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# Fourier Analysis of UNP (Union Pacific Corporation Commo)

UNP (Union Pacific Corporation Commo) appears to have interesting cyclic behaviour every 108 weeks (2.6148*sine), 92 weeks (2.4812*sine), and 102 weeks (2.4158*sine).

UNP (Union Pacific Corporation Commo) has an average price of 20.17 (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 1/2/1980 to 3/20/2017 for UNP (Union Pacific Corporation Commo), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
020.16638   0
117.82747 -16.98533 (1*2π)/19421,942 weeks
28.95898 -16.39043 (2*2π)/1942971 weeks
33.11483 -12.60932 (3*2π)/1942647 weeks
4.92137 -10.55858 (4*2π)/1942486 weeks
5-1.15608 -7.9529 (5*2π)/1942388 weeks
6-1.68797 -5.62809 (6*2π)/1942324 weeks
7-1.2963 -3.35115 (7*2π)/1942277 weeks
8-.6391 -3.7216 (8*2π)/1942243 weeks
9-1.10951 -2.37419 (9*2π)/1942216 weeks
10-.80408 -1.50383 (10*2π)/1942194 weeks
11.46078 -.74272 (11*2π)/1942177 weeks
121.09215 -1.10559 (12*2π)/1942162 weeks
131.19182 -1.83769 (13*2π)/1942149 weeks
14.68318 -1.78187 (14*2π)/1942139 weeks
15.94995 -1.5411 (15*2π)/1942129 weeks
161.27905 -1.47251 (16*2π)/1942121 weeks
171.57554 -2.23781 (17*2π)/1942114 weeks
18.68366 -2.61485 (18*2π)/1942108 weeks
19.75588 -2.41577 (19*2π)/1942102 weeks
20.40075 -2.23037 (20*2π)/194297 weeks
21.51972 -2.48119 (21*2π)/194292 weeks
22-.20932 -2.30295 (22*2π)/194288 weeks
23-.26021 -2.03901 (23*2π)/194284 weeks
24-.46941 -1.60599 (24*2π)/194281 weeks
25-.08467 -1.49025 (25*2π)/194278 weeks
26-.22541 -1.60925 (26*2π)/194275 weeks
27-.462 -1.32208 (27*2π)/194272 weeks
28-.46866 -1.05857 (28*2π)/194269 weeks
29-.07243 -.61164 (29*2π)/194267 weeks
30.43231 -.97616 (30*2π)/194265 weeks
31.21733 -1.43718 (31*2π)/194263 weeks
32-.3449 -1.24705 (32*2π)/194261 weeks
33-.17215 -.80685 (33*2π)/194259 weeks
34.10506 -.89529 (34*2π)/194257 weeks
35.08509 -1.03525 (35*2π)/194255 weeks
36-.0798 -.89162 (36*2π)/194254 weeks
37.10022 -.7339 (37*2π)/194252 weeks
38.20402 -.96254 (38*2π)/194251 weeks
39.13521 -1.04869 (39*2π)/194250 weeks
40-.06811 -1.13642 (40*2π)/194249 weeks
41-.26677 -.83882 (41*2π)/194247 weeks
42-.10109 -.69966 (42*2π)/194246 weeks
43-.02856 -.73852 (43*2π)/194245 weeks
44-.05338 -.77862 (44*2π)/194244 weeks
45-.19476 -.71721 (45*2π)/194243 weeks
46-.16694 -.41883 (46*2π)/194242 weeks
47.12879 -.39536 (47*2π)/194241 weeks
48.25869 -.60845 (48*2π)/194240 weeks
49.25238 -.71716 (49*2π)/194240 weeks
50.13838 -.6958 (50*2π)/194239 weeks
51.27118 -.74982 (51*2π)/194238 weeks
52.11402 -.92555 (52*2π)/194237 weeks
53.02072 -.92315 (53*2π)/194237 weeks
54-.11613 -.81769 (54*2π)/194236 weeks
55-.14884 -.68993 (55*2π)/194235 weeks
