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# Fourier Analysis of GCAP (GAIN Capital Holdings)

GCAP (GAIN Capital Holdings) appears to have interesting cyclic behaviour every 30 weeks (.2731*cosine), 28 weeks (.2371*sine), and 35 weeks (.2366*sine).

GCAP (GAIN Capital Holdings) has an average price of 6.32 (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 12/15/2010 to 4/23/2018 for GCAP (GAIN Capital Holdings), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
06.32338   0
1-.72281 -1.02421 (1*2π)/385385 weeks
21.17305 -.30557 (2*2π)/385193 weeks
3.26466 .18939 (3*2π)/385128 weeks
4-.49888 -.30485 (4*2π)/38596 weeks
5.73872 -.13053 (5*2π)/38577 weeks
6-.1532 .05912 (6*2π)/38564 weeks
7.39277 -.24345 (7*2π)/38555 weeks
8.03381 -.14803 (8*2π)/38548 weeks
9-.06479 .14367 (9*2π)/38543 weeks
10-.21347 -.01246 (10*2π)/38539 weeks
11.05118 .23664 (11*2π)/38535 weeks
12-.10815 .14336 (12*2π)/38532 weeks
13.27313 -.21816 (13*2π)/38530 weeks
14-.12617 .23709 (14*2π)/38528 weeks
15-.00012 -.13767 (15*2π)/38526 weeks
16.06002 .21772 (16*2π)/38524 weeks
17-.10633 .22343 (17*2π)/38523 weeks
18.17603 -.01548 (18*2π)/38521 weeks
19.0482 .22576 (19*2π)/38520 weeks
20-.00071 -.08895 (20*2π)/38519 weeks
21.16178 .05804 (21*2π)/38518 weeks
22-.10852 -.05539 (22*2π)/38518 weeks
23.00195 -.11998 (23*2π)/38517 weeks
24.00059 -.0482 (24*2π)/38516 weeks
25-.00438 .01965 (25*2π)/38515 weeks
26.10264 -.04891 (26*2π)/38515 weeks
27.05316 .0527 (27*2π)/38514 weeks
28.02626 -.05572 (28*2π)/38514 weeks
29.00547 -.03 (29*2π)/38513 weeks
30-.0652 .10352 (30*2π)/38513 weeks
31-.01643 -.11352 (31*2π)/38512 weeks
32-.063 .02835 (32*2π)/38512 weeks
33-.04846 -.02408 (33*2π)/38512 weeks
34-.00003 -.04029 (34*2π)/38511 weeks
35-.08254 .0164 (35*2π)/38511 weeks
36.01519 .02777 (36*2π)/38511 weeks
37-.03866 -.04276 (37*2π)/38510 weeks
38.02984 .03075 (38*2π)/38510 weeks
39-.09125 -.00544 (39*2π)/38510 weeks
40-.00408 .07114 (40*2π)/38510 weeks
41.03799 .03288 (41*2π)/3859 weeks
42.02109 -.04087 (42*2π)/3859 weeks
43-.05435 -.03839 (43*2π)/3859 weeks
44.05267 .03777 (44*2π)/3859 weeks
45.00348 -.02069 (45*2π)/3859 weeks
46-.00872 .11503 (46*2π)/3858 weeks
47.0173 -.08546 (47*2π)/3858 weeks
48.01838 -.02385 (48*2π)/3858 weeks
49.03258 -.07301 (49*2π)/3858 weeks
50.00522 -.1094 (50*2π)/3858 weeks
51.04443 .00604 (51*2π)/3858 weeks
52-.03379 -.12278 (52*2π)/3857 weeks
53.0008 .01032 (53*2π)/3857 weeks
54-.02923 -.03114 (54*2π)/3857 weeks
