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# Fourier Analysis of ZION (Zions Bancorporation)

ZION (Zions Bancorporation) appears to have interesting cyclic behaviour every 211 weeks (2.3806*cosine), 163 weeks (1.7767*sine), and 211 weeks (1.593*sine).

ZION (Zions Bancorporation) has an average price of 22.49 (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 3/17/1980 to 9/8/2020 for ZION (Zions Bancorporation), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
022.4876   0
1-10.0565 -17.90398 (1*2π)/21132,113 weeks
28.92973 1.73037 (2*2π)/21131,057 weeks
32.92152 -8.85249 (3*2π)/2113704 weeks
4-2.59992 -7.46201 (4*2π)/2113528 weeks
5-.73352 1.65913 (5*2π)/2113423 weeks
63.01376 -6.46514 (6*2π)/2113352 weeks
7-3.26843 -2.72742 (7*2π)/2113302 weeks
8-1.39536 -.43008 (8*2π)/2113264 weeks
9.49651 -1.87147 (9*2π)/2113235 weeks
10-2.3806 -1.59302 (10*2π)/2113211 weeks
11-.76284 .70813 (11*2π)/2113192 weeks
12.92308 -.07701 (12*2π)/2113176 weeks
13.63978 -1.77666 (13*2π)/2113163 weeks
14-1.2259 -.37766 (14*2π)/2113151 weeks
15.77162 -.5535 (15*2π)/2113141 weeks
16-.42695 -.78667 (16*2π)/2113132 weeks
17.32582 -.89718 (17*2π)/2113124 weeks
18-.63057 -.96623 (18*2π)/2113117 weeks
19.0432 -.37924 (19*2π)/2113111 weeks
20-.63858 -.64955 (20*2π)/2113106 weeks
21.24557 -.35563 (21*2π)/2113101 weeks
22-.43989 -.57518 (22*2π)/211396 weeks
23-.04387 -.30845 (23*2π)/211392 weeks
24.05708 -.41073 (24*2π)/211388 weeks
25-.28877 -1.1616 (25*2π)/211385 weeks
26-.6303 .15513 (26*2π)/211381 weeks
27-.10804 -.63863 (27*2π)/211378 weeks
28-.65755 -.04337 (28*2π)/211375 weeks
29-.22787 -.06563 (29*2π)/211373 weeks
30-.29792 .57258 (30*2π)/211370 weeks
31.65459 -.47436 (31*2π)/211368 weeks
32-.60168 -.03189 (32*2π)/211366 weeks
33.5289 .23616 (33*2π)/211364 weeks
34.37981 -.59818 (34*2π)/211362 weeks
35-.23517 -.2906 (35*2π)/211360 weeks
36-.02611 -.34512 (36*2π)/211359 weeks
37-.16278 -.08241 (37*2π)/211357 weeks
38-.1032 -.27729 (38*2π)/211356 weeks
39.05981 .1293 (39*2π)/211354 weeks
40.05077 -.42105 (40*2π)/211353 weeks
41-.15493 .00079 (41*2π)/211352 weeks
42-.12743 -.01907 (42*2π)/211350 weeks
43.24218 -.02278 (43*2π)/211349 weeks
44-.01705 -.10675 (44*2π)/211348 weeks
45.24122 -.19439 (45*2π)/211347 weeks
46-.26988 .03221 (46*2π)/211346 weeks
47.52737 -.00354 (47*2π)/211345 weeks
48.04122 -.18955 (48*2π)/211344 weeks
49.1537 -.4565 (49*2π)/211343 weeks
50-.27673 .2693 (50*2π)/211342 weeks
51.58142 -.23258 (51*2π)/211341 weeks
52-.11013 -.05162 (52*2π)/211341 weeks
53.23202 -.29773 (53*2π)/211340 weeks
54.08792 .25088 (54*2π)/211339 weeks
55.57395 -.3623 (55*2π)/211338 weeks
56.13895 -.36064 (56*2π)/211338 weeks
