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Fourier Analysis of CBOE (CBOE Holdings Inc)


CBOE (CBOE Holdings Inc) appears to have interesting cyclic behaviour every 34 weeks (2.2553*sine), 29 weeks (2.0909*sine), and 32 weeks (1.7999*sine).

CBOE (CBOE Holdings Inc) has an average price of 46.46 (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 6/15/2010 to 9/5/2017 for CBOE (CBOE Holdings Inc), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
046.46251   0 
12.05403 -23.26528 (1*2π)/378378 weeks
24.64295 -8.73739 (2*2π)/378189 weeks
31.26593 -6.26579 (3*2π)/378126 weeks
41.7526 -7.20288 (4*2π)/37895 weeks
5.73594 -4.51857 (5*2π)/37876 weeks
6-.0193 -5.16251 (6*2π)/37863 weeks
7-.18216 -3.00745 (7*2π)/37854 weeks
81.45939 -3.46618 (8*2π)/37847 weeks
9-.4525 -3.70051 (9*2π)/37842 weeks
10.46885 -1.25499 (10*2π)/37838 weeks
11.58606 -2.25527 (11*2π)/37834 weeks
12.3043 -1.7999 (12*2π)/37832 weeks
13.15006 -2.09086 (13*2π)/37829 weeks
14.1689 -1.93713 (14*2π)/37827 weeks
15-.39821 -2.00511 (15*2π)/37825 weeks
16.13242 -1.92621 (16*2π)/37824 weeks
17.03567 -1.43284 (17*2π)/37822 weeks
18-.55185 -.94212 (18*2π)/37821 weeks
19.56713 -.84958 (19*2π)/37820 weeks
20.04476 -1.15075 (20*2π)/37819 weeks
21.44389 -1.34462 (21*2π)/37818 weeks
22-.2706 -.82807 (22*2π)/37817 weeks
23-.18949 -1.06655 (23*2π)/37816 weeks
24-.10699 -.62351 (24*2π)/37816 weeks
25-.03143 -1.11391 (25*2π)/37815 weeks
26-.40161 -.53065 (26*2π)/37815 weeks
27-.2032 -.89325 (27*2π)/37814 weeks
28.05229 -.74115 (28*2π)/37814 weeks
29-.00226 -1.00569 (29*2π)/37813 weeks
30-.00111 -.78708 (30*2π)/37813 weeks
31-.01887 -.89502 (31*2π)/37812 weeks
32-.25201 -.87623 (32*2π)/37812 weeks
33-.14567 -.69711 (33*2π)/37811 weeks
34-.3936 -.64585 (34*2π)/37811 weeks
35.00318 -.46735 (35*2π)/37811 weeks
36-.02598 -.57782 (36*2π)/37811 weeks
37-.02421 -.6399 (37*2π)/37810 weeks
38-.11466 -.69756 (38*2π)/37810 weeks
39-.09205 -.75022 (39*2π)/37810 weeks
40-.00269 -.6174 (40*2π)/3789 weeks
41-.14807 -.81363 (41*2π)/3789 weeks
42-.43736 -.42531 (42*2π)/3789 weeks
43-.13283 -.20283 (43*2π)/3789 weeks
44-.08991 -.55031 (44*2π)/3789 weeks
45-.18886 -.56359 (45*2π)/3788 weeks
46-.30303 -.55038 (46*2π)/3788 weeks
47-.12824 -.47657 (47*2π)/3788 weeks
48-.03182 -.47133 (48*2π)/3788 weeks
49-.20568 -.59191 (49*2π)/3788 weeks
50-.2615 -.49019 (50*2π)/3788 weeks
51-.19296 -.5254 (51*2π)/3787 weeks
52-.17522 -.56769 (52*2π)/3787 weeks
53-.13532 -.44182 (53*2π)/3787 weeks