55.00042 -.04856 (55*2π)/3857 weeks
56-.05782 -.01114 (56*2π)/3857 weeks
57.02112 -.03417 (57*2π)/3857 weeks
58-.04564 -.03618 (58*2π)/3857 weeks
59.00104 .03395 (59*2π)/3857 weeks
60-.04293 -.01233 (60*2π)/3856 weeks
61-.00535 .01717 (61*2π)/3856 weeks
62-.03145 -.00474 (62*2π)/3856 weeks
63-.0345 -.03314 (63*2π)/3856 weeks
64-.01258 .04104 (64*2π)/3856 weeks
65-.00214 .01429 (65*2π)/3856 weeks
66-.00666 -.00434 (66*2π)/3856 weeks
67.01293 -.01664 (67*2π)/3856 weeks
68-.03237 .02264 (68*2π)/3856 weeks
69-.02181 -.03053 (69*2π)/3856 weeks
70.02839 -.01857 (70*2π)/3856 weeks
71-.04295 -.03417 (71*2π)/3855 weeks
72.03298 -.04554 (72*2π)/3855 weeks
73-.01187 -.01128 (73*2π)/3855 weeks
74-.0557 -.05879 (74*2π)/3855 weeks
75.03819 .02192 (75*2π)/3855 weeks
76-.04679 -.02335 (76*2π)/3855 weeks
77-.02195 .00616 (77*2π)/3855 weeks
78-.0721 .03228 (78*2π)/3855 weeks
79-.01042 -.01531 (79*2π)/3855 weeks
80-.02844 .0214 (80*2π)/3855 weeks
81-.01551 -.02069 (81*2π)/3855 weeks
82.03054 -.00022 (82*2π)/3855 weeks
83-.02276 .00181 (83*2π)/3855 weeks
84-.0096 .03995 (84*2π)/3855 weeks
85-.00759 .00337 (85*2π)/3855 weeks
86.04849 .00266 (86*2π)/3854 weeks
87.01094 -.01519 (87*2π)/3854 weeks
88.0226 -.01576 (88*2π)/3854 weeks
89.02649 -.02576 (89*2π)/3854 weeks
90-.03322 -.01145 (90*2π)/3854 weeks
91.00267 -.02263 (91*2π)/3854 weeks
92.00507 -.05224 (92*2π)/3854 weeks
93-.0509 -.01277 (93*2π)/3854 weeks
94.00404 -.02878 (94*2π)/3854 weeks
95-.02279 .02207 (95*2π)/3854 weeks
96-.0587 -.0305 (96*2π)/3854 weeks
97-.0119 .0205 (97*2π)/3854 weeks
98-.01399 -.02178 (98*2π)/3854 weeks
99-.01934 .01951 (99*2π)/3854 weeks
100-.00597 .02743 (100*2π)/3854 weeks
101.03527 .01779 (101*2π)/3854 weeks
102-.02993 .02 (102*2π)/3854 weeks
103.01251 .00605 (103*2π)/3854 weeks
104.00081 .01436 (104*2π)/3854 weeks
105-.01432 -.00559 (105*2π)/3854 weeks
106.00845 .0015 (106*2π)/3854 weeks
107.00916 .01917 (107*2π)/3854 weeks
108.01933 -.02001 (108*2π)/3854 weeks
109.02463 .03252 (109*2π)/3854 weeks
110-.00202 .00062 (110*2π)/3854 weeks
111.0163 -.04027 (111*2π)/3853 weeks
112-.00992 .01863 (112*2π)/3853 weeks
113-.01343 -.02834 (113*2π)/3853 weeks
114.03762 -.00118 (114*2π)/3853 weeks
115-.04244 .01835 (115*2π)/3853 weeks
116.01177 -.03147 (116*2π)/3853 weeks
117-.00402 -.0182 (117*2π)/3853 weeks
118-.01036 -.00672 (118*2π)/3853 weeks
119-.00808 -.0347 (119*2π)/3853 weeks
120-.01124 .00361 (120*2π)/3853 weeks
121-.06004 -.00179 (121*2π)/3853 weeks
122-.00043 -.02124 (122*2π)/3853 weeks