56-.07034 -.58627 (56*2π)/194235 weeks
57.06641 -.71393 (57*2π)/194234 weeks
58-.04349 -.72096 (58*2π)/194233 weeks
59-.03472 -.75883 (59*2π)/194233 weeks
60-.15397 -.70836 (60*2π)/194232 weeks
61-.21951 -.72614 (61*2π)/194232 weeks
62-.24295 -.51915 (62*2π)/194231 weeks
63-.10963 -.47085 (63*2π)/194231 weeks
64.07423 -.45271 (64*2π)/194230 weeks
65-.04934 -.72672 (65*2π)/194230 weeks
66-.19389 -.65251 (66*2π)/194229 weeks
67-.23994 -.50385 (67*2π)/194229 weeks
68-.15624 -.41281 (68*2π)/194229 weeks
69-.06958 -.4108 (69*2π)/194228 weeks
70-.06927 -.37409 (70*2π)/194228 weeks
71.07033 -.46098 (71*2π)/194227 weeks
72-.0203 -.55066 (72*2π)/194227 weeks
73-.04377 -.55439 (73*2π)/194227 weeks
74-.16017 -.49204 (74*2π)/194226 weeks
75-.03965 -.35604 (75*2π)/194226 weeks
76-.03279 -.50007 (76*2π)/194226 weeks
77-.04084 -.4244 (77*2π)/194225 weeks
78.00247 -.43027 (78*2π)/194225 weeks
79.07446 -.43249 (79*2π)/194225 weeks
80-.02417 -.54316 (80*2π)/194224 weeks
81-.00561 -.53301 (81*2π)/194224 weeks
82-.09681 -.50624 (82*2π)/194224 weeks
83-.04232 -.50055 (83*2π)/194223 weeks
84-.10848 -.55011 (84*2π)/194223 weeks
85-.17465 -.51102 (85*2π)/194223 weeks
86-.17975 -.44099 (86*2π)/194223 weeks
87-.13452 -.45438 (87*2π)/194222 weeks
88-.15772 -.43335 (88*2π)/194222 weeks
89-.20102 -.3888 (89*2π)/194222 weeks
90-.1534 -.34188 (90*2π)/194222 weeks
91-.11943 -.4025 (91*2π)/194221 weeks
92-.16352 -.40516 (92*2π)/194221 weeks
93-.1968 -.39252 (93*2π)/194221 weeks
94-.25038 -.27778 (94*2π)/194221 weeks
95-.14787 -.2112 (95*2π)/194220 weeks
96-.05999 -.24392 (96*2π)/194220 weeks
97-.12316 -.33009 (97*2π)/194220 weeks
98-.14632 -.23657 (98*2π)/194220 weeks
99-.11537 -.23427 (99*2π)/194220 weeks
100-.11948 -.24028 (100*2π)/194219 weeks
101-.12583 -.20525 (101*2π)/194219 weeks
102-.08022 -.13917 (102*2π)/194219 weeks
103.01143 -.17707 (103*2π)/194219 weeks
104.02953 -.22287 (104*2π)/194219 weeks
105.01748 -.27781 (105*2π)/194218 weeks
106-.01312 -.27545 (106*2π)/194218 weeks
107.04354 -.26646 (107*2π)/194218 weeks
108.05862 -.32017 (108*2π)/194218 weeks
109.04706 -.37586 (109*2π)/194218 weeks
110-.01783 -.39424 (110*2π)/194218 weeks
111-.04775 -.37509 (111*2π)/194217 weeks
112-.02633 -.3501 (112*2π)/194217 weeks
113-.08555 -.39886 (113*2π)/194217 weeks
114-.12244 -.37494 (114*2π)/194217 weeks
115-.17038 -.31136 (115*2π)/194217 weeks
116-.15216 -.21999 (116*2π)/194217 weeks
117-.03919 -.25181 (117*2π)/194217 weeks
118-.04792 -.31434 (118*2π)/194216 weeks
119-.16052 -.33716 (119*2π)/194216 weeks
120-.18017 -.16768 (120*2π)/194216 weeks
121-.06432 -.11785 (121*2π)/194216 weeks
122.01098 -.1616 (122*2π)/194216 weeks
123.02344 -.23257 (123*2π)/194216 weeks
124-.0183 -.26486 (124*2π)/194216 weeks