54-.18495 -.49063 (54*2π)/3787 weeks
55-.19749 -.27877 (55*2π)/3787 weeks
56-.1099 -.46625 (56*2π)/3787 weeks
57-.18311 -.52483 (57*2π)/3787 weeks
58-.11804 -.37179 (58*2π)/3787 weeks
59-.34803 -.43899 (59*2π)/3786 weeks
60-.14836 -.35027 (60*2π)/3786 weeks
61-.24272 -.56384 (61*2π)/3786 weeks
62-.13335 -.33494 (62*2π)/3786 weeks
63-.11705 -.41262 (63*2π)/3786 weeks
64-.1832 -.31889 (64*2π)/3786 weeks
65-.16814 -.2509 (65*2π)/3786 weeks
66-.13511 -.16545 (66*2π)/3786 weeks
67-.22466 -.39671 (67*2π)/3786 weeks
68-.1995 -.16316 (68*2π)/3786 weeks
69-.20059 -.48123 (69*2π)/3785 weeks
70-.19286 -.14266 (70*2π)/3785 weeks
71-.26072 -.27196 (71*2π)/3785 weeks
72-.25651 -.24588 (72*2π)/3785 weeks
73-.27338 -.38354 (73*2π)/3785 weeks
74-.20165 -.1948 (74*2π)/3785 weeks
75-.21514 -.23866 (75*2π)/3785 weeks
76-.03214 -.23767 (76*2π)/3785 weeks
77-.15668 -.36864 (77*2π)/3785 weeks
78-.20167 -.22945 (78*2π)/3785 weeks
79-.14466 -.26695 (79*2π)/3785 weeks
80-.2467 -.31746 (80*2π)/3785 weeks
81-.20644 -.3108 (81*2π)/3785 weeks
82-.29886 -.34901 (82*2π)/3785 weeks
83-.29992 -.1021 (83*2π)/3785 weeks
84-.08679 -.22967 (84*2π)/3785 weeks
85-.18796 -.27817 (85*2π)/3784 weeks
86-.19514 -.22931 (86*2π)/3784 weeks
87-.08799 -.20727 (87*2π)/3784 weeks
88-.18261 -.27495 (88*2π)/3784 weeks
89-.19926 -.22276 (89*2π)/3784 weeks
90-.26826 -.33725 (90*2π)/3784 weeks
91-.36685 -.22731 (91*2π)/3784 weeks
92-.27873 -.07284 (92*2π)/3784 weeks
93-.03311 -.21963 (93*2π)/3784 weeks
94-.25887 -.23635 (94*2π)/3784 weeks
95-.25607 -.15273 (95*2π)/3784 weeks
96-.17136 -.05847 (96*2π)/3784 weeks
97-.16064 -.38669 (97*2π)/3784 weeks
98-.30988 -.16362 (98*2π)/3784 weeks
99-.30756 -.2008 (99*2π)/3784 weeks
100-.31625 -.08521 (100*2π)/3784 weeks
101-.21923 -.1143 (101*2π)/3784 weeks
102-.23478 -.16499 (102*2π)/3784 weeks
103-.05491 -.14417 (103*2π)/3784 weeks
104-.12805 -.25414 (104*2π)/3784 weeks
105-.12551 -.22046 (105*2π)/3784 weeks
106-.27147 -.21745 (106*2π)/3784 weeks
107-.27192 -.18425 (107*2π)/3784 weeks
108-.37841 -.16234 (108*2π)/3784 weeks
109-.18222 -.15951 (109*2π)/3783 weeks
110-.15651 -.13297 (110*2π)/3783 weeks
111-.17126 -.166 (111*2π)/3783 weeks
112-.24379 -.19896 (112*2π)/3783 weeks
113-.22251 -.09854 (113*2π)/3783 weeks
114-.12325 -.19716 (114*2π)/3783 weeks
115-.17216 -.18431 (115*2π)/3783 weeks
116-.21787 -.25153 (116*2π)/3783 weeks
117-.26134 -.17151 (117*2π)/3783 weeks
118-.27322 -.23204 (118*2π)/3783 weeks
119-.1759 -.1864 (119*2π)/3783 weeks
