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Fourier Analysis of WMB (The Williams Companies)


WMB (The Williams Companies) appears to have interesting cyclic behaviour every 192 weeks (1.0759*cosine), 132 weeks (1.0031*sine), and 211 weeks (.9019*sine).

WMB (The Williams Companies) has an average price of 7.93 (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 3/17/1980 to 9/14/2020 for WMB (The Williams Companies), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
07.92626   0 
15.25895 -9.72599 (1*2π)/21142,114 weeks
2-.55524 -5.768 (2*2π)/21141,057 weeks
3-1.19914 -2.97711 (3*2π)/2114705 weeks
4-1.69218 -1.7467 (4*2π)/2114529 weeks
5-.34092 .7755 (5*2π)/2114423 weeks
61.69149 -1.10508 (6*2π)/2114352 weeks
7.04031 -1.87928 (7*2π)/2114302 weeks
8-.20545 -1.2817 (8*2π)/2114264 weeks
9-.44388 -1.14786 (9*2π)/2114235 weeks
10-.68626 -.90191 (10*2π)/2114211 weeks
11-1.07588 -.17323 (11*2π)/2114192 weeks
12-.08986 .66762 (12*2π)/2114176 weeks
13.68062 -.09556 (13*2π)/2114163 weeks
14.37495 -.51944 (14*2π)/2114151 weeks
15.35797 -.63203 (15*2π)/2114141 weeks
16.12991 -1.00314 (16*2π)/2114132 weeks
17-.6521 -1.00036 (17*2π)/2114124 weeks
18-.88595 .00111 (18*2π)/2114117 weeks
19-.13459 .26207 (19*2π)/2114111 weeks
20-.07611 -.00323 (20*2π)/2114106 weeks
21.12225 .15307 (21*2π)/2114101 weeks
22.33763 -.07965 (22*2π)/211496 weeks
23.30141 -.36237 (23*2π)/211492 weeks
24-.0199 -.44824 (24*2π)/211488 weeks
25-.07598 -.1953 (25*2π)/211485 weeks
26.09419 -.25147 (26*2π)/211481 weeks
27-.17978 -.44011 (27*2π)/211478 weeks
28-.35756 .00561 (28*2π)/211476 weeks
29-.01997 .22085 (29*2π)/211473 weeks
30.27443 .09401 (30*2π)/211470 weeks
31.23369 -.13325 (31*2π)/211468 weeks
32.3053 -.08799 (32*2π)/211466 weeks
33.37128 -.42493 (33*2π)/211464 weeks
34.06804 -.6127 (34*2π)/211462 weeks
35-.34354 -.44248 (35*2π)/211460 weeks
36-.33631 -.07689 (36*2π)/211459 weeks
37-.1985 .18711 (37*2π)/211457 weeks
38.19475 .20196 (38*2π)/211456 weeks
39.37503 -.00483 (39*2π)/211454 weeks
40.36889 -.36617 (40*2π)/211453 weeks
41.05931 -.40873 (41*2π)/211452 weeks
42-.02153 -.37679 (42*2π)/211450 weeks
43-.11397 -.28859 (43*2π)/211449 weeks
44-.23356 -.25522 (44*2π)/211448 weeks
45-.23858 .09882 (45*2π)/211447 weeks
46.15246 .12598 (46*2π)/211446 weeks
47.21029 -.17924 (47*2π)/211445 weeks
48.02577 -.25945 (48*2π)/211444 weeks
49-.03566 -.15962 (49*2π)/211443 weeks
50-.05456 -.1729 (50*2π)/211442 weeks
51-.09006 -.06073 (51*2π)/211441 weeks
52.0053 .01491 (52*2π)/211441 weeks
53.10033 -.05281 (53*2π)/211440 weeks
54.07993 -.10245 (54*2π)/211439 weeks
55.07095 -.11897 (55*2π)/211438 weeks
56.06594 -.10809 (56*2π)/211438 weeks