57.07961 -.27628 (57*2π)/211337 weeks
58.36433 -.1642 (58*2π)/211336 weeks
59.0913 -.72613 (59*2π)/211336 weeks
60-.14676 -.2182 (60*2π)/211335 weeks
61.0599 .00002 (61*2π)/211335 weeks
62.40471 -.49519 (62*2π)/211334 weeks
63-.17979 -.45056 (63*2π)/211334 weeks
64-.02085 -.18152 (64*2π)/211333 weeks
65.16901 -.17965 (65*2π)/211333 weeks
66.10231 -.54322 (66*2π)/211332 weeks
67-.15034 -.20279 (67*2π)/211332 weeks
68.17348 -.35986 (68*2π)/211331 weeks
69-.18147 -.50234 (69*2π)/211331 weeks
70-.14912 -.30265 (70*2π)/211330 weeks
71-.26676 -.14823 (71*2π)/211330 weeks
72.16655 -.33311 (72*2π)/211329 weeks
73-.63352 -.22345 (73*2π)/211329 weeks
74.18357 .20753 (74*2π)/211329 weeks
75.03914 -.32991 (75*2π)/211328 weeks
76-.02636 -.30349 (76*2π)/211328 weeks
77-.28038 -.00908 (77*2π)/211327 weeks
78.3691 -.22825 (78*2π)/211327 weeks
79-.34159 -.43253 (79*2π)/211327 weeks
80-.09355 -.13372 (80*2π)/211326 weeks
81-.20157 -.09191 (81*2π)/211326 weeks
82.11923 -.22882 (82*2π)/211326 weeks
83-.42434 -.21637 (83*2π)/211325 weeks
84.00883 .0457 (84*2π)/211325 weeks
85-.00686 -.15643 (85*2π)/211325 weeks
86-.13985 -.30026 (86*2π)/211325 weeks
87-.17411 -.02921 (87*2π)/211324 weeks
88-.09972 -.16065 (88*2π)/211324 weeks
89-.12184 -.033 (89*2π)/211324 weeks
90-.1328 -.13795 (90*2π)/211323 weeks
91-.08593 .05768 (91*2π)/211323 weeks
92.06362 -.11633 (92*2π)/211323 weeks
93-.12129 -.24226 (93*2π)/211323 weeks
94-.19895 -.01012 (94*2π)/211322 weeks
95-.10659 -.03451 (95*2π)/211322 weeks
96-.0481 -.05899 (96*2π)/211322 weeks
97-.18621 -.03151 (97*2π)/211322 weeks
98-.04974 .00801 (98*2π)/211322 weeks
99-.08133 .10906 (99*2π)/211321 weeks
100.03074 .02339 (100*2π)/211321 weeks
101.09243 .06324 (101*2π)/211321 weeks
102.04442 -.19608 (102*2π)/211321 weeks
103.00004 -.01176 (103*2π)/211321 weeks
104-.05357 -.13475 (104*2π)/211320 weeks
105-.01466 .0266 (105*2π)/211320 weeks
106.05448 -.10728 (106*2π)/211320 weeks
107-.04894 -.02476 (107*2π)/211320 weeks
108.03304 -.12617 (108*2π)/211320 weeks
109-.01842 .02028 (109*2π)/211319 weeks
110.09365 -.15373 (110*2π)/211319 weeks
111-.06134 -.09997 (111*2π)/211319 weeks
112.02093 -.1255 (112*2π)/211319 weeks
113-.11097 -.14765 (113*2π)/211319 weeks
114-.09107 .02485 (114*2π)/211319 weeks
115.01066 -.14531 (115*2π)/211318 weeks
116-.22357 .04883 (116*2π)/211318 weeks
117.06847 .07134 (117*2π)/211318 weeks
118.06531 .05969 (118*2π)/211318 weeks
119.10147 -.21782 (119*2π)/211318 weeks
120-.16456 .0125 (120*2π)/211318 weeks
121.06932 .00067 (121*2π)/211317 weeks
122.02401 -.02824 (122*2π)/211317 weeks
123-.00675 -.08894 (123*2π)/211317 weeks
124-.02567 .10311 (124*2π)/211317 weeks
