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# Fourier Analysis of FB (Facebook)

FB (Facebook) appears to have interesting cyclic behaviour every 26 weeks (5.1356*sine), 24 weeks (4.7623*sine), and 31 weeks (3.6621*sine).

FB (Facebook) has an average price of 89.44 (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 5/18/2012 to 3/19/2018 for FB (Facebook), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
089.43973   0
16.10828 -51.11905 (1*2π)/306306 weeks
23.89086 -30.02749 (2*2π)/306153 weeks
34.98593 -19.77492 (3*2π)/306102 weeks
4-.60579 -14.14922 (4*2π)/30677 weeks
5-1.77775 -9.87306 (5*2π)/30661 weeks
6-2.18748 -8.35263 (6*2π)/30651 weeks
71.59728 -8.09399 (7*2π)/30644 weeks
8.66789 -6.55408 (8*2π)/30638 weeks
9-.42337 -5.25543 (9*2π)/30634 weeks
10.16393 -3.66212 (10*2π)/30631 weeks
11-.60961 -2.80818 (11*2π)/30628 weeks
12-.24687 -5.13556 (12*2π)/30626 weeks
13.09502 -4.76231 (13*2π)/30624 weeks
14-1.58838 -1.79917 (14*2π)/30622 weeks
15-.66513 -2.29645 (15*2π)/30620 weeks
16-.64087 -4.05002 (16*2π)/30619 weeks
17-.21154 -2.21494 (17*2π)/30618 weeks
18-.59086 -2.77274 (18*2π)/30617 weeks
19-.68101 -1.65984 (19*2π)/30616 weeks
20.24595 -2.69063 (20*2π)/30615 weeks
21-1.2815 -1.90212 (21*2π)/30615 weeks
22-.81542 -2.74046 (22*2π)/30614 weeks
23-1.22543 -1.95044 (23*2π)/30613 weeks
24-.98054 -1.3381 (24*2π)/30613 weeks
25-.22792 -1.60691 (25*2π)/30612 weeks
26-.41791 -1.74062 (26*2π)/30612 weeks
27-.71273 -1.36144 (27*2π)/30611 weeks
28-.4089 -1.84068 (28*2π)/30611 weeks
29.06752 -2.47962 (29*2π)/30611 weeks
30-.62484 -1.4151 (30*2π)/30610 weeks
31-.71547 -1.50632 (31*2π)/30610 weeks
32-.21836 -1.7382 (32*2π)/30610 weeks
33.02979 -1.7134 (33*2π)/3069 weeks
34-.20323 -.99959 (34*2π)/3069 weeks
35-.03492 -1.49873 (35*2π)/3069 weeks
36-.33464 -1.7504 (36*2π)/3069 weeks
37-.37512 -1.28278 (37*2π)/3068 weeks
38-.56847 -1.36667 (38*2π)/3068 weeks
39-.61128 -1.23396 (39*2π)/3068 weeks
40-.55461 -1.19406 (40*2π)/3068 weeks
41-.35854 -1.00387 (41*2π)/3067 weeks
42-.62277 -1.67968 (42*2π)/3067 weeks
43-.35622 -.78446 (43*2π)/3067 weeks
44-.03791 -.98515 (44*2π)/3067 weeks
45-.35633 -1.16874 (45*2π)/3067 weeks
46-.39562 -1.02419 (46*2π)/3067 weeks
47-.95674 -1.66314 (47*2π)/3067 weeks
48-.77023 -.69529 (48*2π)/3066 weeks
49-.41656 -.58572 (49*2π)/3066 weeks
50-.68424 -1.02725 (50*2π)/3066 weeks
51-.5175 -.77161 (51*2π)/3066 weeks
52-.35187 -.71757 (52*2π)/3066 weeks
53-.16144 -.84815 (53*2π)/3066 weeks
54-.40836 -.8537 (54*2π)/3066 weeks
55-.53255 -.74382 (55*2π)/3066 weeks
56-1.01425 -.51136 (56*2π)/3065 weeks
57-.61018 -.54481 (57*2π)/3065 weeks
58-.43101 -.62766 (58*2π)/3065 weeks
59-.65485 -.44775 (59*2π)/3065 weeks
60-.59107 -.65578 (60*2π)/3065 weeks
61-.63547 -.47212 (61*2π)/3065 weeks
62-.33031 -.45147 (62*2π)/3065 weeks
63-.49411 -.89818 (63*2π)/3065 weeks
64-.3918 -.39181 (64*2π)/3065 weeks
65-.12101 -.55811 (65*2π)/3065 weeks
66-.80327 -.76219 (66*2π)/3065 weeks
67-.35283 -.18877 (67*2π)/3065 weeks
68-.10704 -.34564 (68*2π)/3065 weeks