57.06701 -.1579 (57*2π)/211437 weeks
58-.00111 -.09298 (58*2π)/211436 weeks
59.13334 -.05204 (59*2π)/211436 weeks
60.18325 -.18609 (60*2π)/211435 weeks
61.08804 -.28143 (61*2π)/211435 weeks
62.00481 -.25245 (62*2π)/211434 weeks
63-.04823 -.24579 (63*2π)/211434 weeks
64-.08409 -.14427 (64*2π)/211433 weeks
65.01272 -.11832 (65*2π)/211433 weeks
66.03274 -.1852 (66*2π)/211432 weeks
67-.0395 -.2661 (67*2π)/211432 weeks
68-.16208 -.18743 (68*2π)/211431 weeks
69-.13101 -.09045 (69*2π)/211431 weeks
70-.08749 -.06863 (70*2π)/211430 weeks
71-.10392 -.0531 (71*2π)/211430 weeks
72-.01778 .03923 (72*2π)/211429 weeks
73.05606 -.07844 (73*2π)/211429 weeks
74-.00123 -.07102 (74*2π)/211429 weeks
75.05437 -.09901 (75*2π)/211428 weeks
76.01488 -.13809 (76*2π)/211428 weeks
77-.00862 -.16095 (77*2π)/211427 weeks
78-.0818 -.12221 (78*2π)/211427 weeks
79-.01989 -.06474 (79*2π)/211427 weeks
80-.01748 -.11395 (80*2π)/211426 weeks
81-.02122 -.1028 (81*2π)/211426 weeks
82-.02296 -.11772 (82*2π)/211426 weeks
83-.05786 -.15372 (83*2π)/211425 weeks
84-.1328 -.08531 (84*2π)/211425 weeks
85-.05077 -.00361 (85*2π)/211425 weeks
86.00004 -.09208 (86*2π)/211425 weeks
87-.08699 -.11522 (87*2π)/211424 weeks
88-.10811 -.03472 (88*2π)/211424 weeks
89-.08254 -.00725 (89*2π)/211424 weeks
90-.05291 .04736 (90*2π)/211423 weeks
91.0564 .02686 (91*2π)/211423 weeks
92.06363 -.06072 (92*2π)/211423 weeks
93.01553 -.11951 (93*2π)/211423 weeks
94-.05889 -.09087 (94*2π)/211422 weeks
95-.07389 -.05064 (95*2π)/211422 weeks
96-.03541 .02863 (96*2π)/211422 weeks
97.03288 -.04396 (97*2π)/211422 weeks
98-.02861 -.05142 (98*2π)/211422 weeks
99-.02761 -.03028 (99*2π)/211421 weeks
100-.01039 .00169 (100*2π)/211421 weeks
101.00581 -.01853 (101*2π)/211421 weeks
102.02368 -.00827 (102*2π)/211421 weeks
103.02841 -.03316 (103*2π)/211421 weeks
104.05108 -.03199 (104*2π)/211420 weeks
105.0342 -.09264 (105*2π)/211420 weeks
106-.0202 -.07006 (106*2π)/211420 weeks
107-.01347 -.02813 (107*2π)/211420 weeks
108.00956 -.02974 (108*2π)/211420 weeks
109.02839 .01099 (109*2π)/211419 weeks
110.12081 -.05969 (110*2π)/211419 weeks
111.04736 -.15049 (111*2π)/211419 weeks
112-.02833 -.15701 (112*2π)/211419 weeks
113-.12638 -.08672 (113*2π)/211419 weeks
114-.07414 .03512 (114*2π)/211419 weeks
115.00335 .03604 (115*2π)/211418 weeks
116.05131 .01959 (116*2π)/211418 weeks
117.07374 -.02859 (117*2π)/211418 weeks
118.06884 -.06013 (118*2π)/211418 weeks
119.0423 -.09212 (119*2π)/211418 weeks
120.00733 -.07725 (120*2π)/211418 weeks
121.00639 -.06338 (121*2π)/211417 weeks
122.00508 -.05483 (122*2π)/211417 weeks
123.02184 -.03262 (123*2π)/211417 weeks
124.05666 -.06092 (124*2π)/211417 weeks