120-.31281 -.24963 (120*2π)/3783 weeks
121-.28205 -.11288 (121*2π)/3783 weeks
122-.29 -.11734 (122*2π)/3783 weeks
123-.19305 -.07019 (123*2π)/3783 weeks
124-.13544 -.13475 (124*2π)/3783 weeks
125-.14601 -.12381 (125*2π)/3783 weeks
126-.22717 -.18837 (126*2π)/3783 weeks
127-.24669 -.11629 (127*2π)/3783 weeks
128-.18977 -.04329 (128*2π)/3783 weeks
129-.17772 -.03197 (129*2π)/3783 weeks
130-.22603 -.17544 (130*2π)/3783 weeks
131-.25804 -.11354 (131*2π)/3783 weeks
132-.18057 -.08897 (132*2π)/3783 weeks
133-.17003 -.07954 (133*2π)/3783 weeks
134-.18615 -.1348 (134*2π)/3783 weeks
135-.24016 -.06003 (135*2π)/3783 weeks
136-.21805 -.14746 (136*2π)/3783 weeks
137-.27195 .08273 (137*2π)/3783 weeks
138-.08795 -.09533 (138*2π)/3783 weeks
139-.17066 -.04709 (139*2π)/3783 weeks
140-.14792 -.05381 (140*2π)/3783 weeks
141-.12101 -.15564 (141*2π)/3783 weeks
142-.18932 -.04062 (142*2π)/3783 weeks
143-.17219 -.19102 (143*2π)/3783 weeks
144-.2002 -.00959 (144*2π)/3783 weeks
145-.16857 -.11699 (145*2π)/3783 weeks
146-.21954 -.05969 (146*2π)/3783 weeks
147-.22678 -.08238 (147*2π)/3783 weeks
148-.14014 -.05509 (148*2π)/3783 weeks
149-.19175 -.1507 (149*2π)/3783 weeks
150-.24696 -.12834 (150*2π)/3783 weeks
151-.22737 -.06899 (151*2π)/3783 weeks
152-.24702 -.0871 (152*2π)/3782 weeks
153-.26494 -.02047 (153*2π)/3782 weeks
154-.21247 .053 (154*2π)/3782 weeks
155-.1368 -.04104 (155*2π)/3782 weeks
156-.15662 -.18053 (156*2π)/3782 weeks
157-.25349 -.11816 (157*2π)/3782 weeks
158-.22685 -.06373 (158*2π)/3782 weeks
159-.24955 .03446 (159*2π)/3782 weeks
160-.13475 -.0187 (160*2π)/3782 weeks
161-.26991 -.06904 (161*2π)/3782 weeks
162-.22704 -.03736 (162*2π)/3782 weeks
163-.22923 -.08249 (163*2π)/3782 weeks
164-.19947 -.1382 (164*2π)/3782 weeks
165-.16475 -.07473 (165*2π)/3782 weeks
166-.24303 -.16809 (166*2π)/3782 weeks
167-.24914 -.08796 (167*2π)/3782 weeks
168-.25961 -.05566 (168*2π)/3782 weeks
169-.1681 -.00378 (169*2π)/3782 weeks
170-.17888 -.10257 (170*2π)/3782 weeks
171-.22981 -.07606 (171*2π)/3782 weeks
172-.22698 -.01057 (172*2π)/3782 weeks
173-.21518 -.01263 (173*2π)/3782 weeks
174-.24952 -.04463 (174*2π)/3782 weeks
175-.28719 .00927 (175*2π)/3782 weeks
176-.18897 .01176 (176*2π)/3782 weeks
177-.21125 .04443 (177*2π)/3782 weeks
178-.18299 -.00937 (178*2π)/3782 weeks
179-.21543 -.0869 (179*2π)/3782 weeks
180-.21743 .03986 (180*2π)/3782 weeks
181-.30609 -.07813 (181*2π)/3782 weeks
182-.24481 .07346 (182*2π)/3782 weeks
