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# Fourier Analysis of OKE (ONEOK, Inc. Common Stock)

OKE (ONEOK, Inc. Common Stock) appears to have interesting cyclic behaviour every 119 weeks (2.0567*sine), 112 weeks (1.9031*sine), and 159 weeks (1.6336*cosine).

OKE (ONEOK, Inc. Common Stock) has an average price of 9.69 (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 10/1/1980 to 3/20/2017 for OKE (ONEOK, Inc. Common Stock), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
09.69311   0
19.09464 -9.37561 (1*2π)/19031,903 weeks
23.59773 -8.07593 (2*2π)/1903952 weeks
3.92348 -6.22726 (3*2π)/1903634 weeks
4-.49746 -4.99298 (4*2π)/1903476 weeks
5-1.61208 -2.9711 (5*2π)/1903381 weeks
6-.91184 -1.20966 (6*2π)/1903317 weeks
7.17179 -.73992 (7*2π)/1903272 weeks
8.21356 -1.18454 (8*2π)/1903238 weeks
9.04996 -.64977 (9*2π)/1903211 weeks
10.32748 -.2488 (10*2π)/1903190 weeks
111.25752 -.09667 (11*2π)/1903173 weeks
121.63363 -.85746 (12*2π)/1903159 weeks
131.25951 -1.13044 (13*2π)/1903146 weeks
141.2249 -1.32873 (14*2π)/1903136 weeks
151.23365 -1.53147 (15*2π)/1903127 weeks
16.89028 -2.05666 (16*2π)/1903119 weeks
17.26268 -1.90314 (17*2π)/1903112 weeks
18.00346 -1.57881 (18*2π)/1903106 weeks
19-.1388 -1.37524 (19*2π)/1903100 weeks
20-.06108 -1.14815 (20*2π)/190395 weeks
21-.06397 -1.12665 (21*2π)/190391 weeks
22-.15301 -.99646 (22*2π)/190387 weeks
23-.1385 -.78277 (23*2π)/190383 weeks
24.09855 -.59593 (24*2π)/190379 weeks
25.32542 -.9715 (25*2π)/190376 weeks
26-.02547 -1.07583 (26*2π)/190373 weeks
27-.09326 -.97889 (27*2π)/190370 weeks
28-.25184 -.88289 (28*2π)/190368 weeks
29-.15064 -.74525 (29*2π)/190366 weeks
30-.24676 -.82731 (30*2π)/190363 weeks
31-.33384 -.72031 (31*2π)/190361 weeks
32-.37252 -.58787 (32*2π)/190359 weeks
33-.35037 -.38263 (33*2π)/190358 weeks
34-.2252 -.37876 (34*2π)/190356 weeks
35-.23872 -.31537 (35*2π)/190354 weeks
36-.15342 -.22882 (36*2π)/190353 weeks
37-.01828 -.2193 (37*2π)/190351 weeks
38-.02654 -.30424 (38*2π)/190350 weeks
39-.0709 -.24825 (39*2π)/190349 weeks
40.0315 -.11986 (40*2π)/190348 weeks
41.23831 -.16962 (41*2π)/190346 weeks
42.28598 -.36066 (42*2π)/190345 weeks
43.18295 -.4394 (43*2π)/190344 weeks
44.16597 -.46727 (44*2π)/190343 weeks
45.07792 -.501 (45*2π)/190342 weeks
46.05551 -.47009 (46*2π)/190341 weeks
47.0489 -.43934 (47*2π)/190340 weeks
48.02435 -.45632 (48*2π)/190340 weeks
49.00872 -.41426 (49*2π)/190339 weeks
50.01215 -.44858 (50*2π)/190338 weeks
51-.05979 -.42888 (51*2π)/190337 weeks
52-.05712 -.32454 (52*2π)/190337 weeks
53.02081 -.2697 (53*2π)/190336 weeks
54.08936 -.35144 (54*2π)/190335 weeks