69-.70521 -.46283 (69*2π)/3064 weeks
70.06113 -.1323 (70*2π)/3064 weeks
71-.45703 -.70882 (71*2π)/3064 weeks
72-.37935 -.62193 (72*2π)/3064 weeks
73-.33307 -.28745 (73*2π)/3064 weeks
74-.20211 -.64336 (74*2π)/3064 weeks
75-.59426 -.09592 (75*2π)/3064 weeks
76-.45577 -.32439 (76*2π)/3064 weeks
77-.32377 -.53191 (77*2π)/3064 weeks
78.04476 -.47406 (78*2π)/3064 weeks
79-.41371 -.63061 (79*2π)/3064 weeks
80-.82762 -.43407 (80*2π)/3064 weeks
81-.37539 -.26313 (81*2π)/3064 weeks
82-.32604 -.40934 (82*2π)/3064 weeks
83-.34931 -.2762 (83*2π)/3064 weeks
84-.55674 -.55523 (84*2π)/3064 weeks
85-.66814 -.50741 (85*2π)/3064 weeks
86-.46865 -.42393 (86*2π)/3064 weeks
87-.47775 -.40074 (87*2π)/3064 weeks
88-.99282 -.51123 (88*2π)/3063 weeks
89-.61692 -.28069 (89*2π)/3063 weeks
90-.76116 -.17313 (90*2π)/3063 weeks
91-.57557 -.16559 (91*2π)/3063 weeks
92-.43828 -.34447 (92*2π)/3063 weeks
93-.75653 -.08009 (93*2π)/3063 weeks
94-.65242 .00017 (94*2π)/3063 weeks
95-.5869 .09735 (95*2π)/3063 weeks
96-.48966 -.19138 (96*2π)/3063 weeks
97-.6322 .19106 (97*2π)/3063 weeks
98-.40241 -.15046 (98*2π)/3063 weeks
99-.32378 -.0112 (99*2π)/3063 weeks
100-.16554 .17376 (100*2π)/3063 weeks
101-.47223 -.4538 (101*2π)/3063 weeks
102-.13631 -.09206 (102*2π)/3063 weeks
103-.3345 -.22029 (103*2π)/3063 weeks
104-.30639 -.08554 (104*2π)/3063 weeks
105-.32547 -.12424 (105*2π)/3063 weeks
106-.18116 -.25702 (106*2π)/3063 weeks
107-.20248 -.33526 (107*2π)/3063 weeks
108-.35768 -.1117 (108*2π)/3063 weeks
109-.37483 -.2712 (109*2π)/3063 weeks
110-.61808 -.10603 (110*2π)/3063 weeks
111-.15264 -.0746 (111*2π)/3063 weeks
112-.57499 -.05514 (112*2π)/3063 weeks
113-.38177 -.11282 (113*2π)/3063 weeks
114-.33146 .02915 (114*2π)/3063 weeks
115-.38267 -.32506 (115*2π)/3063 weeks
116-.30988 -.37687 (116*2π)/3063 weeks
117-.44614 -.27587 (117*2π)/3063 weeks
118-.3115 -.02555 (118*2π)/3063 weeks
119-.38952 -.07054 (119*2π)/3063 weeks
120-.20432 -.15193 (120*2π)/3063 weeks
121-.3846 -.03334 (121*2π)/3063 weeks
122-.34373 -.0634 (122*2π)/3063 weeks
123-.30069 -.40211 (123*2π)/3062 weeks
124-.3535 -.07261 (124*2π)/3062 weeks
125-.32001 -.30345 (125*2π)/3062 weeks
126-.46795 -.20722 (126*2π)/3062 weeks
127-.28105 -.25108 (127*2π)/3062 weeks
128-.43381 -.22983 (128*2π)/3062 weeks
129-.44358 .07171 (129*2π)/3062 weeks
130-.1902 -.13637 (130*2π)/3062 weeks
131-.35139 .00795 (131*2π)/3062 weeks
132-.23536 -.18591 (132*2π)/3062 weeks
133-.44856 -.19796 (133*2π)/3062 weeks
134-.30182 -.08763 (134*2π)/3062 weeks
135-.37921 -.02935 (135*2π)/3062 weeks
136-.42071 -.27376 (136*2π)/3062 weeks
137-.56714 -.2114 (137*2π)/3062 weeks
138-.4684 .07603 (138*2π)/3062 weeks
139-.53055 -.06415 (139*2π)/3062 weeks
140-.3447 -.04104 (140*2π)/3062 weeks
141-.37766 -.22591 (141*2π)/3062 weeks
142-.54088 -.18698 (142*2π)/3062 weeks
143-.63912 .12226 (143*2π)/3062 weeks
144-.33285 -.07147 (144*2π)/3062 weeks
145-.50079 .06502 (145*2π)/3062 weeks
146-.61241 .09095 (146*2π)/3062 weeks
147-.40324 -.03036 (147*2π)/3062 weeks