183-.24093 .01299 (183*2π)/3782 weeks
184-.24543 -.02634 (184*2π)/3782 weeks
185-.29402 .00132 (185*2π)/3782 weeks
186-.21795 .04494 (186*2π)/3782 weeks
187-.19807 -.01984 (187*2π)/3782 weeks
188-.15314 -.08538 (188*2π)/3782 weeks
189-.26925   (189*2π)/3782 weeks
190-.15314 .08538 (190*2π)/3782 weeks
191-.19807 .01984 (191*2π)/3782 weeks
192-.21795 -.04494 (192*2π)/3782 weeks
193-.29402 -.00132 (193*2π)/3782 weeks
194-.24543 .02634 (194*2π)/3782 weeks
195-.24093 -.01299 (195*2π)/3782 weeks
196-.24481 -.07346 (196*2π)/3782 weeks
197-.30609 .07813 (197*2π)/3782 weeks
198-.21743 -.03986 (198*2π)/3782 weeks
199-.21543 .0869 (199*2π)/3782 weeks
200-.18299 .00937 (200*2π)/3782 weeks
201-.21125 -.04443 (201*2π)/3782 weeks
202-.18897 -.01176 (202*2π)/3782 weeks
203-.28719 -.00927 (203*2π)/3782 weeks
204-.24952 .04463 (204*2π)/3782 weeks
205-.21518 .01263 (205*2π)/3782 weeks
206-.22698 .01057 (206*2π)/3782 weeks
207-.22981 .07606 (207*2π)/3782 weeks
208-.17888 .10257 (208*2π)/3782 weeks
209-.1681 .00378 (209*2π)/3782 weeks
210-.25961 .05566 (210*2π)/3782 weeks
211-.24914 .08796 (211*2π)/3782 weeks
212-.24303 .16809 (212*2π)/3782 weeks
213-.16475 .07473 (213*2π)/3782 weeks
214-.19947 .1382 (214*2π)/3782 weeks
215-.22923 .08249 (215*2π)/3782 weeks
216-.22704 .03736 (216*2π)/3782 weeks
217-.26991 .06904 (217*2π)/3782 weeks
218-.13475 .0187 (218*2π)/3782 weeks
219-.24955 -.03446 (219*2π)/3782 weeks
220-.22685 .06373 (220*2π)/3782 weeks
221-.25349 .11816 (221*2π)/3782 weeks
222-.15662 .18053 (222*2π)/3782 weeks
223-.1368 .04104 (223*2π)/3782 weeks
224-.21247 -.053 (224*2π)/3782 weeks
225-.26494 .02047 (225*2π)/3782 weeks
226-.24702 .0871 (226*2π)/3782 weeks
227-.22737 .06899 (227*2π)/3782 weeks
228-.24696 .12834 (228*2π)/3782 weeks
229-.19175 .1507 (229*2π)/3782 weeks
230-.14014 .05509 (230*2π)/3782 weeks
231-.22678 .08238 (231*2π)/3782 weeks
232-.21954 .05969 (232*2π)/3782 weeks
233-.16857 .11699 (233*2π)/3782 weeks
234-.2002 .00959 (234*2π)/3782 weeks
235-.17219 .19102 (235*2π)/3782 weeks
236-.18932 .04062 (236*2π)/3782 weeks
237-.12101 .15564 (237*2π)/3782 weeks
238-.14792 .05381 (238*2π)/3782 weeks
239-.17066 .04709 (239*2π)/3782 weeks
240-.08795 .09533 (240*2π)/3782 weeks
241-.27195 -.08273 (241*2π)/3782 weeks
242-.21805 .14746 (242*2π)/3782 weeks
243-.24016 .06003 (243*2π)/3782 weeks
244-.18615 .1348 (244*2π)/3782 weeks
245-.17003 .07954 (245*2π)/3782 weeks
246-.18057 .08897 (246*2π)/3782 weeks
247-.25804 .11354 (247*2π)/3782 weeks