123-.03165 .00214 (123*2π)/3853 weeks
124-.00003 -.02435 (124*2π)/3853 weeks
125.00954 .00934 (125*2π)/3853 weeks
126-.04365 -.00192 (126*2π)/3853 weeks
127.01867 -.00284 (127*2π)/3853 weeks
128-.01385 .0053 (128*2π)/3853 weeks
129.01678 .01334 (129*2π)/3853 weeks
130.03891 .01046 (130*2π)/3853 weeks
131.02687 -.0022 (131*2π)/3853 weeks
132.01458 .00256 (132*2π)/3853 weeks
133.01552 -.02453 (133*2π)/3853 weeks
134-.0132 .00248 (134*2π)/3853 weeks
135.00911 -.01858 (135*2π)/3853 weeks
136-.00492 -.02397 (136*2π)/3853 weeks
137.00468 .02402 (137*2π)/3853 weeks
138.01457 -.00562 (138*2π)/3853 weeks
139-.005 .0061 (139*2π)/3853 weeks
140.01674 -.02288 (140*2π)/3853 weeks
141-.02235 -.00595 (141*2π)/3853 weeks
142-.00715 -.00986 (142*2π)/3853 weeks
143-.00349 .01173 (143*2π)/3853 weeks
144.00165 -.00411 (144*2π)/3853 weeks
145-.00448 .0248 (145*2π)/3853 weeks
146.00489 -.01549 (146*2π)/3853 weeks
147-.02125 .00426 (147*2π)/3853 weeks
148-.01201 .01788 (148*2π)/3853 weeks
149.01237 -.00831 (149*2π)/3853 weeks
150.02154 .01173 (150*2π)/3853 weeks
151.00848 -.00504 (151*2π)/3853 weeks
152.02345 .00152 (152*2π)/3853 weeks
153-.03714 .00215 (153*2π)/3853 weeks
154.012 .00563 (154*2π)/3853 weeks
155-.00778 .01098 (155*2π)/3852 weeks
156.00606 -.00462 (156*2π)/3852 weeks
157.00612 -.01677 (157*2π)/3852 weeks
158-.01169 -.00834 (158*2π)/3852 weeks
159-.00324 -.03043 (159*2π)/3852 weeks
160.03453 .01305 (160*2π)/3852 weeks
161-.04299 -.02267 (161*2π)/3852 weeks
162.03844 .01227 (162*2π)/3852 weeks
163-.02988 .02752 (163*2π)/3852 weeks
164-.00869 -.00755 (164*2π)/3852 weeks
165-.00468 .01741 (165*2π)/3852 weeks
166.00633 .01666 (166*2π)/3852 weeks
167.00382 -.00817 (167*2π)/3852 weeks
168.02411 .03771 (168*2π)/3852 weeks
169.0026 .00755 (169*2π)/3852 weeks
170.01393 .00283 (170*2π)/3852 weeks
171.0017 .01496 (171*2π)/3852 weeks
172-.01128 -.0292 (172*2π)/3852 weeks
173.01614 .00994 (173*2π)/3852 weeks
174-.02782 -.02275 (174*2π)/3852 weeks
175.01589 -.0198 (175*2π)/3852 weeks
176-.0154 .00364 (176*2π)/3852 weeks
177-.00939 -.0116 (177*2π)/3852 weeks
178-.02866 -.0162 (178*2π)/3852 weeks
179-.01676 -.00598 (179*2π)/3852 weeks
180-.04026 .01899 (180*2π)/3852 weeks
181.01575 -.02527 (181*2π)/3852 weeks
182-.02354 .01789 (182*2π)/3852 weeks
183-.00474 -.00802 (183*2π)/3852 weeks
184.01008 -.01241 (184*2π)/3852 weeks
185-.01341 -.00823 (185*2π)/3852 weeks
186.00462 -.01231 (186*2π)/3852 weeks
187.02182 -.00003 (187*2π)/3852 weeks