125.04088 -.08997 (125*2π)/211417 weeks
126.01264 -.11622 (126*2π)/211417 weeks
127-.02703 -.07973 (127*2π)/211417 weeks
128-.00707 -.06357 (128*2π)/211417 weeks
129-.01247 -.05208 (129*2π)/211416 weeks
130-.01276 -.0312 (130*2π)/211416 weeks
131.05614 .00186 (131*2π)/211416 weeks
132.10572 -.1017 (132*2π)/211416 weeks
133.01201 -.15983 (133*2π)/211416 weeks
134-.03973 -.08953 (134*2π)/211416 weeks
135.00591 -.06977 (135*2π)/211416 weeks
136-.00539 -.09957 (136*2π)/211416 weeks
137-.02818 -.06676 (137*2π)/211415 weeks
138.02862 -.0665 (138*2π)/211415 weeks
139-.01924 -.10704 (139*2π)/211415 weeks
140.01067 -.05856 (140*2π)/211415 weeks
141.01482 -.12607 (141*2π)/211415 weeks
142-.03146 -.1155 (142*2π)/211415 weeks
143-.03801 -.11661 (143*2π)/211415 weeks
144-.07806 -.12011 (144*2π)/211415 weeks
145-.10927 -.05467 (145*2π)/211415 weeks
146-.06266 -.02693 (146*2π)/211414 weeks
147-.06494 -.01561 (147*2π)/211414 weeks
148-.0234 .00206 (148*2π)/211414 weeks
149.00674 -.02448 (149*2π)/211414 weeks
150-.00142 -.04919 (150*2π)/211414 weeks
151.0054 -.04673 (151*2π)/211414 weeks
152-.01075 -.08343 (152*2π)/211414 weeks
153-.03052 -.05335 (153*2π)/211414 weeks
154-.01861 -.0682 (154*2π)/211414 weeks
155-.0383 -.07125 (155*2π)/211414 weeks
156-.06101 -.05228 (156*2π)/211414 weeks
157-.04503 -.02519 (157*2π)/211413 weeks
158-.0285 -.01853 (158*2π)/211413 weeks
159-.00115 -.0427 (159*2π)/211413 weeks
160-.04578 -.0725 (160*2π)/211413 weeks
161-.06148 -.02615 (161*2π)/211413 weeks
162-.05418 -.00204 (162*2π)/211413 weeks
163-.00217 .02414 (163*2π)/211413 weeks
164.02422 -.02985 (164*2π)/211413 weeks
165-.00174 -.05288 (165*2π)/211413 weeks
166-.02819 -.0411 (166*2π)/211413 weeks
167-.00477 -.01572 (167*2π)/211413 weeks
168.00697 -.04512 (168*2π)/211413 weeks
169-.00867 -.0567 (169*2π)/211413 weeks
170-.03659 -.04957 (170*2π)/211412 weeks
171-.01811 -.01142 (171*2π)/211412 weeks
172.00063 -.03404 (172*2π)/211412 weeks
173.00286 -.03277 (173*2π)/211412 weeks
174.0087 -.0628 (174*2π)/211412 weeks
175-.01368 -.07648 (175*2π)/211412 weeks
176-.06196 -.06686 (176*2π)/211412 weeks
177-.04221 -.00742 (177*2π)/211412 weeks
178-.00966 -.0315 (178*2π)/211412 weeks
179-.0218 -.03921 (179*2π)/211412 weeks
180-.02213 -.03318 (180*2π)/211412 weeks
181-.00011 -.04156 (181*2π)/211412 weeks
182-.02546 -.09231 (182*2π)/211412 weeks
183-.10198 -.05862 (183*2π)/211412 weeks
184-.07699 .00995 (184*2π)/211411 weeks
185-.06359 .01104 (185*2π)/211411 weeks
186-.0316 .04581 (186*2π)/211411 weeks
187.01253 .02743 (187*2π)/211411 weeks
188.0256 -.01753 (188*2π)/211411 weeks
189-.01315 -.02904 (189*2π)/211411 weeks
190-.01828 -.0191 (190*2π)/211411 weeks