55.09471 -.3532 (55*2π)/190335 weeks
56.16426 -.46351 (56*2π)/190334 weeks
57.03069 -.55872 (57*2π)/190333 weeks
58-.02377 -.55031 (58*2π)/190333 weeks
59-.13545 -.52876 (59*2π)/190332 weeks
60-.2044 -.48244 (60*2π)/190332 weeks
61-.22224 -.36355 (61*2π)/190331 weeks
62-.14473 -.32015 (62*2π)/190331 weeks
63-.11959 -.36207 (63*2π)/190330 weeks
64-.19703 -.40072 (64*2π)/190330 weeks
65-.28688 -.29398 (65*2π)/190329 weeks
66-.22017 -.19524 (66*2π)/190329 weeks
67-.20569 -.19656 (67*2π)/190328 weeks
68-.19302 -.13578 (68*2π)/190328 weeks
69-.11722 -.0616 (69*2π)/190328 weeks
70-.02078 -.08194 (70*2π)/190327 weeks
71.01473 -.13064 (71*2π)/190327 weeks
72.0095 -.2024 (72*2π)/190326 weeks
73-.00842 -.17121 (73*2π)/190326 weeks
74.04328 -.21283 (74*2π)/190326 weeks
75.03342 -.22612 (75*2π)/190325 weeks
76.01274 -.31212 (76*2π)/190325 weeks
77-.10148 -.28898 (77*2π)/190325 weeks
78-.07659 -.23327 (78*2π)/190324 weeks
79-.08241 -.21499 (79*2π)/190324 weeks
80-.07288 -.18312 (80*2π)/190324 weeks
81-.0284 -.18205 (81*2π)/190323 weeks
82-.0296 -.23506 (82*2π)/190323 weeks
83-.05418 -.24112 (83*2π)/190323 weeks
84-.07898 -.248 (84*2π)/190323 weeks
85-.09794 -.22584 (85*2π)/190322 weeks
86-.16782 -.20996 (86*2π)/190322 weeks
87-.16976 -.09638 (87*2π)/190322 weeks
88-.07626 -.03501 (88*2π)/190322 weeks
89.01687 -.10138 (89*2π)/190321 weeks
90.00617 -.13339 (90*2π)/190321 weeks
91-.01445 -.16429 (91*2π)/190321 weeks
92-.00843 -.13406 (92*2π)/190321 weeks
93-.00141 -.1766 (93*2π)/190320 weeks
94-.01985 -.17512 (94*2π)/190320 weeks
95-.03615 -.17898 (95*2π)/190320 weeks
96-.03546 -.1516 (96*2π)/190320 weeks
97-.01738 -.17446 (97*2π)/190320 weeks
98-.05695 -.19992 (98*2π)/190319 weeks
99-.07844 -.12854 (99*2π)/190319 weeks
100-.03627 -.1265 (100*2π)/190319 weeks
101-.02382 -.10941 (101*2π)/190319 weeks
102.01715 -.13853 (102*2π)/190319 weeks
103.00797 -.18454 (103*2π)/190318 weeks
104-.02047 -.19082 (104*2π)/190318 weeks
105-.05212 -.19255 (105*2π)/190318 weeks
106-.04513 -.18564 (106*2π)/190318 weeks
107-.08791 -.18151 (107*2π)/190318 weeks
108-.08661 -.14924 (108*2π)/190318 weeks
109-.089 -.11868 (109*2π)/190317 weeks
110-.05486 -.10166 (110*2π)/190317 weeks
111-.04773 -.11615 (111*2π)/190317 weeks
112-.04831 -.11832 (112*2π)/190317 weeks
113-.04661 -.11266 (113*2π)/190317 weeks
114-.05143 -.0966 (114*2π)/190317 weeks
115-.0024 -.10276 (115*2π)/190317 weeks
116-.03622 -.16249 (116*2π)/190316 weeks
117-.08759 -.13828 (117*2π)/190316 weeks
118-.11008 -.07413 (118*2π)/190316 weeks
119-.02971 -.01554 (119*2π)/190316 weeks
120.02453 -.06342 (120*2π)/190316 weeks
121.00358 -.10717 (121*2π)/190316 weeks
