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# Fourier Analysis of FIT (Fitbit)

FIT (Fitbit) appears to have interesting cyclic behaviour every 13 weeks (1.6819*sine), 15 weeks (1.3711*sine), and 11 weeks (.6693*cosine).

FIT (Fitbit) has an average price of 14.77 (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 6/18/2015 to 3/19/2018 for FIT (Fitbit), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
014.768   0
16.97816 9.88916 (1*2π)/145145 weeks
23.32872 6.13752 (2*2π)/14573 weeks
3-.36662 6.15284 (3*2π)/14548 weeks
4-.69536 2.7297 (4*2π)/14536 weeks
5-.06664 2.30238 (5*2π)/14529 weeks
6.80147 1.39079 (6*2π)/14524 weeks
7.81277 2.64922 (7*2π)/14521 weeks
8-.42394 1.90862 (8*2π)/14518 weeks
9.11067 1.53786 (9*2π)/14516 weeks
10.0917 1.37106 (10*2π)/14515 weeks
11-.07558 1.68191 (11*2π)/14513 weeks
12-.60858 1.1616 (12*2π)/14512 weeks
13-.66927 .84109 (13*2π)/14511 weeks
14-.6301 .36556 (14*2π)/14510 weeks
15-.15537 .29861 (15*2π)/14510 weeks
16.20195 .21765 (16*2π)/1459 weeks
17.32034 .50217 (17*2π)/1459 weeks
18-.06708 .65115 (18*2π)/1458 weeks
19-.11614 .20702 (19*2π)/1458 weeks
20.08187 .15228 (20*2π)/1457 weeks
21.23729 .17564 (21*2π)/1457 weeks
22.40522 .21679 (22*2π)/1457 weeks
23.50352 .65144 (23*2π)/1456 weeks
24.14775 .70441 (24*2π)/1456 weeks
25-.04436 .6387 (25*2π)/1456 weeks
26-.07018 .31326 (26*2π)/1456 weeks
27-.15786 .50107 (27*2π)/1455 weeks
28-.36417 -.10648 (28*2π)/1455 weeks
29.20461 -.2274 (29*2π)/1455 weeks
30.30479 -.00598 (30*2π)/1455 weeks
31.47992 .17223 (31*2π)/1455 weeks
32.2372 .3007 (32*2π)/1455 weeks
33.21686 .45032 (33*2π)/1454 weeks
34-.07357 .24143 (34*2π)/1454 weeks
35.14974 .01615 (35*2π)/1454 weeks
36.27575 .066 (36*2π)/1454 weeks
37.43073 .30858 (37*2π)/1454 weeks
38.01148 .49192 (38*2π)/1454 weeks
39-.00108 .23262 (39*2π)/1454 weeks
40-.13074 .15736 (40*2π)/1454 weeks
41.09489 -.18051 (41*2π)/1454 weeks
42.27588 .11003 (42*2π)/1453 weeks
43.20755 .20396 (43*2π)/1453 weeks
44.04373 .13282 (44*2π)/1453 weeks
45.17169 -.002 (45*2π)/1453 weeks
46.22056 .10326 (46*2π)/1453 weeks
47.22251 .20636 (47*2π)/1453 weeks
48.07952 .09548 (48*2π)/1453 weeks
49.11099 .05764 (49*2π)/1453 weeks
50.0597 .04981 (50*2π)/1453 weeks
51.20175 -.0964 (51*2π)/1453 weeks
52.22697 .02973 (52*2π)/1453 weeks
53.26525 -.0198 (53*2π)/1453 weeks
54.22021 .13074 (54*2π)/1453 weeks
55.23514 .09594 (55*2π)/1453 weeks
56.11724 .08947 (56*2π)/1453 weeks
57.24986 -.09962 (57*2π)/1453 weeks
58.22188 .18432 (58*2π)/1453 weeks
59.10326 .1128 (59*2π)/1452 weeks
60.0654 .07506 (60*2π)/1452 weeks
61.1485 .00671 (61*2π)/1452 weeks
62.06964 .07122 (62*2π)/1452 weeks
63-.06431 -.1407 (63*2π)/1452 weeks
64.10063 -.21321 (64*2π)/1452 weeks
65.21006 -.31301 (65*2π)/1452 weeks
66.40191 -.16857 (66*2π)/1452 weeks
67.43185 -.05631 (67*2π)/1452 weeks