125.21013 -.03904 (125*2π)/211317 weeks
126.02758 -.19701 (126*2π)/211317 weeks
127-.11162 .03075 (127*2π)/211317 weeks
128.28271 -.03396 (128*2π)/211317 weeks
129-.04279 -.20591 (129*2π)/211316 weeks
130.03186 -.11014 (130*2π)/211316 weeks
131-.07388 .01545 (131*2π)/211316 weeks
132.19745 -.13272 (132*2π)/211316 weeks
133-.13384 -.14273 (133*2π)/211316 weeks
134.04133 -.03948 (134*2π)/211316 weeks
135.02015 -.0428 (135*2π)/211316 weeks
136.0136 -.11852 (136*2π)/211316 weeks
137.01832 -.01109 (137*2π)/211315 weeks
138.08363 -.07745 (138*2π)/211315 weeks
139.05943 -.13352 (139*2π)/211315 weeks
140.01761 -.09284 (140*2π)/211315 weeks
141.05093 -.11383 (141*2π)/211315 weeks
142.06707 -.15489 (142*2π)/211315 weeks
143-.06495 -.19237 (143*2π)/211315 weeks
144-.0215 -.0936 (144*2π)/211315 weeks
145-.07247 -.12265 (145*2π)/211315 weeks
146.00215 -.09352 (146*2π)/211314 weeks
147-.11955 -.05549 (147*2π)/211314 weeks
148.03926 -.02324 (148*2π)/211314 weeks
149.00994 -.07823 (149*2π)/211314 weeks
150-.01248 -.10899 (150*2π)/211314 weeks
151.03913 -.02136 (151*2π)/211314 weeks
152.00321 -.15788 (152*2π)/211314 weeks
153.03233 -.07437 (153*2π)/211314 weeks
154-.05468 -.09307 (154*2π)/211314 weeks
155.08734 -.12395 (155*2π)/211314 weeks
156-.08765 -.14902 (156*2π)/211314 weeks
157-.03145 -.12995 (157*2π)/211313 weeks
158-.09989 .01478 (158*2π)/211313 weeks
159.11743 -.12953 (159*2π)/211313 weeks
160-.10518 -.13463 (160*2π)/211313 weeks
161.02417 -.05465 (161*2π)/211313 weeks
162-.0476 -.15926 (162*2π)/211313 weeks
163-.07727 -.08934 (163*2π)/211313 weeks
164.01043 -.15225 (164*2π)/211313 weeks
165-.24895 -.16717 (165*2π)/211313 weeks
166-.10143 .07378 (166*2π)/211313 weeks
167-.08742 -.01666 (167*2π)/211313 weeks
168.03414 .03526 (168*2π)/211313 weeks
169-.07801 -.08303 (169*2π)/211313 weeks
170-.02289 .01263 (170*2π)/211312 weeks
171-.01686 -.00853 (171*2π)/211312 weeks
172.03421 -.00793 (172*2π)/211312 weeks
173.00285 -.09585 (173*2π)/211312 weeks
174-.06618 .03711 (174*2π)/211312 weeks
175.13058 -.04091 (175*2π)/211312 weeks
176-.05574 -.07552 (176*2π)/211312 weeks
177.10013 -.05381 (177*2π)/211312 weeks
178-.0189 -.10985 (178*2π)/211312 weeks
179.01653 -.08154 (179*2π)/211312 weeks
180.00803 -.09593 (180*2π)/211312 weeks
181-.01041 -.12096 (181*2π)/211312 weeks
182-.01831 -.10734 (182*2π)/211312 weeks
183-.02578 -.10823 (183*2π)/211312 weeks
184-.0489 -.16335 (184*2π)/211311 weeks
185-.19182 -.10402 (185*2π)/211311 weeks
186-.06254 .08675 (186*2π)/211311 weeks
187-.01972 -.14428 (187*2π)/211311 weeks
188-.14141 .01453 (188*2π)/211311 weeks
189-.02679 .00195 (189*2π)/211311 weeks
190-.01942 .00796 (190*2π)/211311 weeks