125-.0542 -.21828 (125*2π)/194216 weeks
126.01649 -.25239 (126*2π)/194215 weeks
127-.02308 -.24777 (127*2π)/194215 weeks
128-.02412 -.26552 (128*2π)/194215 weeks
129-.05471 -.26865 (129*2π)/194215 weeks
130-.02775 -.22161 (130*2π)/194215 weeks
131.02134 -.25327 (131*2π)/194215 weeks
132-.02016 -.30129 (132*2π)/194215 weeks
133-.05698 -.27157 (133*2π)/194215 weeks
134-.04904 -.29079 (134*2π)/194214 weeks
135-.05738 -.2632 (135*2π)/194214 weeks
136-.04496 -.26848 (136*2π)/194214 weeks
137-.07415 -.25311 (137*2π)/194214 weeks
138-.04034 -.25693 (138*2π)/194214 weeks
139-.04596 -.304 (139*2π)/194214 weeks
140-.14041 -.27573 (140*2π)/194214 weeks
141-.13064 -.16149 (141*2π)/194214 weeks
142-.04671 -.14014 (142*2π)/194214 weeks
143.05519 -.20073 (143*2π)/194214 weeks
144-.00637 -.31266 (144*2π)/194213 weeks
145-.02248 -.23808 (145*2π)/194213 weeks
146-.02254 -.31957 (146*2π)/194213 weeks
147-.09535 -.28732 (147*2π)/194213 weeks
148-.10174 -.30039 (148*2π)/194213 weeks
149-.16792 -.19723 (149*2π)/194213 weeks
150-.05673 -.18626 (150*2π)/194213 weeks
151-.06083 -.1865 (151*2π)/194213 weeks
152-.05963 -.24545 (152*2π)/194213 weeks
153-.1236 -.20699 (153*2π)/194213 weeks
154-.06135 -.14913 (154*2π)/194213 weeks
155-.03431 -.15823 (155*2π)/194213 weeks
156-.00687 -.18302 (156*2π)/194212 weeks
157.00349 -.1887 (157*2π)/194212 weeks
158.03373 -.23013 (158*2π)/194212 weeks
159.03485 -.26149 (159*2π)/194212 weeks
160.00174 -.32943 (160*2π)/194212 weeks
161-.05774 -.34253 (161*2π)/194212 weeks
162-.13573 -.3013 (162*2π)/194212 weeks
163-.1135 -.23458 (163*2π)/194212 weeks
164-.07741 -.2617 (164*2π)/194212 weeks
165-.14087 -.30161 (165*2π)/194212 weeks
166-.20291 -.24819 (166*2π)/194212 weeks
167-.19452 -.17751 (167*2π)/194212 weeks
168-.13755 -.10851 (168*2π)/194212 weeks
169-.10195 -.12877 (169*2π)/194211 weeks
170-.10443 -.12924 (170*2π)/194211 weeks
171-.0823 -.1058 (171*2π)/194211 weeks
172-.02068 -.09183 (172*2π)/194211 weeks
173.04138 -.16509 (173*2π)/194211 weeks
174-.01588 -.22742 (174*2π)/194211 weeks
175-.05075 -.1984 (175*2π)/194211 weeks
176-.03138 -.18244 (176*2π)/194211 weeks
177-.00532 -.25092 (177*2π)/194211 weeks
178-.0668 -.25614 (178*2π)/194211 weeks
179-.09803 -.24046 (179*2π)/194211 weeks
180-.08962 -.19893 (180*2π)/194211 weeks
181-.07237 -.21715 (181*2π)/194211 weeks
182-.10015 -.23778 (182*2π)/194211 weeks
183-.11393 -.21768 (183*2π)/194211 weeks
184-.13877 -.20665 (184*2π)/194211 weeks
185-.14867 -.16918 (185*2π)/194210 weeks
186-.11364 -.16204 (186*2π)/194210 weeks
187-.12526 -.16955 (187*2π)/194210 weeks
188-.12358 -.15369 (188*2π)/194210 weeks
189-.14731 -.15387 (189*2π)/194210 weeks
190-.14576 -.08639 (190*2π)/194210 weeks
191-.04942 -.10088 (191*2π)/194210 weeks