148-.57919 .03158 (148*2π)/3062 weeks
149-.26606 .2466 (149*2π)/3062 weeks
150-.38203 -.16897 (150*2π)/3062 weeks
151-.55196 .21255 (151*2π)/3062 weeks
152-.24856 -.1839 (152*2π)/3062 weeks
153-.11679   (153*2π)/3062 weeks
154-.24856 .1839 (154*2π)/3062 weeks
155-.55196 -.21255 (155*2π)/3062 weeks
156-.38203 .16897 (156*2π)/3062 weeks
157-.26606 -.2466 (157*2π)/3062 weeks
158-.57919 -.03158 (158*2π)/3062 weeks
159-.40324 .03036 (159*2π)/3062 weeks
160-.61241 -.09095 (160*2π)/3062 weeks
161-.50079 -.06502 (161*2π)/3062 weeks
162-.33285 .07147 (162*2π)/3062 weeks
163-.63912 -.12226 (163*2π)/3062 weeks
164-.54088 .18698 (164*2π)/3062 weeks
165-.37766 .22591 (165*2π)/3062 weeks
166-.3447 .04104 (166*2π)/3062 weeks
167-.53055 .06415 (167*2π)/3062 weeks
168-.4684 -.07603 (168*2π)/3062 weeks
169-.56714 .2114 (169*2π)/3062 weeks
170-.42071 .27376 (170*2π)/3062 weeks
171-.37921 .02935 (171*2π)/3062 weeks
172-.30182 .08763 (172*2π)/3062 weeks
173-.44856 .19796 (173*2π)/3062 weeks
174-.23536 .18591 (174*2π)/3062 weeks
175-.35139 -.00795 (175*2π)/3062 weeks
176-.1902 .13637 (176*2π)/3062 weeks
177-.44358 -.07171 (177*2π)/3062 weeks
178-.43381 .22983 (178*2π)/3062 weeks
179-.28105 .25108 (179*2π)/3062 weeks
180-.46795 .20722 (180*2π)/3062 weeks
181-.32001 .30345 (181*2π)/3062 weeks
182-.3535 .07261 (182*2π)/3062 weeks
183-.30069 .40211 (183*2π)/3062 weeks
184-.34373 .0634 (184*2π)/3062 weeks
185-.3846 .03334 (185*2π)/3062 weeks
186-.20432 .15193 (186*2π)/3062 weeks
187-.38952 .07054 (187*2π)/3062 weeks
188-.3115 .02555 (188*2π)/3062 weeks
189-.44614 .27587 (189*2π)/3062 weeks
190-.30988 .37687 (190*2π)/3062 weeks
191-.38267 .32506 (191*2π)/3062 weeks
192-.33146 -.02915 (192*2π)/3062 weeks
193-.38177 .11282 (193*2π)/3062 weeks
194-.57499 .05514 (194*2π)/3062 weeks
195-.15264 .0746 (195*2π)/3062 weeks
196-.61808 .10603 (196*2π)/3062 weeks
197-.37483 .2712 (197*2π)/3062 weeks
198-.35768 .1117 (198*2π)/3062 weeks
199-.20248 .33526 (199*2π)/3062 weeks
200-.18116 .25702 (200*2π)/3062 weeks
201-.32547 .12424 (201*2π)/3062 weeks
202-.30639 .08554 (202*2π)/3062 weeks
203-.3345 .22029 (203*2π)/3062 weeks
204-.13631 .09206 (204*2π)/3062 weeks
205-.47223 .4538 (205*2π)/3061 weeks
206-.16554 -.17376 (206*2π)/3061 weeks
207-.32378 .0112 (207*2π)/3061 weeks
208-.40241 .15046 (208*2π)/3061 weeks
209-.6322 -.19106 (209*2π)/3061 weeks
210-.48966 .19138 (210*2π)/3061 weeks
211-.5869 -.09735 (211*2π)/3061 weeks
212-.65242 -.00017 (212*2π)/3061 weeks
213-.75653 .08009 (213*2π)/3061 weeks
214-.43828 .34447 (214*2π)/3061 weeks
215-.57557 .16559 (215*2π)/3061 weeks
216-.76116 .17313 (216*2π)/3061 weeks
217-.61692 .28069 (217*2π)/3061 weeks
218-.99282 .51123 (218*2π)/3061 weeks
219-.47775 .40074 (219*2π)/3061 weeks
220-.46865 .42393 (220*2π)/3061 weeks
221-.66814 .50741 (221*2π)/3061 weeks
222-.55674 .55523 (222*2π)/3061 weeks
223-.34931 .2762 (223*2π)/3061 weeks
224-.32604 .40934 (224*2π)/3061 weeks
225-.37539 .26313 (225*2π)/3061 weeks
226-.82762 .43407 (226*2π)/3061 weeks