191-.04406 -.07075 (191*2π)/211311 weeks
192-.0689 .0653 (192*2π)/211311 weeks
193.0435 -.01254 (193*2π)/211311 weeks
194-.01746 -.01978 (194*2π)/211311 weeks
195.01979 -.02484 (195*2π)/211311 weeks
196-.01591 -.01374 (196*2π)/211311 weeks
197.05183 -.04705 (197*2π)/211311 weeks
198-.07117 -.04615 (198*2π)/211311 weeks
199.06098 .0134 (199*2π)/211311 weeks
200.00427 -.06586 (200*2π)/211311 weeks
201-.02311 -.06335 (201*2π)/211311 weeks
202.00984 .04926 (202*2π)/211310 weeks
203.05685 -.06328 (203*2π)/211310 weeks
204.06738 -.0428 (204*2π)/211310 weeks
205-.03627 -.08232 (205*2π)/211310 weeks
206.16607 .01118 (206*2π)/211310 weeks
207-.00136 -.23737 (207*2π)/211310 weeks
208-.02188 -.04577 (208*2π)/211310 weeks
209.03648 -.09995 (209*2π)/211310 weeks
210-.01868 -.17431 (210*2π)/211310 weeks
211-.09514 -.09592 (211*2π)/211310 weeks
212-.02639 -.02978 (212*2π)/211310 weeks
213-.02074 -.14586 (213*2π)/211310 weeks
214-.15599 -.02602 (214*2π)/211310 weeks
215.04877 .02485 (215*2π)/211310 weeks
216-.0071 -.13864 (216*2π)/211310 weeks
217-.10839 -.05227 (217*2π)/211310 weeks
218.00549 -.01435 (218*2π)/211310 weeks
219-.05058 -.05219 (219*2π)/211310 weeks
220.01448 -.06903 (220*2π)/211310 weeks
221-.08003 -.00632 (221*2π)/211310 weeks
222.05069 -.08016 (222*2π)/211310 weeks
223-.09246 -.0254 (223*2π)/21139 weeks
224.05567 -.07328 (224*2π)/21139 weeks
225-.07564 -.03796 (225*2π)/21139 weeks
226.0282 -.08769 (226*2π)/21139 weeks
227-.04218 -.05574 (227*2π)/21139 weeks
228-.05753 -.08851 (228*2π)/21139 weeks
229-.04725 -.00041 (229*2π)/21139 weeks
230.0032 -.11081 (230*2π)/21139 weeks
231-.10242 -.00883 (231*2π)/21139 weeks
232-.00821 -.07118 (232*2π)/21139 weeks
233-.05719 .04173 (233*2π)/21139 weeks
234.04235 -.10126 (234*2π)/21139 weeks
235-.07525 -.02493 (235*2π)/21139 weeks
236-.02047 -.06661 (236*2π)/21139 weeks
237-.00246 .04497 (237*2π)/21139 weeks
238.03164 -.16472 (238*2π)/21139 weeks
239-.12837 -.04223 (239*2π)/21139 weeks
240-.00086 .02871 (240*2π)/21139 weeks
241.00597 -.11172 (241*2π)/21139 weeks
242-.05865 -.0238 (242*2π)/21139 weeks
243-.02699 -.05611 (243*2π)/21139 weeks
244.01161 -.06104 (244*2π)/21139 weeks
245-.12349 -.11987 (245*2π)/21139 weeks
246-.05428 .06892 (246*2π)/21139 weeks
247.0268 -.06747 (247*2π)/21139 weeks
248-.04073 -.10783 (248*2π)/21139 weeks
249-.10976 -.01223 (249*2π)/21138 weeks
250.02639 -.04084 (250*2π)/21138 weeks
251-.11936 -.10507 (251*2π)/21138 weeks
252-.08763 -.00384 (252*2π)/21138 weeks
253-.05933 .0367 (253*2π)/21138 weeks
254-.03679 -.09639 (254*2π)/21138 weeks
255-.10654 .0487 (255*2π)/21138 weeks
256-.03631 -.00868 (256*2π)/21138 weeks