122-.03973 -.09104 (122*2π)/190316 weeks
123.00207 -.06852 (123*2π)/190315 weeks
124.017 -.08157 (124*2π)/190315 weeks
125-.00175 -.09579 (125*2π)/190315 weeks
126.00798 -.06469 (126*2π)/190315 weeks
127.0362 -.07313 (127*2π)/190315 weeks
128.05266 -.08778 (128*2π)/190315 weeks
129.05683 -.10483 (129*2π)/190315 weeks
130.08719 -.11983 (130*2π)/190315 weeks
131.08055 -.18767 (131*2π)/190315 weeks
132.04359 -.20268 (132*2π)/190314 weeks
133-.01127 -.2336 (133*2π)/190314 weeks
134-.07052 -.19748 (134*2π)/190314 weeks
135-.07858 -.14859 (135*2π)/190314 weeks
136-.07377 -.11346 (136*2π)/190314 weeks
137-.06792 -.08727 (137*2π)/190314 weeks
138-.03397 -.06166 (138*2π)/190314 weeks
139.01056 -.05381 (139*2π)/190314 weeks
140.06673 -.10374 (140*2π)/190314 weeks
141.025 -.15931 (141*2π)/190313 weeks
142-.00092 -.16088 (142*2π)/190313 weeks
143-.02166 -.17306 (143*2π)/190313 weeks
144-.06701 -.14985 (144*2π)/190313 weeks
145-.0833 -.10379 (145*2π)/190313 weeks
146-.05552 -.05729 (146*2π)/190313 weeks
147-.01219 -.04727 (147*2π)/190313 weeks
148.04435 -.0731 (148*2π)/190313 weeks
149.02149 -.11686 (149*2π)/190313 weeks
150.01687 -.10862 (150*2π)/190313 weeks
151.02762 -.11554 (151*2π)/190313 weeks
152.03097 -.14662 (152*2π)/190313 weeks
153-.00015 -.15491 (153*2π)/190312 weeks
154-.00564 -.14759 (154*2π)/190312 weeks
155-.0089 -.13546 (155*2π)/190312 weeks
156-.01143 -.14105 (156*2π)/190312 weeks
157-.00496 -.14174 (157*2π)/190312 weeks
158.0009 -.16251 (158*2π)/190312 weeks
159-.02634 -.16458 (159*2π)/190312 weeks
160-.03459 -.16239 (160*2π)/190312 weeks
161-.04158 -.16792 (161*2π)/190312 weeks
162-.07387 -.17476 (162*2π)/190312 weeks
163-.10015 -.15598 (163*2π)/190312 weeks
164-.11924 -.10274 (164*2π)/190312 weeks
165-.09137 -.06689 (165*2π)/190312 weeks
166-.0661 -.07124 (166*2π)/190311 weeks
167-.06282 -.05575 (167*2π)/190311 weeks
168-.03193 -.0484 (168*2π)/190311 weeks
169-.01038 -.04894 (169*2π)/190311 weeks
170.01936 -.06706 (170*2π)/190311 weeks
171.01595 -.10313 (171*2π)/190311 weeks
172.00753 -.12169 (172*2π)/190311 weeks
173-.00929 -.12687 (173*2π)/190311 weeks
174-.00495 -.13045 (174*2π)/190311 weeks
175-.02903 -.14608 (175*2π)/190311 weeks
176-.05862 -.1362 (176*2π)/190311 weeks
177-.06094 -.11856 (177*2π)/190311 weeks
178-.05792 -.11082 (178*2π)/190311 weeks
179-.05666 -.09984 (179*2π)/190311 weeks
180-.05798 -.09756 (180*2π)/190311 weeks
181-.06587 -.08262 (181*2π)/190311 weeks
182-.04993 -.07934 (182*2π)/190310 weeks
183-.04051 -.07154 (183*2π)/190310 weeks
184-.02883 -.07168 (184*2π)/190310 weeks
185-.02079 -.08124 (185*2π)/190310 weeks
