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# Fourier Analysis of CAPX (Elkhorn S&P 500 Capital Expendi)

CAPX (Elkhorn S&P 500 Capital Expendi) appears to have interesting cyclic behaviour every 6 weeks (.1792*cosine), 8 weeks (.1742*sine), and 6 weeks (.1161*sine).

CAPX (Elkhorn S&P 500 Capital Expendi) has an average price of 23.77 (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 5/27/2015 to 3/13/2017 for CAPX (Elkhorn S&P 500 Capital Expendi), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
023.77422   0
11.20385 -1.61632 (1*2π)/9595 weeks
2.37644 -.29494 (2*2π)/9548 weeks
3.17777 -.67367 (3*2π)/9532 weeks
4.31121 -.22131 (4*2π)/9524 weeks
5-.26494 .21647 (5*2π)/9519 weeks
6.00601 -.25197 (6*2π)/9516 weeks
7.06397 -.28918 (7*2π)/9514 weeks
8-.05146 -.2031 (8*2π)/9512 weeks
9.03354 -.20866 (9*2π)/9511 weeks
10-.11246 .04593 (10*2π)/9510 weeks
11-.04824 -.0169 (11*2π)/959 weeks
12-.04124 -.1742 (12*2π)/958 weeks
13-.06592 -.04614 (13*2π)/957 weeks
14-.05029 -.05658 (14*2π)/957 weeks
15-.14862 .02105 (15*2π)/956 weeks
16.02688 -.02512 (16*2π)/956 weeks
17-.17916 -.11611 (17*2π)/956 weeks
18.04286 -.06953 (18*2π)/955 weeks
19.0581 -.01391 (19*2π)/955 weeks
20-.05228 -.01079 (20*2π)/955 weeks
21-.01082 -.05898 (21*2π)/955 weeks
22-.04249 -.08496 (22*2π)/954 weeks
23-.09838 -.05596 (23*2π)/954 weeks
24-.01831 -.11056 (24*2π)/954 weeks
25.00776 .0426 (25*2π)/954 weeks
26.0045 .02796 (26*2π)/954 weeks
27-.05727 -.12126 (27*2π)/954 weeks
28.00201 -.01679 (28*2π)/953 weeks
29-.03026 -.03499 (29*2π)/953 weeks
30-.03504 .00041 (30*2π)/953 weeks
31.00343 .03653 (31*2π)/953 weeks
32-.0489 -.02233 (32*2π)/953 weeks
33-.09036 -.01705 (33*2π)/953 weeks
34.0212 -.06932 (34*2π)/953 weeks
35-.01648 .02583 (35*2π)/953 weeks
36.00941 -.02996 (36*2π)/953 weeks
37-.02913 .00683 (37*2π)/953 weeks
38-.10724 .00713 (38*2π)/953 weeks
39-.02202 -.01982 (39*2π)/952 weeks
40-.05966 -.04174 (40*2π)/952 weeks
41-.00408 -.01762 (41*2π)/952 weeks
42-.03923 -.00466 (42*2π)/952 weeks
43-.03409 .02462 (43*2π)/952 weeks
44.04301 .00748 (44*2π)/952 weeks
45-.02628 .00557 (45*2π)/952 weeks
46-.05558 .0557 (46*2π)/952 weeks
47-.09576 .00528 (47*2π)/952 weeks
48-.09576 -.00528 (48*2π)/952 weeks
49-.05558 -.0557 (49*2π)/952 weeks
50-.02628 -.00557 (50*2π)/952 weeks
51.04301 -.00748 (51*2π)/952 weeks
52-.03409 -.02462 (52*2π)/952 weeks
53-.03923 .00466 (53*2π)/952 weeks
54-.00408 .01762 (54*2π)/952 weeks
55-.05966 .04174 (55*2π)/952 weeks
56-.02202 .01982 (56*2π)/952 weeks
57-.10724 -.00713 (57*2π)/952 weeks
58-.02913 -.00683 (58*2π)/952 weeks
59.00941 .02996 (59*2π)/952 weeks
60-.01648 -.02583 (60*2π)/952 weeks
61.0212 .06932 (61*2π)/952 weeks
62-.09036 .01705 (62*2π)/952 weeks
63-.0489 .02233 (63*2π)/952 weeks
64.00343 -.03653 (64*2π)/951 weeks
65-.03504 -.00041 (65*2π)/951 weeks
66-.03026 .03499 (66*2π)/951 weeks
67.00201 .01679 (67*2π)/951 weeks
68-.05727 .12126 (68*2π)/951 weeks
69.0045 -.02796 (69*2π)/951 weeks
70.00776 -.0426 (70*2π)/951 weeks
71-.01831 .11056 (71*2π)/951 weeks
72-.09838 .05596 (72*2π)/951 weeks
73-.04249 .08496 (73*2π)/951 weeks
74-.01082 .05898 (74*2π)/951 weeks
75-.05228 .01079 (75*2π)/951 weeks
76.0581 .01391 (76*2π)/951 weeks
77.04286 .06953 (77*2π)/951 weeks
78-.17916 .11611 (78*2π)/951 weeks
79.02688 .02512 (79*2π)/951 weeks
80-.14862 -.02105 (80*2π)/951 weeks
81-.05029 .05658 (81*2π)/951 weeks
82-.06592 .04614 (82*2π)/951 weeks
83-.04124 .1742 (83*2π)/951 weeks
84-.04824 .0169 (84*2π)/951 weeks
85-.11246 -.04593 (85*2π)/951 weeks
86.03354 .20866 (86*2π)/951 weeks
87-.05146 .2031 (87*2π)/951 weeks
88.06397 .28918 (88*2π)/951 weeks
89.00601 .25197 (89*2π)/951 weeks
90-.26494 -.21647 (90*2π)/951 weeks
91.31121 .22131 (91*2π)/951 weeks
92.17777 .67367 (92*2π)/951 weeks
93.37644 .29494 (93*2π)/951 weeks