257-.02137 -.00307 (257*2π)/21138 weeks
258-.12298 -.05508 (258*2π)/21138 weeks
259-.06071 .13959 (259*2π)/21138 weeks
260.02896 -.01314 (260*2π)/21138 weeks
261-.01787 -.01152 (261*2π)/21138 weeks
262-.09369 .02919 (262*2π)/21138 weeks
263.09028 .0627 (263*2π)/21138 weeks
264-.07191 -.07139 (264*2π)/21138 weeks
265.02798 .05198 (265*2π)/21138 weeks
266-.05493 .01906 (266*2π)/21138 weeks
267.08562 -.04022 (267*2π)/21138 weeks
268-.11893 -.00405 (268*2π)/21138 weeks
269.02624 .07352 (269*2π)/21138 weeks
270.08357 .00059 (270*2π)/21138 weeks
271-.04441 -.09652 (271*2π)/21138 weeks
272-.02978 .06891 (272*2π)/21138 weeks
273.03339 .01479 (273*2π)/21138 weeks
274.03059 -.04811 (274*2π)/21138 weeks
275-.01429 .05079 (275*2π)/21138 weeks
276.05081 -.04824 (276*2π)/21138 weeks
277.05663 .01888 (277*2π)/21138 weeks
278-.0059 -.13106 (278*2π)/21138 weeks
279-.01582 .00396 (279*2π)/21138 weeks
280-.07524 -.02651 (280*2π)/21138 weeks
281.06198 .02963 (281*2π)/21138 weeks
282-.09614 -.0215 (282*2π)/21137 weeks
283.10853 .08187 (283*2π)/21137 weeks
284-.00339 -.03852 (284*2π)/21137 weeks
285.08051 .00017 (285*2π)/21137 weeks
286.01363 -.00395 (286*2π)/21137 weeks
287.09688 -.03174 (287*2π)/21137 weeks
288.03146 -.07346 (288*2π)/21137 weeks
289.04311 -.05645 (289*2π)/21137 weeks
290.02883 -.02967 (290*2π)/21137 weeks
291.06475 -.05411 (291*2π)/21137 weeks
292.04675 -.10062 (292*2π)/21137 weeks
293.00656 -.10052 (293*2π)/21137 weeks
294-.01668 -.09 (294*2π)/21137 weeks
295-.01798 -.0774 (295*2π)/21137 weeks
296-.00221 -.0569 (296*2π)/21137 weeks
297-.02387 -.05947 (297*2π)/21137 weeks
298.02819 -.09953 (298*2π)/21137 weeks
299-.13895 -.07332 (299*2π)/21137 weeks
300.03434 .06241 (300*2π)/21137 weeks
301.02204 -.16259 (301*2π)/21137 weeks
302-.1317 -.00399 (302*2π)/21137 weeks
303.02041 .02586 (303*2π)/21137 weeks
304.04944 -.0345 (304*2π)/21137 weeks
305-.00348 -.12628 (305*2π)/21137 weeks
306-.10024 -.02455 (306*2π)/21137 weeks
307.02585 .01139 (307*2π)/21137 weeks
308.00151 -.08955 (308*2π)/21137 weeks
309-.0602 -.02624 (309*2π)/21137 weeks
310-.00492 -.01473 (310*2π)/21137 weeks
311.04427 -.04961 (311*2π)/21137 weeks
312-.07216 -.10528 (312*2π)/21137 weeks
313-.04211 .03312 (313*2π)/21137 weeks
314.0354 -.03989 (314*2π)/21137 weeks
315-.03309 -.06179 (315*2π)/21137 weeks
316-.02366 -.02173 (316*2π)/21137 weeks
317.01287 -.01974 (317*2π)/21137 weeks
318-.00311 -.04262 (318*2π)/21137 weeks
319-.02322 -.07927 (319*2π)/21137 weeks
320-.03001 .02491 (320*2π)/21137 weeks
321.05645 -.09553 (321*2π)/21137 weeks
322-.05634 -.07291 (322*2π)/21137 weeks
323-.06946 -.01073 (323*2π)/21137 weeks
324.08552 -.01104 (324*2π)/21137 weeks