248-.22603 .17544 (248*2π)/3782 weeks
249-.17772 .03197 (249*2π)/3782 weeks
250-.18977 .04329 (250*2π)/3782 weeks
251-.24669 .11629 (251*2π)/3782 weeks
252-.22717 .18837 (252*2π)/3782 weeks
253-.14601 .12381 (253*2π)/3781 weeks
254-.13544 .13475 (254*2π)/3781 weeks
255-.19305 .07019 (255*2π)/3781 weeks
256-.29 .11734 (256*2π)/3781 weeks
257-.28205 .11288 (257*2π)/3781 weeks
258-.31281 .24963 (258*2π)/3781 weeks
259-.1759 .1864 (259*2π)/3781 weeks
260-.27322 .23204 (260*2π)/3781 weeks
261-.26134 .17151 (261*2π)/3781 weeks
262-.21787 .25153 (262*2π)/3781 weeks
263-.17216 .18431 (263*2π)/3781 weeks
264-.12325 .19716 (264*2π)/3781 weeks
265-.22251 .09854 (265*2π)/3781 weeks
266-.24379 .19896 (266*2π)/3781 weeks
267-.17126 .166 (267*2π)/3781 weeks
268-.15651 .13297 (268*2π)/3781 weeks
269-.18222 .15951 (269*2π)/3781 weeks
270-.37841 .16234 (270*2π)/3781 weeks
271-.27192 .18425 (271*2π)/3781 weeks
272-.27147 .21745 (272*2π)/3781 weeks
273-.12551 .22046 (273*2π)/3781 weeks
274-.12805 .25414 (274*2π)/3781 weeks
275-.05491 .14417 (275*2π)/3781 weeks
276-.23478 .16499 (276*2π)/3781 weeks
277-.21923 .1143 (277*2π)/3781 weeks
278-.31625 .08521 (278*2π)/3781 weeks
279-.30756 .2008 (279*2π)/3781 weeks
280-.30988 .16362 (280*2π)/3781 weeks
281-.16064 .38669 (281*2π)/3781 weeks
282-.17136 .05847 (282*2π)/3781 weeks
283-.25607 .15273 (283*2π)/3781 weeks
284-.25887 .23635 (284*2π)/3781 weeks
285-.03311 .21963 (285*2π)/3781 weeks
286-.27873 .07284 (286*2π)/3781 weeks
287-.36685 .22731 (287*2π)/3781 weeks
288-.26826 .33725 (288*2π)/3781 weeks
289-.19926 .22276 (289*2π)/3781 weeks
290-.18261 .27495 (290*2π)/3781 weeks
291-.08799 .20727 (291*2π)/3781 weeks
292-.19514 .22931 (292*2π)/3781 weeks
293-.18796 .27817 (293*2π)/3781 weeks
294-.08679 .22967 (294*2π)/3781 weeks
295-.29992 .1021 (295*2π)/3781 weeks
296-.29886 .34901 (296*2π)/3781 weeks
297-.20644 .3108 (297*2π)/3781 weeks
298-.2467 .31746 (298*2π)/3781 weeks
299-.14466 .26695 (299*2π)/3781 weeks
300-.20167 .22945 (300*2π)/3781 weeks
301-.15668 .36864 (301*2π)/3781 weeks
302-.03214 .23767 (302*2π)/3781 weeks
303-.21514 .23866 (303*2π)/3781 weeks
304-.20165 .1948 (304*2π)/3781 weeks
305-.27338 .38354 (305*2π)/3781 weeks
306-.25651 .24588 (306*2π)/3781 weeks
307-.26072 .27196 (307*2π)/3781 weeks
308-.19286 .14266 (308*2π)/3781 weeks
309-.20059 .48123 (309*2π)/3781 weeks
310-.1995 .16316 (310*2π)/3781 weeks
311-.22466 .39671 (311*2π)/3781 weeks
312-.13511 .16545 (312*2π)/3781 weeks
