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Fourier Analysis of VIX


VIX appears to have interesting cyclic behaviour every 10 weeks (443.5019*cosine), 9 weeks (413.5169*cosine), and 6 weeks (372.0335*cosine).

VIX has an average price of 8,321.94 (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 12/4/2014 to 1/9/2017 for VIX, this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
08,321.935   0 
13,067.407 2,145.069 (1*2π)/111111 weeks
2685.2898 2,455.154 (2*2π)/11156 weeks
3552.322 1,917.574 (3*2π)/11137 weeks
4240.7929 1,140.336 (4*2π)/11128 weeks
5108.5175 1,247.046 (5*2π)/11122 weeks
6-313.2316 701.7089 (6*2π)/11119 weeks
7-320.0619 667.5906 (7*2π)/11116 weeks
8-9.49025 353.9166 (8*2π)/11114 weeks
97.07461 -38.23099 (9*2π)/11112 weeks
10230.9506 -61.52185 (10*2π)/11111 weeks
11443.5019 132.3437 (11*2π)/11110 weeks
12413.5169 48.12956 (12*2π)/1119 weeks
13352.476 325.9862 (13*2π)/1119 weeks
14276.5277 174.4507 (14*2π)/1118 weeks
15342.0439 134.936 (15*2π)/1117 weeks
16353.3016 283.785 (16*2π)/1117 weeks
17349.3208 241.0775 (17*2π)/1117 weeks
18237.1878 139.8832 (18*2π)/1116 weeks
19224.0699 159.7691 (19*2π)/1116 weeks
20372.0335 224.4487 (20*2π)/1116 weeks
21348.4083 272.4938 (21*2π)/1115 weeks
22279.5199 306.6758 (22*2π)/1115 weeks
23109.164 230.2778 (23*2π)/1115 weeks
24202.5058 119.841 (24*2π)/1115 weeks
25300.5519 101.516 (25*2π)/1114 weeks
26288.0952 181.7717 (26*2π)/1114 weeks
27108.4503 177.4334 (27*2π)/1114 weeks
28255.3891 19.27615 (28*2π)/1114 weeks
29347.6275 49.68655 (29*2π)/1114 weeks
30281.5548 204.3246 (30*2π)/1114 weeks
31195.2529 267.9116 (31*2π)/1114 weeks
32138.8357 128.7131 (32*2π)/1113 weeks
33158.3727 12.90743 (33*2π)/1113 weeks
34198.3517 98.32043 (34*2π)/1113 weeks
35207.5386 113.6908 (35*2π)/1113 weeks
36156.762 -22.737 (36*2π)/1113 weeks
37176.7897 -55.92745 (37*2π)/1113 weeks
38277.1526 31.96993 (38*2π)/1113 weeks
39365.7977 48.21047 (39*2π)/1113 weeks
40277.2792 108.4523 (40*2π)/1113 weeks
41200.743 68.25809 (41*2π)/1113 weeks
42266.912 73.84161 (42*2π)/1113 weeks
43250.0025 75.59104 (43*2π)/1113 weeks
44261.0909 83.52179 (44*2π)/1113 weeks
45201.6745 86.0756 (45*2π)/1112 weeks
46186.8624 69.82391 (46*2π)/1112 weeks
47246.6449 19.40423 (47*2π)/1112 weeks
48220.2527 69.23428 (48*2π)/1112 weeks
49203.5601 61.2154 (49*2π)/1112 weeks
50191.3906 66.43134 (50*2π)/1112 weeks
51116.9967 56.94401 (51*2π)/1112 weeks
52194.1695 -13.72701 (52*2π)/1112 weeks
53247.9758 -13.56558 (53*2π)/1112 weeks
54148.2411 44.50252 (54*2π)/1112 weeks
55187.3983 -32.95691 (55*2π)/1112 weeks
56187.3983 32.95691 (56*2π)/1112 weeks
57148.2411 -44.50252 (57*2π)/1112 weeks
58247.9758 13.56558 (58*2π)/1112 weeks
59194.1695 13.72701 (59*2π)/1112 weeks
60116.9967 -56.94401 (60*2π)/1112 weeks
61191.3906 -66.43134 (61*2π)/1112 weeks
62203.5601 -61.2154 (62*2π)/1112 weeks
63220.2527 -69.23428 (63*2π)/1112 weeks
64246.6449 -19.40423 (64*2π)/1112 weeks
65186.8624 -69.82391 (65*2π)/1112 weeks
66201.6745 -86.0756 (66*2π)/1112 weeks
67261.0909 -83.52179 (67*2π)/1112 weeks
68250.0025 -75.59104 (68*2π)/1112 weeks
69266.912 -73.84161 (69*2π)/1112 weeks
70200.743 -68.25809 (70*2π)/1112 weeks
71277.2792 -108.4523 (71*2π)/1112 weeks
72365.7977 -48.21047 (72*2π)/1112 weeks
73277.1526 -31.96993 (73*2π)/1112 weeks
74176.7897 55.92745 (74*2π)/1112 weeks
75156.762 22.737 (75*2π)/1111 weeks
76207.5386 -113.6908 (76*2π)/1111 weeks
77198.3517 -98.32043 (77*2π)/1111 weeks
78158.3727 -12.90743 (78*2π)/1111 weeks
79138.8357 -128.7131 (79*2π)/1111 weeks
80195.2529 -267.9116 (80*2π)/1111 weeks
81281.5548 -204.3246 (81*2π)/1111 weeks
82347.6275 -49.68655 (82*2π)/1111 weeks
83255.3891 -19.27615 (83*2π)/1111 weeks
84108.4503 -177.4334 (84*2π)/1111 weeks
85288.0952 -181.7717 (85*2π)/1111 weeks
86300.5519 -101.516 (86*2π)/1111 weeks
87202.5058 -119.841 (87*2π)/1111 weeks
88109.164 -230.2778 (88*2π)/1111 weeks
89279.5199 -306.6758 (89*2π)/1111 weeks
90348.4083 -272.4938 (90*2π)/1111 weeks
91372.0335 -224.4487 (91*2π)/1111 weeks
92224.0699 -159.7691 (92*2π)/1111 weeks
93237.1878 -139.8832 (93*2π)/1111 weeks
94349.3208 -241.0775 (94*2π)/1111 weeks
95353.3016 -283.785 (95*2π)/1111 weeks
96342.0439 -134.936 (96*2π)/1111 weeks
97276.5277 -174.4507 (97*2π)/1111 weeks
98352.476 -325.9862 (98*2π)/1111 weeks
99413.5169 -48.12956 (99*2π)/1111 weeks
100443.5019 -132.3437 (100*2π)/1111 weeks
101230.9506 61.52185 (101*2π)/1111 weeks
1027.07461 38.23099 (102*2π)/1111 weeks
103-9.49025 -353.9166 (103*2π)/1111 weeks
104-320.0619 -667.5906 (104*2π)/1111 weeks
105-313.2316 -701.7089 (105*2π)/1111 weeks
106108.5175 -1,247.046 (106*2π)/1111 weeks
107240.7929 -1,140.336 (107*2π)/1111 weeks
108552.322 -1,917.574 (108*2π)/1111 weeks
109685.2898 -2,455.154 (109*2π)/1111 weeks

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