325-.08189 -.15769 (325*2π)/21137 weeks
326-.0792 .00328 (326*2π)/21136 weeks
327-.01413 -.00425 (327*2π)/21136 weeks
328-.00429 -.06347 (328*2π)/21136 weeks
329-.08273 -.04462 (329*2π)/21136 weeks
330-.05109 .04946 (330*2π)/21136 weeks
331.05467 -.00845 (331*2π)/21136 weeks
332-.01468 -.06509 (332*2π)/21136 weeks
333-.03613 -.04878 (333*2π)/21136 weeks
334-.0137 .02432 (334*2π)/21136 weeks
335.03109 -.1027 (335*2π)/21136 weeks
336-.10668 -.02489 (336*2π)/21136 weeks
337.0013 .02068 (337*2π)/21136 weeks
338.0276 -.03982 (338*2π)/21136 weeks
339-.07781 -.05592 (339*2π)/21136 weeks
340.06259 .02556 (340*2π)/21136 weeks
341-.04116 -.10465 (341*2π)/21136 weeks
342.00312 -.04529 (342*2π)/21136 weeks
343-.09184 -.03648 (343*2π)/21136 weeks
344.01182 -.01737 (344*2π)/21136 weeks
345-.05806 -.03577 (345*2π)/21136 weeks
346-.02422 -.0322 (346*2π)/21136 weeks
347-.04075 .01479 (347*2π)/21136 weeks
348.01397 -.04215 (348*2π)/21136 weeks
349-.0626 -.00667 (349*2π)/21136 weeks
350.02556 -.0102 (350*2π)/21136 weeks
351-.02002 -.0263 (351*2π)/21136 weeks
352-.01243 -.07522 (352*2π)/21136 weeks
353-.03665 .03409 (353*2π)/21136 weeks
354-.00547 -.08284 (354*2π)/21136 weeks
355-.00421 .00604 (355*2π)/21136 weeks
356-.09555 -.07775 (356*2π)/21136 weeks
357.01191 .06329 (357*2π)/21136 weeks
358-.02765 -.0418 (358*2π)/21136 weeks
359.00526 -.01548 (359*2π)/21136 weeks
360-.01309 .01876 (360*2π)/21136 weeks
361.025 -.08284 (361*2π)/21136 weeks
362-.05018 .01858 (362*2π)/21136 weeks
363.03269 -.05937 (363*2π)/21136 weeks
364-.04522 -.01858 (364*2π)/21136 weeks
365.0063 -.03974 (365*2π)/21136 weeks
366-.03671 -.00281 (366*2π)/21136 weeks
367.01306 -.03032 (367*2π)/21136 weeks
368-.00063 .00144 (368*2π)/21136 weeks
369.05729 -.09961 (369*2π)/21136 weeks
370-.09542 -.05354 (370*2π)/21136 weeks
371.02608 -.02497 (371*2π)/21136 weeks
372-.05331 -.07276 (372*2π)/21136 weeks
373-.03193 -.05045 (373*2π)/21136 weeks
374-.09217 -.01077 (374*2π)/21136 weeks
375.02636 -.00355 (375*2π)/21136 weeks
376-.07473 -.06535 (376*2π)/21136 weeks
377-.03165 .04632 (377*2π)/21136 weeks
378.02833 -.04479 (378*2π)/21136 weeks
379-.0502 -.05613 (379*2π)/21136 weeks
380-.04864 -.00268 (380*2π)/21136 weeks
381-.00603 .00411 (381*2π)/21136 weeks
382.00746 -.04918 (382*2π)/21136 weeks
383-.07519 -.05585 (383*2π)/21136 weeks
384-.03645 .0396 (384*2π)/21136 weeks
385-.00236 -.04217 (385*2π)/21135 weeks
386-.03275 -.00452 (386*2π)/21135 weeks
387-.02756 -.02342 (387*2π)/21135 weeks
388-.00176 -.00005 (388*2π)/21135 weeks
389-.02177 -.05115 (389*2π)/21135 weeks
390-.07341 -.04157 (390*2π)/21135 weeks
391-.01882 .06742 (391*2π)/21135 weeks
392.00261 -.0683