313-.16814 .2509 (313*2π)/3781 weeks
314-.1832 .31889 (314*2π)/3781 weeks
315-.11705 .41262 (315*2π)/3781 weeks
316-.13335 .33494 (316*2π)/3781 weeks
317-.24272 .56384 (317*2π)/3781 weeks
318-.14836 .35027 (318*2π)/3781 weeks
319-.34803 .43899 (319*2π)/3781 weeks
320-.11804 .37179 (320*2π)/3781 weeks
321-.18311 .52483 (321*2π)/3781 weeks
322-.1099 .46625 (322*2π)/3781 weeks
323-.19749 .27877 (323*2π)/3781 weeks
324-.18495 .49063 (324*2π)/3781 weeks
325-.13532 .44182 (325*2π)/3781 weeks
326-.17522 .56769 (326*2π)/3781 weeks
327-.19296 .5254 (327*2π)/3781 weeks
328-.2615 .49019 (328*2π)/3781 weeks
329-.20568 .59191 (329*2π)/3781 weeks
330-.03182 .47133 (330*2π)/3781 weeks
331-.12824 .47657 (331*2π)/3781 weeks
332-.30303 .55038 (332*2π)/3781 weeks
333-.18886 .56359 (333*2π)/3781 weeks
334-.08991 .55031 (334*2π)/3781 weeks
335-.13283 .20283 (335*2π)/3781 weeks
336-.43736 .42531 (336*2π)/3781 weeks
337-.14807 .81363 (337*2π)/3781 weeks
338-.00269 .6174 (338*2π)/3781 weeks
339-.09205 .75022 (339*2π)/3781 weeks
340-.11466 .69756 (340*2π)/3781 weeks
341-.02421 .6399 (341*2π)/3781 weeks
342-.02598 .57782 (342*2π)/3781 weeks
343.00318 .46735 (343*2π)/3781 weeks
344-.3936 .64585 (344*2π)/3781 weeks
345-.14567 .69711 (345*2π)/3781 weeks
346-.25201 .87623 (346*2π)/3781 weeks
347-.01887 .89502 (347*2π)/3781 weeks
348-.00111 .78708 (348*2π)/3781 weeks
349-.00226 1.00569 (349*2π)/3781 weeks
350.05229 .74115 (350*2π)/3781 weeks
351-.2032 .89325 (351*2π)/3781 weeks
352-.40161 .53065 (352*2π)/3781 weeks
353-.03143 1.11391 (353*2π)/3781 weeks
354-.10699 .62351 (354*2π)/3781 weeks
355-.18949 1.06655 (355*2π)/3781 weeks
356-.2706 .82807 (356*2π)/3781 weeks
357.44389 1.34462 (357*2π)/3781 weeks
358.04476 1.15075 (358*2π)/3781 weeks
359.56713 .84958 (359*2π)/3781 weeks
360-.55185 .94212 (360*2π)/3781 weeks
361.03567 1.43284 (361*2π)/3781 weeks
362.13242 1.92621 (362*2π)/3781 weeks
363-.39821 2.00511 (363*2π)/3781 weeks
364.1689 1.93713 (364*2π)/3781 weeks
365.15006 2.09086 (365*2π)/3781 weeks
366.3043 1.7999 (366*2π)/3781 weeks
367.58606 2.25527 (367*2π)/3781 weeks
368.46885 1.25499 (368*2π)/3781 weeks
369-.4525 3.70051 (369*2π)/3781 weeks
3701.45939 3.46618 (370*2π)/3781 weeks
371-.18216 3.00745 (371*2π)/3781 weeks
372-.0193 5.16251 (372*2π)/3781 weeks
373.73594 4.51857 (373*2π)/3781 weeks
3741.7526 7.20288 (374*2π)/3781 weeks
3751.26593 6.26579 (375*2π)/3781 weeks
3764.64295 8.73739 (376*2π)/3781 weeks



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