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Fourier Analysis of INDEX (Index Funds S&P 500 Equal Weigh)


INDEX (Index Funds S&P 500 Equal Weigh) appears to have interesting cyclic behaviour every 4 weeks (.1567*cosine), 6 weeks (.1475*sine), and 2 weeks (.1237*cosine).

INDEX (Index Funds S&P 500 Equal Weigh) has an average price of 23.57 (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.

Right click on the graph above to see the menu of operations (download, full screen, etc.)

Fourier Analysis

Using data from 5/11/2015 to 1/17/2017 for INDEX (Index Funds S&P 500 Equal Weigh), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
023.57131   0 
11.01302 -1.29551 (1*2π)/8989 weeks
2.04773 -.08835 (2*2π)/8945 weeks
3.35469 -.44804 (3*2π)/8930 weeks
4.27453 .0683 (4*2π)/8922 weeks
5-.39619 -.42401 (5*2π)/8918 weeks
6.00564 -.21097 (6*2π)/8915 weeks
7-.08374 -.13041 (7*2π)/8913 weeks
8.06512 -.10352 (8*2π)/8911 weeks
9-.08822 .09833 (9*2π)/8910 weeks
10.00399 -.039 (10*2π)/899 weeks
11.03026 -.10771 (11*2π)/898 weeks
12-.02333 -.121 (12*2π)/897 weeks
13.00458 -.07493 (13*2π)/897 weeks
14-.06194 -.14748 (14*2π)/896 weeks
15-.04 .04784 (15*2π)/896 weeks
16.09259 -.09816 (16*2π)/896 weeks
17-.05206 .04139 (17*2π)/895 weeks
18-.10293 -.07791 (18*2π)/895 weeks
19.05629 -.09033 (19*2π)/895 weeks
20-.04916 .03618 (20*2π)/894 weeks
21-.03114 -.12094 (21*2π)/894 weeks
22.01107 .03719 (22*2π)/894 weeks
23-.15672 .05006 (23*2π)/894 weeks
24-.04557 -.01921 (24*2π)/894 weeks
25.0247 .03051 (25*2π)/894 weeks
26-.02312 .0008 (26*2π)/893 weeks
27-.01825 -.03724 (27*2π)/893 weeks
28-.05434 -.06067 (28*2π)/893 weeks
29-.0038 -.03499 (29*2π)/893 weeks
30-.00943 .00548 (30*2π)/893 weeks
31-.02428 .00008 (31*2π)/893 weeks
32-.06567 .00082 (32*2π)/893 weeks
33.01492 -.00742 (33*2π)/893 weeks
34-.03736 -.02628 (34*2π)/893 weeks
35-.0165 -.00998 (35*2π)/893 weeks
36-.01722 -.00302 (36*2π)/892 weeks
37-.07317 .04583 (37*2π)/892 weeks
38-.02971 -.01588 (38*2π)/892 weeks
39.01072 -.0374 (39*2π)/892 weeks
40-.00183 -.05057 (40*2π)/892 weeks
41-.0119 .00298 (41*2π)/892 weeks
42.00827 -.05612 (42*2π)/892 weeks
43-.04009 .04219 (43*2π)/892 weeks
44-.12371 .01277 (44*2π)/892 weeks
45-.12371 -.01277 (45*2π)/892 weeks
46-.04009 -.04219 (46*2π)/892 weeks
47.00827 .05612 (47*2π)/892 weeks
48-.0119 -.00298 (48*2π)/892 weeks
49-.00183 .05057 (49*2π)/892 weeks
50.01072 .0374 (50*2π)/892 weeks
51-.02971 .01588 (51*2π)/892 weeks
52-.07317 -.04583 (52*2π)/892 weeks
53-.01722 .00302 (53*2π)/892 weeks
54-.0165 .00998 (54*2π)/892 weeks
55-.03736 .02628 (55*2π)/892 weeks
56.01492 .00742 (56*2π)/892 weeks
57-.06567 -.00082 (57*2π)/892 weeks
58-.02428 -.00008 (58*2π)/892 weeks
59-.00943 -.00548 (59*2π)/892 weeks
60-.0038 .03499 (60*2π)/891 weeks
61-.05434 .06067 (61*2π)/891 weeks
62-.01825 .03724 (62*2π)/891 weeks
63-.02312 -.0008 (63*2π)/891 weeks
64.0247 -.03051 (64*2π)/891 weeks
65-.04557 .01921 (65*2π)/891 weeks
66-.15672 -.05006 (66*2π)/891 weeks
67.01107 -.03719 (67*2π)/891 weeks
68-.03114 .12094 (68*2π)/891 weeks
69-.04916 -.03618 (69*2π)/891 weeks
70.05629 .09033 (70*2π)/891 weeks
71-.10293 .07791 (71*2π)/891 weeks
72-.05206 -.04139 (72*2π)/891 weeks
73.09259 .09816 (73*2π)/891 weeks
74-.04 -.04784 (74*2π)/891 weeks
75-.06194 .14748 (75*2π)/891 weeks
76.00458 .07493 (76*2π)/891 weeks
77-.02333 .121 (77*2π)/891 weeks
78.03026 .10771 (78*2π)/891 weeks
79.00399 .039 (79*2π)/891 weeks
80-.08822 -.09833 (80*2π)/891 weeks
81.06512 .10352 (81*2π)/891 weeks
82-.08374 .13041 (82*2π)/891 weeks
83.00564 .21097 (83*2π)/891 weeks
84-.39619 .42401 (84*2π)/891 weeks
85.27453 -.0683 (85*2π)/891 weeks
86.35469 .44804 (86*2π)/891 weeks
87.04773 .08835 (87*2π)/891 weeks

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