186-.01375 -.08533 (186*2π)/190310 weeks
187-.00046 -.10827 (187*2π)/190310 weeks
188-.03155 -.1364 (188*2π)/190310 weeks
189-.05626 -.12804 (189*2π)/190310 weeks
190-.07188 -.09989 (190*2π)/190310 weeks
191-.0499 -.09514 (191*2π)/190310 weeks
192-.05124 -.10711 (192*2π)/190310 weeks
193-.07569 -.11432 (193*2π)/190310 weeks
194-.10177 -.07834 (194*2π)/190310 weeks
195-.07038 -.0437 (195*2π)/190310 weeks
196-.05114 -.05912 (196*2π)/190310 weeks
197-.0528 -.06817 (197*2π)/190310 weeks
198-.06837 -.05451 (198*2π)/190310 weeks
199-.05007 -.02623 (199*2π)/190310 weeks
200-.01074 -.04805 (200*2π)/190310 weeks
201-.02548 -.0618 (201*2π)/19039 weeks
202-.01344 -.07085 (202*2π)/19039 weeks
203-.02692 -.09222 (203*2π)/19039 weeks
204-.04803 -.08752 (204*2π)/19039 weeks
205-.06265 -.07543 (205*2π)/19039 weeks
206-.06629 -.05915 (206*2π)/19039 weeks
207-.06931 -.03088 (207*2π)/19039 weeks
208-.03322 .00899 (208*2π)/19039 weeks
209.02062 -.00595 (209*2π)/19039 weeks
210.04717 -.05462 (210*2π)/19039 weeks
211.01931 -.10709 (211*2π)/19039 weeks
212-.01634 -.09083 (212*2π)/19039 weeks
213-.02222 -.10014 (213*2π)/19039 weeks
214-.03683 -.07242 (214*2π)/19039 weeks
215-.01648 -.0743 (215*2π)/19039 weeks
216-.02262 -.07725 (216*2π)/19039 weeks
217-.01522 -.08496 (217*2π)/19039 weeks
218-.02781 -.10439 (218*2π)/19039 weeks
219-.05112 -.09736 (219*2π)/19039 weeks
220-.05685 -.07518 (220*2π)/19039 weeks
221-.0507 -.05948 (221*2π)/19039 weeks
222-.03535 -.06465 (222*2π)/19039 weeks
223-.05446 -.08219 (223*2π)/19039 weeks
224-.06598 -.04417 (224*2π)/19038 weeks
225-.04715 -.03754 (225*2π)/19038 weeks
226-.03494 -.03168 (226*2π)/19038 weeks
227-.02631 -.02999 (227*2π)/19038 weeks
228-.00571 -.02295 (228*2π)/19038 weeks
229.02099 -.05212 (229*2π)/19038 weeks
230.01579 -.09087 (230*2π)/19038 weeks
231-.03348 -.1068 (231*2π)/19038 weeks
232-.05661 -.07884 (232*2π)/19038 weeks
233-.06431 -.06034 (233*2π)/19038 weeks
234-.05998 -.04526 (234*2π)/19038 weeks
235-.06085 -.02127 (235*2π)/19038 weeks
236-.02412 .01175 (236*2π)/19038 weeks
237.01126 -.01644 (237*2π)/19038 weeks
238.01092 -.04529 (238*2π)/19038 weeks
239-.00887 -.04022 (239*2π)/19038 weeks
240.01224 -.02919 (240*2π)/19038 weeks
241.01743 -.05057 (241*2π)/19038 weeks
242.02639 -.04745 (242*2π)/19038 weeks
243.03206 -.07167 (243*2π)/19038 weeks
244.02279 -.08848 (244*2π)/19038 weeks
245-.00454 -.09645 (245*2π)/19038 weeks
246-.017 -.06907 (246*2π)/19038 weeks
247.01572 -.05811 (247*2π)/19038 weeks
248.02359 -.09855 (248*2π)/19038 weeks
249-.00799 -.10456 (249*2π)/19038 weeks
250-.01751 -.09402 (250*2π)/19038 weeks
