks
51.32196 2.76626 (5*2π)/15230 weeks
62.05118 .87497 (6*2π)/15225 weeks
71.33171 -.7737 (7*2π)/15222 weeks
8-.11487 -.11166 (8*2π)/15219 weeks
9-.53002 .34182 (9*2π)/15217 weeks
10-.91189 .84585 (10*2π)/15215 weeks
11-.50495 1.15399 (11*2π)/15214 weeks
12.31124 1.26882 (12*2π)/15213 weeks
13.71476 .90551 (13*2π)/15212 weeks
14.91679 .51631 (14*2π)/15211 weeks
15.45829 -.26652 (15*2π)/15210 weeks
16-.23973 -.16338 (16*2π)/15210 weeks
17-.60544 .06932 (17*2π)/1529 weeks
18-.54985 .56282 (18*2π)/1528 weeks
19-.11702 .8834 (19*2π)/1528 weeks
20.47838 .83717 (20*2π)/1528 weeks
21.44541 .41051 (21*2π)/1527 weeks
22.55371 .22572 (22*2π)/1527 weeks
23.34408 .00398 (23*2π)/1527 weeks
24-.07274 -.08677 (24*2π)/1526 weeks
25-.35235 .3176 (25*2π)/1526 weeks
26-.2476 .44409 (26*2π)/1526 weeks
27.10589 .86439 (27*2π)/1526 weeks
28.35238 .41111 (28*2π)/1525 weeks
29.48328 .43821 (29*2π)/1525 weeks
30.56624 .0066 (30*2π)/1525 weeks
31.13955 -.04634 (31*2π)/1525 weeks
32.06575 -.27504 (32*2π)/1525 weeks
33-.17966 .20561 (33*2π)/1525 weeks
34.06556 .54038 (34*2π)/1524 weeks
35.10308 .41382 (35*2π)/1524 weeks
36.52642 .27324 (36*2π)/1524 weeks
37.48762 .13091 (37*2π)/1524 weeks
38.36462 -.02932 (38*2π)/1524 weeks
39.16733 -.18182 (39*2π)/1524 weeks
40-.01201 -.00939 (40*2π)/1524 weeks
41-.09084 .10072 (41*2π)/1524 weeks
42-.0987 .30153 (42*2π)/1524 weeks
43.10014 .31904 (43*2π)/1524 weeks
44.29986 .27299 (44*2π)/1523 weeks
45.37742 -.04682 (45*2π)/1523 weeks
46.2247 -.16413 (46*2π)/1523 weeks
47.00599 -.15068 (47*2π)/1523 weeks
48.01919 -.10892 (48*2π)/1523 weeks
49-.11646 .13724 (49*2π)/1523 weeks
50-.05414 .29315 (50*2π)/1523 weeks
51.15625 .36166 (51*2π)/1523 weeks
52.3169 .13552 (52*2π)/1523 weeks
53.35868 .08274 (53*2π)/1523 weeks
54.1857 -.08277 (54*2π)/1523 weeks
55.07621 -.17687 (55*2π)/1523 weeks
56-.10523 .03672 (56*2π)/1523 weeks
57-.1514 .15311 (57*2π)/1523 weeks
58.12338 .24234 (58*2π)/1523 weeks
59.21113 .31534 (59*2π)/1523 weeks
60.42926 .05127 (60*2π)/1523 weeks
61.28402 .00948 (61*2π)/1522 weeks
62.29283 -.14817 (62*2π)/1522 weeks
63.03877 -.16548 (63*2π)/1522 weeks
64.03977 -.06413 (64*2π)/1522 weeks
65-.02764 .22159 (65*2π)/1522 weeks
66.2056 .26183 (66*2π)/1522 weeks
67.21886 .24065 (67*2π)/1522 weeks
68.40684 .0311 (68*2π)/1522 weeks
69.29923 -.04618 (69*2π)/1522 weeks
70.22501 -.20578 (70*2π)/1522 weeks
71-.00172 -.11589 (71*2π)/1522 weeks
72-.09424 .04276 (72*2π)/1522 weeks
73-.00954 .20672 (73*2π)/1522 weeks
74.02615 .14455 (74*2π)/1522 weeks
75.3347 .18324 (75*2π)/1522 weeks
76.24278   (76*2π)/1522 weeks
77.3347 -.18324 (77*2π)/1522 weeks
78.02615 -.14455 (78*2π)/1522 weeks
79-.00954 -.20672 (79*2π)/1522 weeks