188-.01798 -.01189 (188*2π)/3852 weeks
189-.00344 .01415 (189*2π)/3852 weeks
190-.00483 -.0231 (190*2π)/3852 weeks
191-.01934 -.00197 (191*2π)/3852 weeks
192-.0113 -.00606 (192*2π)/3852 weeks
193-.0113 .00606 (193*2π)/3852 weeks
194-.01934 .00197 (194*2π)/3852 weeks
195-.00483 .0231 (195*2π)/3852 weeks
196-.00344 -.01415 (196*2π)/3852 weeks
197-.01798 .01189 (197*2π)/3852 weeks
198.02182 .00003 (198*2π)/3852 weeks
199.00462 .01231 (199*2π)/3852 weeks
200-.01341 .00823 (200*2π)/3852 weeks
201.01008 .01241 (201*2π)/3852 weeks
202-.00474 .00802 (202*2π)/3852 weeks
203-.02354 -.01789 (203*2π)/3852 weeks
204.01575 .02527 (204*2π)/3852 weeks
205-.04026 -.01899 (205*2π)/3852 weeks
206-.01676 .00598 (206*2π)/3852 weeks
207-.02866 .0162 (207*2π)/3852 weeks
208-.00939 .0116 (208*2π)/3852 weeks
209-.0154 -.00364 (209*2π)/3852 weeks
210.01589 .0198 (210*2π)/3852 weeks
211-.02782 .02275 (211*2π)/3852 weeks
212.01614 -.00994 (212*2π)/3852 weeks
213-.01128 .0292 (213*2π)/3852 weeks
214.0017 -.01496 (214*2π)/3852 weeks
215.01393 -.00283 (215*2π)/3852 weeks
216.0026 -.00755 (216*2π)/3852 weeks
217.02411 -.03771 (217*2π)/3852 weeks
218.00382 .00817 (218*2π)/3852 weeks
219.00633 -.01666 (219*2π)/3852 weeks
220-.00468 -.01741 (220*2π)/3852 weeks
221-.00869 .00755 (221*2π)/3852 weeks
222-.02988 -.02752 (222*2π)/3852 weeks
223.03844 -.01227 (223*2π)/3852 weeks
224-.04299 .02267 (224*2π)/3852 weeks
225.03453 -.01305 (225*2π)/3852 weeks
226-.00324 .03043 (226*2π)/3852 weeks
227-.01169 .00834 (227*2π)/3852 weeks
228.00612 .01677 (228*2π)/3852 weeks
229.00606 .00462 (229*2π)/3852 weeks
230-.00778 -.01098 (230*2π)/3852 weeks
231.012 -.00563 (231*2π)/3852 weeks
232-.03714 -.00215 (232*2π)/3852 weeks
233.02345 -.00152 (233*2π)/3852 weeks
234.00848 .00504 (234*2π)/3852 weeks
235.02154 -.01173 (235*2π)/3852 weeks
236.01237 .00831 (236*2π)/3852 weeks
237-.01201 -.01788 (237*2π)/3852 weeks
238-.02125 -.00426 (238*2π)/3852 weeks
239.00489 .01549 (239*2π)/3852 weeks
240-.00448 -.0248 (240*2π)/3852 weeks
241.00165 .00411 (241*2π)/3852 weeks
242-.00349 -.01173 (242*2π)/3852 weeks
243-.00715 .00986 (243*2π)/3852 weeks
244-.02235 .00595 (244*2π)/3852 weeks
245.01674 .02288 (245*2π)/3852 weeks
246-.005 -.0061 (246*2π)/3852 weeks
247.01457 .00562 (247*2π)/3852 weeks
248.00468 -.02402 (248*2π)/3852 weeks
249-.00492 .02397 (249*2π)/3852 weeks
250.00911 .01858 (250*2π)/3852 weeks
251-.0132 -.00248 (251*2π)/3852 weeks
252.01552 .02453 (252*2π)/3852 weeks