251-.01822 -.08399 (251*2π)/19038 weeks
252.00081 -.09342 (252*2π)/19038 weeks
253-.02777 -.11444 (253*2π)/19038 weeks
254-.04212 -.08999 (254*2π)/19037 weeks
255-.03688 -.0741 (255*2π)/19037 weeks
256-.01968 -.07305 (256*2π)/19037 weeks
257-.02142 -.08738 (257*2π)/19037 weeks
258-.02922 -.08412 (258*2π)/19037 weeks
259-.01157 -.08426 (259*2π)/19037 weeks
260-.01691 -.11421 (260*2π)/19037 weeks
261-.04303 -.11333 (261*2π)/19037 weeks
262-.06557 -.10992 (262*2π)/19037 weeks
263-.0739 -.10496 (263*2π)/19037 weeks
264-.09668 -.08478 (264*2π)/19037 weeks
265-.09747 -.05139 (265*2π)/19037 weeks
266-.07556 -.02604 (266*2π)/19037 weeks
267-.05348 -.02665 (267*2π)/19037 weeks
268-.04207 -.03104 (268*2π)/19037 weeks
269-.02675 -.04197 (269*2π)/19037 weeks
270-.04295 -.06313 (270*2π)/19037 weeks
271-.06681 -.0382 (271*2π)/19037 weeks
272-.04316 -.00301 (272*2π)/19037 weeks
273-.0095 -.01484 (273*2π)/19037 weeks
274.00945 -.03989 (274*2π)/19037 weeks
275-.01128 -.06825 (275*2π)/19037 weeks
276-.01451 -.04744 (276*2π)/19037 weeks
277-.00628 -.06789 (277*2π)/19037 weeks
278-.0179 -.06689 (278*2π)/19037 weeks
279-.02534 -.07879 (279*2π)/19037 weeks
280-.03073 -.0759 (280*2π)/19037 weeks
281-.04094 -.07116 (281*2π)/19037 weeks
282-.03516 -.06783 (282*2π)/19037 weeks
283-.04757 -.07561 (283*2π)/19037 weeks
284-.06493 -.06318 (284*2π)/19037 weeks
285-.061 -.04472 (285*2π)/19037 weeks
286-.04455 -.03584 (286*2π)/19037 weeks
287-.04161 -.03927 (287*2π)/19037 weeks
288-.03742 -.03319 (288*2π)/19037 weeks
289-.02847 -.03032 (289*2π)/19037 weeks
290-.01568 -.05047 (290*2π)/19037 weeks
291-.03764 -.05447 (291*2π)/19037 weeks
292-.0384 -.04064 (292*2π)/19037 weeks
293-.03595 -.02989 (293*2π)/19036 weeks
294-.01898 -.03149 (294*2π)/19036 weeks
295-.01994 -.04923 (295*2π)/19036 weeks
296-.01993 -.05167 (296*2π)/19036 weeks
297-.02416 -.05447 (297*2π)/19036 weeks
298-.03881 -.05285 (298*2π)/19036 weeks
299-.03033 -.03822 (299*2π)/19036 weeks
300-.02508 -.05164 (300*2π)/19036 weeks
301-.03001 -.05074 (301*2π)/19036 weeks
302-.04287 -.05592 (302*2π)/19036 weeks
303-.04438 -.02239 (303*2π)/19036 weeks
304-.01903 -.02764 (304*2π)/19036 weeks
305-.02066 -.03291 (305*2π)/19036 weeks
306-.01332 -.0357 (306*2π)/19036 weeks
307-.01286 -.04513 (307*2π)/19036 weeks
308-.01076 -.03722 (308*2π)/19036 weeks
309-.00076 -.05185 (309*2π)/19036 weeks
310-.01525 -.06916 (310*2π)/19036 weeks
311-.02324 -.05872 (311*2π)/19036 weeks
312-.01919 -.0596 (312*2π)/19036 weeks
313-.03302 -.06819 (313*2π)/19036 weeks
314-.04226 -.06149 (314*2π)/19036 weeks
315-.04206 -.04728 (315*2π)/19036 weeks
316-.03975 -.04139 (316*2π)/19036 weeks