191-.03627 .00199 (191*2π)/211411 weeks
192-.00464 .03181 (192*2π)/211411 weeks
193.03256 .02587 (193*2π)/211411 weeks
194.0606 -.0106 (194*2π)/211411 weeks
195.04883 -.05192 (195*2π)/211411 weeks
196.01201 -.07028 (196*2π)/211411 weeks
197-.01161 -.05843 (197*2π)/211411 weeks
198-.03435 -.04558 (198*2π)/211411 weeks
199-.01989 -.00634 (199*2π)/211411 weeks
200-.00915 -.0121 (200*2π)/211411 weeks
201.01752 .00908 (201*2π)/211411 weeks
202.04517 -.03451 (202*2π)/211410 weeks
203.01654 -.06219 (203*2π)/211410 weeks
204-.00581 -.05353 (204*2π)/211410 weeks
205-.00772 -.04097 (205*2π)/211410 weeks
206-.01235 -.04942 (206*2π)/211410 weeks
207-.02034 -.01335 (207*2π)/211410 weeks
208.03394 -.02779 (208*2π)/211410 weeks
209.01111 -.07298 (209*2π)/211410 weeks
210-.0229 -.07248 (210*2π)/211410 weeks
211-.0376 -.04232 (211*2π)/211410 weeks
212-.0255 -.04049 (212*2π)/211410 weeks
213-.04042 -.02722 (213*2π)/211410 weeks
214-.03149 -.001 (214*2π)/211410 weeks
215.02325 .00803 (215*2π)/211410 weeks
216.02556 -.06087 (216*2π)/211410 weeks
217-.02173 -.05684 (217*2π)/211410 weeks
218-.02157 -.0334 (218*2π)/211410 weeks
219-.01312 -.04382 (219*2π)/211410 weeks
220-.04491 -.03252 (220*2π)/211410 weeks
221-.01764 .00522 (221*2π)/211410 weeks
222.01447 -.02182 (222*2π)/211410 weeks
223-.00604 -.04956 (223*2π)/21149 weeks
224-.03018 -.02015 (224*2π)/21149 weeks
225.01559 -.01104 (225*2π)/21149 weeks
226.00518 -.0508 (226*2π)/21149 weeks
227-.00923 -.03553 (227*2π)/21149 weeks
228.00745 -.04324 (228*2π)/21149 weeks
229-.00669 -.07861 (229*2π)/21149 weeks
230-.06306 -.06854 (230*2π)/21149 weeks
231-.06853 .00073 (231*2π)/21149 weeks
232.00145 .01132 (232*2π)/21149 weeks
233.00242 -.03694 (233*2π)/21149 weeks
234-.01582 -.03839 (234*2π)/21149 weeks
235-.01613 -.04202 (235*2π)/21149 weeks
236-.04228 -.05405 (236*2π)/21149 weeks
237-.06876 -.00744 (237*2π)/21149 weeks
238-.02063 .02083 (238*2π)/21149 weeks
239-.01327 -.00606 (239*2π)/21149 weeks
240-.00304 .01856 (240*2π)/21149 weeks
241.04035 -.01458 (241*2π)/21149 weeks
242.01925 -.05848 (242*2π)/21149 weeks
243-.01992 -.07148 (243*2π)/21149 weeks
244-.0488 -.03519 (244*2π)/21149 weeks
245-.03269 -.02147 (245*2π)/21149 weeks
246-.02973 -.00733 (246*2π)/21149 weeks
247-.01339 -.00731 (247*2π)/21149 weeks
248.005 -.01248 (248*2π)/21149 weeks
249.00174 -.0538 (249*2π)/21148 weeks
250-.04729 -.04794 (250*2π)/21148 weeks
251-.0428 -.01503 (251*2π)/21148 weeks
252-.03799 -.01153 (252*2π)/21148 weeks
253-.03577 .00561 (253*2π)/21148 weeks
254-.00626 .01093 (254*2π)/21148 weeks
255.00676 -.01749 (255*2π)/21148 weeks
256-.01537 -.03771 (256*2π)/21148 weeks