253.01458 -.00256 (253*2π)/3852 weeks
254.02687 .0022 (254*2π)/3852 weeks
255.03891 -.01046 (255*2π)/3852 weeks
256.01678 -.01334 (256*2π)/3852 weeks
257-.01385 -.0053 (257*2π)/3851 weeks
258.01867 .00284 (258*2π)/3851 weeks
259-.04365 .00192 (259*2π)/3851 weeks
260.00954 -.00934 (260*2π)/3851 weeks
261-.00003 .02435 (261*2π)/3851 weeks
262-.03165 -.00214 (262*2π)/3851 weeks
263-.00043 .02124 (263*2π)/3851 weeks
264-.06004 .00179 (264*2π)/3851 weeks
265-.01124 -.00361 (265*2π)/3851 weeks
266-.00808 .0347 (266*2π)/3851 weeks
267-.01036 .00672 (267*2π)/3851 weeks
268-.00402 .0182 (268*2π)/3851 weeks
269.01177 .03147 (269*2π)/3851 weeks
270-.04244 -.01835 (270*2π)/3851 weeks
271.03762 .00118 (271*2π)/3851 weeks
272-.01343 .02834 (272*2π)/3851 weeks
273-.00992 -.01863 (273*2π)/3851 weeks
274.0163 .04027 (274*2π)/3851 weeks
275-.00202 -.00062 (275*2π)/3851 weeks
276.02463 -.03252 (276*2π)/3851 weeks
277.01933 .02001 (277*2π)/3851 weeks
278.00916 -.01917 (278*2π)/3851 weeks
279.00845 -.0015 (279*2π)/3851 weeks
280-.01432 .00559 (280*2π)/3851 weeks
281.00081 -.01436 (281*2π)/3851 weeks
282.01251 -.00605 (282*2π)/3851 weeks
283-.02993 -.02 (283*2π)/3851 weeks
284.03527 -.01779 (284*2π)/3851 weeks
285-.00597 -.02743 (285*2π)/3851 weeks
286-.01934 -.01951 (286*2π)/3851 weeks
287-.01399 .02178 (287*2π)/3851 weeks
288-.0119 -.0205 (288*2π)/3851 weeks
289-.0587 .0305 (289*2π)/3851 weeks
290-.02279 -.02207 (290*2π)/3851 weeks
291.00404 .02878 (291*2π)/3851 weeks
292-.0509 .01277 (292*2π)/3851 weeks
293.00507 .05224 (293*2π)/3851 weeks
294.00267 .02263 (294*2π)/3851 weeks
295-.03322 .01145 (295*2π)/3851 weeks
296.02649 .02576 (296*2π)/3851 weeks
297.0226 .01576 (297*2π)/3851 weeks
298.01094 .01519 (298*2π)/3851 weeks
299.04849 -.00266 (299*2π)/3851 weeks
300-.00759 -.00337 (300*2π)/3851 weeks
301-.0096 -.03995 (301*2π)/3851 weeks
302-.02276 -.00181 (302*2π)/3851 weeks
303.03054 .00022 (303*2π)/3851 weeks
304-.01551 .02069 (304*2π)/3851 weeks
305-.02844 -.0214 (305*2π)/3851 weeks
306-.01042 .01531 (306*2π)/3851 weeks
307-.0721 -.03228 (307*2π)/3851 weeks
308-.02195 -.00616 (308*2π)/3851 weeks
309-.04679 .02335 (309*2π)/3851 weeks
310.03819 -.02192 (310*2π)/3851 weeks
311-.0557 .05879 (311*2π)/3851 weeks
312-.01187 .01128 (312*2π)/3851 weeks
313.03298 .04554 (313*2π)/3851 weeks
314-.04295 .03417 (314*2π)/3851 weeks
315.02839 .01857 (315*2π)/3851 weeks
316-.02181 .03053 (316*2π)/3851 weeks
317-.03237 -.02264 (317*2π)/3851 weeks
318.01293 .01664 (318*2π)/3851 weeks
