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# Fourier Analysis of SPEC (SpectralCast)

SPEC (SpectralCast) appears to have interesting cyclic behaviour every 9 weeks (.0228*cosine), 9 weeks (.0209*sine), and 4 weeks (.0182*cosine).

SPEC (SpectralCast) has an average price of .12 (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 1/8/2016 to 4/16/2018 for SPEC (SpectralCast), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0.11758   0
1.00666 -.04378 (1*2π)/104104 weeks
2-.01152 .00502 (2*2π)/10452 weeks
3.00754 .03837 (3*2π)/10435 weeks
4.016 .02326 (4*2π)/10426 weeks
5.02119 -.02336 (5*2π)/10421 weeks
6-.00974 -.00393 (6*2π)/10417 weeks
7.00476 .01336 (7*2π)/10415 weeks
8.00697 .00476 (8*2π)/10413 weeks
9.01035 .00788 (9*2π)/10412 weeks
10.00164 -.00586 (10*2π)/10410 weeks
11-.01249 .02088 (11*2π)/1049 weeks
12.02283 .00325 (12*2π)/1049 weeks
13-.00384 -.00463 (13*2π)/1048 weeks
14-.01208 .008 (14*2π)/1047 weeks
15-.0072 -.0024 (15*2π)/1047 weeks
16.00214 .01856 (16*2π)/1047 weeks
17.00913 -.0115 (17*2π)/1046 weeks
18.00048 -.0074 (18*2π)/1046 weeks
19.00419 .00746 (19*2π)/1045 weeks
20-.00729 -.00153 (20*2π)/1045 weeks
21.00619 .01559 (21*2π)/1045 weeks
22.00111 .00147 (22*2π)/1045 weeks
23-.00138 .0017 (23*2π)/1045 weeks
24.00731 -.00501 (24*2π)/1044 weeks
25-.01818 -.00397 (25*2π)/1044 weeks
26.00441 .00768 (26*2π)/1044 weeks
27.00511 -.00413 (27*2π)/1044 weeks
28.00283 .00096 (28*2π)/1044 weeks
29.00679 -.00934 (29*2π)/1044 weeks
30-.00385 .00671 (30*2π)/1043 weeks
31.0054 .00551 (31*2π)/1043 weeks
32-.00235 -.00493 (32*2π)/1043 weeks
33-.0001 .00676 (33*2π)/1043 weeks
34-.00084 -.00058 (34*2π)/1043 weeks
35.00289 -.0001 (35*2π)/1043 weeks
36.00684 -.00381 (36*2π)/1043 weeks
37-.00954 -.00017 (37*2π)/1043 weeks
38.00372 .00385 (38*2π)/1043 weeks
39.00392 -.00051 (39*2π)/1043 weeks
40.00256 .0036 (40*2π)/1043 weeks
41.00452 -.00612 (41*2π)/1043 weeks
42.00012 .00275 (42*2π)/1042 weeks
43.00142 .00383 (43*2π)/1042 weeks
44-.0027 -.00022 (44*2π)/1042 weeks
45.00463 .00597 (45*2π)/1042 weeks
46.00157 .00053 (46*2π)/1042 weeks
47-.00298 -.00522 (47*2π)/1042 weeks
48-.00146 .00036 (48*2π)/1042 weeks
49-.00369 .00326 (49*2π)/1042 weeks
50.00497 -.00566 (50*2π)/1042 weeks
51.0047 -.00213 (51*2π)/1042 weeks
52-.0025   (52*2π)/1042 weeks
53.0047 .00213 (53*2π)/1042 weeks
54.00497 .00566 (54*2π)/1042 weeks
55-.00369 -.00326 (55*2π)/1042 weeks
56-.00146 -.00036 (56*2π)/1042 weeks
57-.00298 .00522 (57*2π)/1042 weeks
58.00157 -.00053 (58*2π)/1042 weeks
59.00463 -.00597 (59*2π)/1042 weeks
60-.0027 .00022 (60*2π)/1042 weeks
61.00142 -.00383 (61*2π)/1042 weeks
62.00012 -.00275 (62*2π)/1042 weeks
63.00452 .00612 (63*2π)/1042 weeks
64.00256 -.0036 (64*2π)/1042 weeks
65.00392 .00051 (65*2π)/1042 weeks
66.00372 -.00385 (66*2π)/1042 weeks
67-.00954 .00017 (67*2π)/1042 weeks
68.00684 .00381 (68*2π)/1042 weeks
69.00289 .0001 (69*2π)/1042 weeks
70-.00084 .00058 (70*2π)/1041 weeks
71-.0001 -.00676 (71*2π)/1041 weeks
72-.00235 .00493 (72*2π)/1041 weeks
73.0054 -.00551 (73*2π)/1041 weeks
74-.00385 -.00671 (74*2π)/1041 weeks
75.00679 .00934 (75*2π)/1041 weeks
76.00283 -.00096 (76*2π)/1041 weeks
77.00511 .00413 (77*2π)/1041 weeks
78.00441 -.00768 (78*2π)/1041 weeks
79-.01818 .00397 (79*2π)/1041 weeks
80.00731 .00501 (80*2π)/1041 weeks
81-.00138 -.0017 (81*2π)/1041 weeks
82.00111 -.00147 (82*2π)/1041 weeks
83.00619 -.01559 (83*2π)/1041 weeks
84-.00729 .00153 (84*2π)/1041 weeks
85.00419 -.00746 (85*2π)/1041 weeks
86.00048 .0074 (86*2π)/1041 weeks
87.00913 .0115 (87*2π)/1041 weeks
88.00214 -.01856 (88*2π)/1041 weeks
89-.0072 .0024 (89*2π)/1041 weeks
90-.01208 -.008 (90*2π)/1041 weeks
91-.00384 .00463 (91*2π)/1041 weeks
92.02283 -.00325 (92*2π)/1041 weeks
93-.01249 -.02088 (93*2π)/1041 weeks
94.00164 .00586 (94*2π)/1041 weeks
95.01035 -.00788 (95*2π)/1041 weeks
96.00697 -.00476 (96*2π)/1041 weeks
97.00476 -.01336 (97*2π)/1041 weeks
98-.00974 .00393 (98*2π)/1041 weeks
99.02119 .02336 (99*2π)/1041 weeks
100.016 -.02326 (100*2π)/1041 weeks
101.00754 -.03837 (101*2π)/1041 weeks
102-.01152 -.00502 (102*2π)/1041 weeks