257-.0506 -.02227 (257*2π)/21148 weeks
258-.02889 .01657 (258*2π)/21148 weeks
259-.01446 .00034 (259*2π)/21148 weeks
260-.01156 .0065 (260*2π)/21148 weeks
261-.0032 -.00625 (261*2π)/21148 weeks
262-.01977 -.01401 (262*2π)/21148 weeks
263-.03107 .01261 (263*2π)/21148 weeks
264.00405 .03085 (264*2π)/21148 weeks
265.02197 -.0056 (265*2π)/21148 weeks
266-.0068 -.0041 (266*2π)/21148 weeks
267.0104 .01214 (267*2π)/21148 weeks
268.02126 -.00386 (268*2π)/21148 weeks
269.02164 -.00977 (269*2π)/21148 weeks
270.02531 -.02216 (270*2π)/21148 weeks
271.00554 -.03105 (271*2π)/21148 weeks
272.01433 -.00904 (272*2π)/21148 weeks
273.02855 -.03906 (273*2π)/21148 weeks
274-.00219 -.0506 (274*2π)/21148 weeks
275-.00876 -.02611 (275*2π)/21148 weeks
276.0043 -.03573 (276*2π)/21148 weeks
277-.02144 -.03795 (277*2π)/21148 weeks
278-.02363 -.0152 (278*2π)/21148 weeks
279.00096 .00166 (279*2π)/21148 weeks
280.01002 -.03467 (280*2π)/21148 weeks
281-.02164 -.02533 (281*2π)/21148 weeks
282-.00569 .00113 (282*2π)/21147 weeks
283.01796 -.01609 (283*2π)/21147 weeks
284-.00208 -.03513 (284*2π)/21147 weeks
285-.0154 -.00506 (285*2π)/21147 weeks
286.03088 .00111 (286*2π)/21147 weeks
287.02981 -.04904 (287*2π)/21147 weeks
288-.00391 -.04879 (288*2π)/21147 weeks
289-.00622 -.04028 (289*2π)/21147 weeks
290-.01359 -.03438 (290*2π)/21147 weeks
291-.01394 -.02503 (291*2π)/21147 weeks
292-.00058 -.01938 (292*2π)/21147 weeks
293.00372 -.03194 (293*2π)/21147 weeks
294-.00141 -.03759 (294*2π)/21147 weeks
295-.00241 -.03269 (295*2π)/21147 weeks
296.01221 -.05597 (296*2π)/21147 weeks
297-.0362 -.07194 (297*2π)/21147 weeks
298-.06091 -.03436 (298*2π)/21147 weeks
299-.0382 .00209 (299*2π)/21147 weeks
300-.02171 -.01146 (300*2π)/21147 weeks
301-.02603 .00487 (301*2π)/21147 weeks
302.00383 .01318 (302*2π)/21147 weeks
303.03187 -.00904 (303*2π)/21147 weeks
304.02834 -.05355 (304*2π)/21147 weeks
305-.01415 -.06928 (305*2π)/21147 weeks
306-.03623 -.05284 (306*2π)/21147 weeks
307-.05717 -.02883 (307*2π)/21147 weeks
308-.04263 .00554 (308*2π)/21147 weeks
309-.01282 .01895 (309*2π)/21147 weeks
310.0189 -.00696 (310*2π)/21147 weeks
311.00907 -.03242 (311*2π)/21147 weeks
312-.00171 -.04284 (312*2π)/21147 weeks
313-.01746 -.05175 (313*2π)/21147 weeks
314-.04854 -.05032 (314*2π)/21147 weeks
315-.07046 -.00916 (315*2π)/21147 weeks
316-.03877 .03402 (316*2π)/21147 weeks
317.0088 .02935 (317*2π)/21147 weeks
318.03316 -.00632 (318*2π)/21147 weeks
319.02185 -.05067 (319*2π)/21147 weeks
320-.02415 -.06117 (320*2π)/21147 weeks
321-.05017 -.03556 (321*2π)/21147 weeks
322-.04759 .00128 (322*2π)/21147 weeks
323-.02286 .0034 (323*2π)/21147 weeks
324-.02152 .00654 (324*2π)/21147 weeks