317-.03698 -.03732 (317*2π)/19036 weeks
318-.02817 -.02619 (318*2π)/19036 weeks
319-.01376 -.03629 (319*2π)/19036 weeks
320-.01527 -.03888 (320*2π)/19036 weeks
321-.00336 -.04374 (321*2π)/19036 weeks
322-.00999 -.05708 (322*2π)/19036 weeks
323-.01137 -.05855 (323*2π)/19036 weeks
324-.022 -.07017 (324*2π)/19036 weeks
325-.02517 -.05823 (325*2π)/19036 weeks
326-.01658 -.06093 (326*2π)/19036 weeks
327-.01361 -.06817 (327*2π)/19036 weeks
328-.02183 -.08712 (328*2π)/19036 weeks
329-.04359 -.08794 (329*2π)/19036 weeks
330-.05337 -.08873 (330*2π)/19036 weeks
331-.07892 -.07818 (331*2π)/19036 weeks
332-.08157 -.0532 (332*2π)/19036 weeks
333-.07674 -.03119 (333*2π)/19036 weeks
334-.06035 -.02329 (334*2π)/19036 weeks
335-.05339 -.03053 (335*2π)/19036 weeks
336-.05823 -.02412 (336*2π)/19036 weeks
337-.04633 -.01092 (337*2π)/19036 weeks
338-.02795 -.0165 (338*2π)/19036 weeks
339-.03362 -.0356 (339*2π)/19036 weeks
340-.04993 -.02223 (340*2π)/19036 weeks
341-.02316 -.00894 (341*2π)/19036 weeks
342-.02236 -.03247 (342*2π)/19036 weeks
343-.03017 -.02948 (343*2π)/19036 weeks
344-.03259 -.02621 (344*2π)/19036 weeks
345-.0264 -.0136 (345*2π)/19036 weeks
346-.01261 -.0266 (346*2π)/19036 weeks
347-.02513 -.03622 (347*2π)/19035 weeks
348-.02247 -.01603 (348*2π)/19035 weeks
349-.00686 -.02211 (349*2π)/19035 weeks
350-.00241 -.02992 (350*2π)/19035 weeks
351-.00168 -.04517 (351*2π)/19035 weeks
352-.00993 -.05212 (352*2π)/19035 weeks
353-.01931 -.04962 (353*2π)/19035 weeks
354-.01456 -.04554 (354*2π)/19035 weeks
355-.01589 -.05052 (355*2π)/19035 weeks
356-.01603 -.05038 (356*2π)/19035 weeks
357-.01758 -.05477 (357*2π)/19035 weeks
358-.01707 -.05579 (358*2π)/19035 weeks
359-.01773 -.06666 (359*2π)/19035 weeks
360-.02389 -.07382 (360*2π)/19035 weeks
361-.04535 -.08406 (361*2π)/19035 weeks
362-.06973 -.06872 (362*2π)/19035 weeks
363-.06813 -.043 (363*2π)/19035 weeks
364-.04738 -.03593 (364*2π)/19035 weeks
365-.05694 -.04902 (365*2π)/19035 weeks
366-.06421 -.04177 (366*2π)/19035 weeks
367-.07529 -.02034 (367*2π)/19035 weeks
368-.05058 -.00885 (368*2π)/19035 weeks
369-.05677 -.01709 (369*2π)/19035 weeks
370-.04924 .00851 (370*2π)/19035 weeks
371-.02396 .00639 (371*2π)/19035 weeks
372-.01036 -.00747 (372*2π)/19035 weeks
373-.01724 -.01589 (373*2π)/19035 weeks
374-.01031 -.0174 (374*2π)/19035 weeks
375-.00803 -.01677 (375*2π)/19035 weeks
376.00166 -.02302 (376*2π)/19035 weeks
377.01145 -.03837 (377*2π)/19035 weeks
378.00476 -.06196 (378*2π)/19035 weeks
379-.02327 -.07027 (379*2π)/19035 weeks
380-.03206 -.05796 (380*2π)/19035 weeks
381-.03615 -.05554 (381*2π)/19035 weeks
382-.0432 -.05801