227-.41371 .63061 (227*2π)/3061 weeks
228.04476 .47406 (228*2π)/3061 weeks
229-.32377 .53191 (229*2π)/3061 weeks
230-.45577 .32439 (230*2π)/3061 weeks
231-.59426 .09592 (231*2π)/3061 weeks
232-.20211 .64336 (232*2π)/3061 weeks
233-.33307 .28745 (233*2π)/3061 weeks
234-.37935 .62193 (234*2π)/3061 weeks
235-.45703 .70882 (235*2π)/3061 weeks
236.06113 .1323 (236*2π)/3061 weeks
237-.70521 .46283 (237*2π)/3061 weeks
238-.10704 .34564 (238*2π)/3061 weeks
239-.35283 .18877 (239*2π)/3061 weeks
240-.80327 .76219 (240*2π)/3061 weeks
241-.12101 .55811 (241*2π)/3061 weeks
242-.3918 .39181 (242*2π)/3061 weeks
243-.49411 .89818 (243*2π)/3061 weeks
244-.33031 .45147 (244*2π)/3061 weeks
245-.63547 .47212 (245*2π)/3061 weeks
246-.59107 .65578 (246*2π)/3061 weeks
247-.65485 .44775 (247*2π)/3061 weeks
248-.43101 .62766 (248*2π)/3061 weeks
249-.61018 .54481 (249*2π)/3061 weeks
250-1.01425 .51136 (250*2π)/3061 weeks
251-.53255 .74382 (251*2π)/3061 weeks
252-.40836 .8537 (252*2π)/3061 weeks
253-.16144 .84815 (253*2π)/3061 weeks
254-.35187 .71757 (254*2π)/3061 weeks
255-.5175 .77161 (255*2π)/3061 weeks
256-.68424 1.02725 (256*2π)/3061 weeks
257-.41656 .58572 (257*2π)/3061 weeks
258-.77023 .69529 (258*2π)/3061 weeks
259-.95674 1.66314 (259*2π)/3061 weeks
260-.39562 1.02419 (260*2π)/3061 weeks
261-.35633 1.16874 (261*2π)/3061 weeks
262-.03791 .98515 (262*2π)/3061 weeks
263-.35622 .78446 (263*2π)/3061 weeks
264-.62277 1.67968 (264*2π)/3061 weeks
265-.35854 1.00387 (265*2π)/3061 weeks
266-.55461 1.19406 (266*2π)/3061 weeks
267-.61128 1.23396 (267*2π)/3061 weeks
268-.56847 1.36667 (268*2π)/3061 weeks
269-.37512 1.28278 (269*2π)/3061 weeks
270-.33464 1.7504 (270*2π)/3061 weeks
271-.03492 1.49873 (271*2π)/3061 weeks
272-.20323 .99959 (272*2π)/3061 weeks
273.02979 1.7134 (273*2π)/3061 weeks
274-.21836 1.7382 (274*2π)/3061 weeks
275-.71547 1.50632 (275*2π)/3061 weeks
276-.62484 1.4151 (276*2π)/3061 weeks
277.06752 2.47962 (277*2π)/3061 weeks
278-.4089 1.84068 (278*2π)/3061 weeks
279-.71273 1.36144 (279*2π)/3061 weeks
280-.41791 1.74062 (280*2π)/3061 weeks
281-.22792 1.60691 (281*2π)/3061 weeks
282-.98054 1.3381 (282*2π)/3061 weeks
283-1.22543 1.95044 (283*2π)/3061 weeks
284-.81542 2.74046 (284*2π)/3061 weeks
285-1.2815 1.90212 (285*2π)/3061 weeks
286.24595 2.69063 (286*2π)/3061 weeks
287-.68101 1.65984 (287*2π)/3061 weeks
288-.59086 2.77274 (288*2π)/3061 weeks
289-.21154 2.21494 (289*2π)/3061 weeks
290-.64087 4.05002 (290*2π)/3061 weeks
291-.66513 2.29645 (291*2π)/3061 weeks
292-1.58838 1.79917 (292*2π)/3061 weeks
293.09502 4.76231 (293*2π)/3061 weeks
294-.24687 5.13556 (294*2π)/3061 weeks
295-.60961 2.80818 (295*2π)/3061 weeks
296.16393 3.66212 (296*2π)/3061 weeks
297-.42337 5.25543 (297*2π)/3061 weeks
298.66789 6.55408 (298*2π)/3061 weeks
2991.59728 8.09399 (299*2π)/3061 weeks
300-2.18748 8.35263 (300*2π)/3061 weeks
301-1.77775 9.87306 (301*2π)/3061 weeks
302-.60579 14.14922 (302*2π)/3061 weeks
3034.98593 19.77492 (303*2π)/3061 weeks
3043.89086 30.02749 (304*2π)/3061 weeks