325-.00269 .0048 (325*2π)/21147 weeks
326.00435 -.00602 (326*2π)/21146 weeks
327.00645 -.03019 (327*2π)/21146 weeks
328-.02831 -.04121 (328*2π)/21146 weeks
329-.05373 -.00844 (329*2π)/21146 weeks
330-.02899 .02737 (330*2π)/21146 weeks
331.00625 .02258 (331*2π)/21146 weeks
332.01501 -.00864 (332*2π)/21146 weeks
333.00178 -.01351 (333*2π)/21146 weeks
334.00274 -.02141 (334*2π)/21146 weeks
335-.01533 -.02667 (335*2π)/21146 weeks
336-.02605 -.00611 (336*2π)/21146 weeks
337-.0058 .00373 (337*2π)/21146 weeks
338-.00462 -.00939 (338*2π)/21146 weeks
339-.00695 -.00432 (339*2π)/21146 weeks
340.00219 -.00166 (340*2π)/21146 weeks
341.00649 -.01739 (341*2π)/21146 weeks
342-.0029 -.01904 (342*2π)/21146 weeks
343-.01571 -.02281 (343*2π)/21146 weeks
344-.0138 .00272 (344*2π)/21146 weeks
345.00151 -.01085 (345*2π)/21146 weeks
346-.01361 -.00673 (346*2π)/21146 weeks
347.00249 .00306 (347*2π)/21146 weeks
348.01348 -.01249 (348*2π)/21146 weeks
349-.00194 -.01944 (349*2π)/21146 weeks
350.00581 -.01142 (350*2π)/21146 weeks
351.00552 -.03051 (351*2π)/21146 weeks
352-.0173 -.0326 (352*2π)/21146 weeks
353-.02699 -.01422 (353*2π)/21146 weeks
354-.02497 .00293 (354*2π)/21146 weeks
355-.00222 .01816 (355*2π)/21146 weeks
356.01246 -.00066 (356*2π)/21146 weeks
357.01312 .00021 (357*2π)/21146 weeks
358.02363 -.01453 (358*2π)/21146 weeks
359.01926 -.03253 (359*2π)/21146 weeks
360-.00653 -.03546 (360*2π)/21146 weeks
361-.00675 -.0167 (361*2π)/21146 weeks
362.00013 -.01795 (362*2π)/21146 weeks
363.00197 -.02411 (363*2π)/21146 weeks
364-.00765 -.02299 (364*2π)/21146 weeks
365-.0028 -.01758 (365*2π)/21146 weeks
366-.00359 -.01651 (366*2π)/21146 weeks
367.00968 -.02022 (367*2π)/21146 weeks
368-.00218 -.03906 (368*2π)/21146 weeks
369-.01833 -.03381 (369*2π)/21146 weeks
370-.02625 -.01631 (370*2π)/21146 weeks
371-.00664 -.00911 (371*2π)/21146 weeks
372-.01206 -.02153 (372*2π)/21146 weeks
373-.016 -.00823 (373*2π)/21146 weeks
374-.00695 -.00979 (374*2π)/21146 weeks
375-.00956 -.01025 (375*2π)/21146 weeks
376-.00206 -.00436 (376*2π)/21146 weeks
377.00834 -.00879 (377*2π)/21146 weeks
378.01087 -.03068 (378*2π)/21146 weeks
379-.01994 -.03032 (379*2π)/21146 weeks
380-.01151 -.00559 (380*2π)/21146 weeks
381.00059 -.01553 (381*2π)/21146 weeks
382-.00524 -.02 (382*2π)/21146 weeks
383-.00495 -.01352 (383*2π)/21146 weeks
384-.00102 -.02329 (384*2π)/21146 weeks
385-.01356 -.0196 (385*2π)/21145 weeks
386-.00363 -.0125 (386*2π)/21145 weeks
387-.00301 -.02324 (387*2π)/21145 weeks
388-.00877 -.02437 (388*2π)/21145 weeks
389-.01599 -.02404 (389*2π)/21145 weeks
390-.02357 -.01534 (390*2π)/21145 weeks
391-.01323 .00006 (391*2π)/21145 weeks
392-.00636