319-.00666 .00434 (319*2π)/3851 weeks
320-.00214 -.01429 (320*2π)/3851 weeks
321-.01258 -.04104 (321*2π)/3851 weeks
322-.0345 .03314 (322*2π)/3851 weeks
323-.03145 .00474 (323*2π)/3851 weeks
324-.00535 -.01717 (324*2π)/3851 weeks
325-.04293 .01233 (325*2π)/3851 weeks
326.00104 -.03395 (326*2π)/3851 weeks
327-.04564 .03618 (327*2π)/3851 weeks
328.02112 .03417 (328*2π)/3851 weeks
329-.05782 .01114 (329*2π)/3851 weeks
330.00042 .04856 (330*2π)/3851 weeks
331-.02923 .03114 (331*2π)/3851 weeks
332.0008 -.01032 (332*2π)/3851 weeks
333-.03379 .12278 (333*2π)/3851 weeks
334.04443 -.00604 (334*2π)/3851 weeks
335.00522 .1094 (335*2π)/3851 weeks
336.03258 .07301 (336*2π)/3851 weeks
337.01838 .02385 (337*2π)/3851 weeks
338.0173 .08546 (338*2π)/3851 weeks
339-.00872 -.11503 (339*2π)/3851 weeks
340.00348 .02069 (340*2π)/3851 weeks
341.05267 -.03777 (341*2π)/3851 weeks
342-.05435 .03839 (342*2π)/3851 weeks
343.02109 .04087 (343*2π)/3851 weeks
344.03799 -.03288 (344*2π)/3851 weeks
345-.00408 -.07114 (345*2π)/3851 weeks
346-.09125 .00544 (346*2π)/3851 weeks
347.02984 -.03075 (347*2π)/3851 weeks
348-.03866 .04276 (348*2π)/3851 weeks
349.01519 -.02777 (349*2π)/3851 weeks
350-.08254 -.0164 (350*2π)/3851 weeks
351-.00003 .04029 (351*2π)/3851 weeks
352-.04846 .02408 (352*2π)/3851 weeks
353-.063 -.02835 (353*2π)/3851 weeks
354-.01643 .11352 (354*2π)/3851 weeks
355-.0652 -.10352 (355*2π)/3851 weeks
356.00547 .03 (356*2π)/3851 weeks
357.02626 .05572 (357*2π)/3851 weeks
358.05316 -.0527 (358*2π)/3851 weeks
359.10264 .04891 (359*2π)/3851 weeks
360-.00438 -.01965 (360*2π)/3851 weeks
361.00059 .0482 (361*2π)/3851 weeks
362.00195 .11998 (362*2π)/3851 weeks
363-.10852 .05539 (363*2π)/3851 weeks
364.16178 -.05804 (364*2π)/3851 weeks
365-.00071 .08895 (365*2π)/3851 weeks
366.0482 -.22576 (366*2π)/3851 weeks
367.17603 .01548 (367*2π)/3851 weeks
368-.10633 -.22343 (368*2π)/3851 weeks
369.06002 -.21772 (369*2π)/3851 weeks
370-.00012 .13767 (370*2π)/3851 weeks
371-.12617 -.23709 (371*2π)/3851 weeks
372.27313 .21816 (372*2π)/3851 weeks
373-.10815 -.14336 (373*2π)/3851 weeks
374.05118 -.23664 (374*2π)/3851 weeks
375-.21347 .01246 (375*2π)/3851 weeks
376-.06479 -.14367 (376*2π)/3851 weeks
377.03381 .14803 (377*2π)/3851 weeks
378.39277 .24345 (378*2π)/3851 weeks
379-.1532 -.05912 (379*2π)/3851 weeks
380.73872 .13053 (380*2π)/3851 weeks
381-.49888 .30485 (381*2π)/3851 weeks
382.26466 -.18939 (382*2π)/3851 weeks
3831.17305 .30557 (383*2π)/3851 weeks