80-.09424 -.04276 (80*2π)/1522 weeks
81-.00172 .11589 (81*2π)/1522 weeks
82.22501 .20578 (82*2π)/1522 weeks
83.29923 .04618 (83*2π)/1522 weeks
84.40684 -.0311 (84*2π)/1522 weeks
85.21886 -.24065 (85*2π)/1522 weeks
86.2056 -.26183 (86*2π)/1522 weeks
87-.02764 -.22159 (87*2π)/1522 weeks
88.03977 .06413 (88*2π)/1522 weeks
89.03877 .16548 (89*2π)/1522 weeks
90.29283 .14817 (90*2π)/1522 weeks
91.28402 -.00948 (91*2π)/1522 weeks
92.42926 -.05127 (92*2π)/1522 weeks
93.21113 -.31534 (93*2π)/1522 weeks
94.12338 -.24234 (94*2π)/1522 weeks
95-.1514 -.15311 (95*2π)/1522 weeks
96-.10523 -.03672 (96*2π)/1522 weeks
97.07621 .17687 (97*2π)/1522 weeks
98.1857 .08277 (98*2π)/1522 weeks
99.35868 -.08274 (99*2π)/1522 weeks
100.3169 -.13552 (100*2π)/1522 weeks
101.15625 -.36166 (101*2π)/1522 weeks
102-.05414 -.29315 (102*2π)/1521 weeks
103-.11646 -.13724 (103*2π)/1521 weeks
104.01919 .10892 (104*2π)/1521 weeks
105.00599 .15068 (105*2π)/1521 weeks
106.2247 .16413 (106*2π)/1521 weeks
107.37742 .04682 (107*2π)/1521 weeks
108.29986 -.27299 (108*2π)/1521 weeks
109.10014 -.31904 (109*2π)/1521 weeks
110-.0987 -.30153 (110*2π)/1521 weeks
111-.09084 -.10072 (111*2π)/1521 weeks
112-.01201 .00939 (112*2π)/1521 weeks
113.16733 .18182 (113*2π)/1521 weeks
114.36462 .02932 (114*2π)/1521 weeks
115.48762 -.13091 (115*2π)/1521 weeks
116.52642 -.27324 (116*2π)/1521 weeks
117.10308 -.41382 (117*2π)/1521 weeks
118.06556 -.54038 (118*2π)/1521 weeks
119-.17966 -.20561 (119*2π)/1521 weeks
120.06575 .27504 (120*2π)/1521 weeks
121.13955 .04634 (121*2π)/1521 weeks
122.56624 -.0066 (122*2π)/1521 weeks
123.48328 -.43821 (123*2π)/1521 weeks
124.35238 -.41111 (124*2π)/1521 weeks
125.10589 -.86439 (125*2π)/1521 weeks
126-.2476 -.44409 (126*2π)/1521 weeks
127-.35235 -.3176 (127*2π)/1521 weeks
128-.07274 .08677 (128*2π)/1521 weeks
129.34408 -.00398 (129*2π)/1521 weeks
130.55371 -.22572 (130*2π)/1521 weeks
131.44541 -.41051 (131*2π)/1521 weeks
132.47838 -.83717 (132*2π)/1521 weeks
133-.11702 -.8834 (133*2π)/1521 weeks
134-.54985 -.56282 (134*2π)/1521 weeks
135-.60544 -.06932 (135*2π)/1521 weeks
136-.23973 .16338 (136*2π)/1521 weeks
137.45829 .26652 (137*2π)/1521 weeks
138.91679 -.51631 (138*2π)/1521 weeks
139.71476 -.90551 (139*2π)/1521 weeks
140.31124 -1.26882 (140*2π)/1521 weeks
141-.50495 -1.15399 (141*2π)/1521 weeks
142-.91189 -.84585 (142*2π)/1521 weeks
143-.53002 -.34182 (143*2π)/1521 weeks
144-.11487 .11166 (144*2π)/1521 weeks
1451.33171 .7737 (145*2π)/1521 weeks
1462.05118 -.87497 (146*2π)/1521 weeks
1471.32196 -2.76626 (147*2π)/1521 weeks
148.12984 -3.97349 (148*2π)/1521 weeks
149-3.17237 -5.56581 (149*2π)/1521 weeks
150-3.2543 -2.7819 (150*2π)/1521 weeks