68.32312 .08744 (68*2π)/1452 weeks
69.15864 .00196 (69*2π)/1452 weeks
70.24504 -.07821 (70*2π)/1452 weeks
71.39048 -.04244 (71*2π)/1452 weeks
72.30659 .06408 (72*2π)/1452 weeks
73.30659 -.06408 (73*2π)/1452 weeks
74.39048 .04244 (74*2π)/1452 weeks
75.24504 .07821 (75*2π)/1452 weeks
76.15864 -.00196 (76*2π)/1452 weeks
77.32312 -.08744 (77*2π)/1452 weeks
78.43185 .05631 (78*2π)/1452 weeks
79.40191 .16857 (79*2π)/1452 weeks
80.21006 .31301 (80*2π)/1452 weeks
81.10063 .21321 (81*2π)/1452 weeks
82-.06431 .1407 (82*2π)/1452 weeks
83.06964 -.07122 (83*2π)/1452 weeks
84.1485 -.00671 (84*2π)/1452 weeks
85.0654 -.07506 (85*2π)/1452 weeks
86.10326 -.1128 (86*2π)/1452 weeks
87.22188 -.18432 (87*2π)/1452 weeks
88.24986 .09962 (88*2π)/1452 weeks
89.11724 -.08947 (89*2π)/1452 weeks
90.23514 -.09594 (90*2π)/1452 weeks
91.22021 -.13074 (91*2π)/1452 weeks
92.26525 .0198 (92*2π)/1452 weeks
93.22697 -.02973 (93*2π)/1452 weeks
94.20175 .0964 (94*2π)/1452 weeks
95.0597 -.04981 (95*2π)/1452 weeks
96.11099 -.05764 (96*2π)/1452 weeks
97.07952 -.09548 (97*2π)/1451 weeks
98.22251 -.20636 (98*2π)/1451 weeks
99.22056 -.10326 (99*2π)/1451 weeks
100.17169 .002 (100*2π)/1451 weeks
101.04373 -.13282 (101*2π)/1451 weeks
102.20755 -.20396 (102*2π)/1451 weeks
103.27588 -.11003 (103*2π)/1451 weeks
104.09489 .18051 (104*2π)/1451 weeks
105-.13074 -.15736 (105*2π)/1451 weeks
106-.00108 -.23262 (106*2π)/1451 weeks
107.01148 -.49192 (107*2π)/1451 weeks
108.43073 -.30858 (108*2π)/1451 weeks
109.27575 -.066 (109*2π)/1451 weeks
110.14974 -.01615 (110*2π)/1451 weeks
111-.07357 -.24143 (111*2π)/1451 weeks
112.21686 -.45032 (112*2π)/1451 weeks
113.2372 -.3007 (113*2π)/1451 weeks
114.47992 -.17223 (114*2π)/1451 weeks
115.30479 .00598 (115*2π)/1451 weeks
116.20461 .2274 (116*2π)/1451 weeks
117-.36417 .10648 (117*2π)/1451 weeks
118-.15786 -.50107 (118*2π)/1451 weeks
119-.07018 -.31326 (119*2π)/1451 weeks
120-.04436 -.6387 (120*2π)/1451 weeks
121.14775 -.70441 (121*2π)/1451 weeks
122.50352 -.65144 (122*2π)/1451 weeks
123.40522 -.21679 (123*2π)/1451 weeks
124.23729 -.17564 (124*2π)/1451 weeks
125.08187 -.15228 (125*2π)/1451 weeks
126-.11614 -.20702 (126*2π)/1451 weeks
127-.06708 -.65115 (127*2π)/1451 weeks
128.32034 -.50217 (128*2π)/1451 weeks
129.20195 -.21765 (129*2π)/1451 weeks
130-.15537 -.29861 (130*2π)/1451 weeks
131-.6301 -.36556 (131*2π)/1451 weeks
132-.66927 -.84109 (132*2π)/1451 weeks
133-.60858 -1.1616 (133*2π)/1451 weeks
134-.07558 -1.68191 (134*2π)/1451 weeks
135.0917 -1.37106 (135*2π)/1451 weeks
136.11067 -1.53786 (136*2π)/1451 weeks
137-.42394 -1.90862 (137*2π)/1451 weeks
138.81277 -2.64922 (138*2π)/1451 weeks
139.80147 -1.39079 (139*2π)/1451 weeks
140-.06664 -2.30238 (140*2π)/1451 weeks
141-.69536 -2.7297 (141*2π)/1451 weeks
142-.36662 -6.15284 (142*2π)/1451 weeks
1433.32872 -6.13752 (143*2π)/1451 weeks