192-.09563 -.15542 (192*2π)/194210 weeks
193-.1056 -.14332 (193*2π)/194210 weeks
194-.12495 -.10589 (194*2π)/194210 weeks
195-.07527 -.10265 (195*2π)/194210 weeks
196-.10657 -.12851 (196*2π)/194210 weeks
197-.10822 -.10755 (197*2π)/194210 weeks
198-.13554 -.0507 (198*2π)/194210 weeks
199-.04294 -.02559 (199*2π)/194210 weeks
200-.03081 -.03693 (200*2π)/194210 weeks
201.0346 -.08889 (201*2π)/194210 weeks
202.00301 -.11467 (202*2π)/194210 weeks
203.00447 -.10475 (203*2π)/194210 weeks
204.03044 -.15429 (204*2π)/194210 weeks
205-.0281 -.17972 (205*2π)/19429 weeks
206-.03622 -.15733 (206*2π)/19429 weeks
207-.04649 -.14814 (207*2π)/19429 weeks
208-.02312 -.14628 (208*2π)/19429 weeks
209-.06123 -.14348 (209*2π)/19429 weeks
210-.03069 -.13895 (210*2π)/19429 weeks
211-.03722 -.14511 (211*2π)/19429 weeks
212-.02742 -.13271 (212*2π)/19429 weeks
213-.02927 -.1414 (213*2π)/19429 weeks
214-.03075 -.1648 (214*2π)/19429 weeks
215-.06873 -.15567 (215*2π)/19429 weeks
216-.0583 -.13847 (216*2π)/19429 weeks
217-.07141 -.15267 (217*2π)/19429 weeks
218-.10032 -.10714 (218*2π)/19429 weeks
219-.05453 -.07412 (219*2π)/19429 weeks
220-.00899 -.11006 (220*2π)/19429 weeks
221-.01197 -.14973 (221*2π)/19429 weeks
222-.05743 -.15006 (222*2π)/19429 weeks
223-.0508 -.14394 (223*2π)/19429 weeks
224-.07871 -.1267 (224*2π)/19429 weeks
225-.06393 -.12291 (225*2π)/19429 weeks
226-.09544 -.08483 (226*2π)/19429 weeks
227-.02952 -.05861 (227*2π)/19429 weeks
228-.01667 -.09259 (228*2π)/19429 weeks
229-.01784 -.08656 (229*2π)/19428 weeks
230.00268 -.11557 (230*2π)/19428 weeks
231-.00546 -.08937 (231*2π)/19428 weeks
232.02895 -.11595 (232*2π)/19428 weeks
233.03406 -.12153 (233*2π)/19428 weeks
234.05352 -.17272 (234*2π)/19428 weeks
235.02559 -.20295 (235*2π)/19428 weeks
236-.0075 -.23328 (236*2π)/19428 weeks
237-.06092 -.20429 (237*2π)/19428 weeks
238-.10785 -.18211 (238*2π)/19428 weeks
239-.07127 -.11308 (239*2π)/19428 weeks
240-.05295 -.14728 (240*2π)/19428 weeks
241-.04832 -.12563 (241*2π)/19428 weeks
242-.03718 -.12483 (242*2π)/19428 weeks
243-.02701 -.12394 (243*2π)/19428 weeks
244-.03012 -.14745 (244*2π)/19428 weeks
245-.03408 -.13631 (245*2π)/19428 weeks
246-.02919 -.13046 (246*2π)/19428 weeks
247.00668 -.11554 (247*2π)/19428 weeks
248.03517 -.16734 (248*2π)/19428 weeks
249.01109 -.21505 (249*2π)/19428 weeks
250-.05153 -.23292 (250*2π)/19428 weeks
251-.07795 -.16867 (251*2π)/19428 weeks
252-.01657 -.14651 (252*2π)/19428 weeks
253-.01719 -.24347 (253*2π)/19428 weeks
254-.11718 -.25375 (254*2π)/19428 weeks
255-.1593 -.17583 (255*2π)/19428 weeks
256-.12796 -.11408 (256*2π)/19428 weeks
257-.07325 -.13537 (257*2π)/19428 weeks
258-.09647 -.16255 (258*2π)/19428 weeks
259-.14678 -.1447 (259*2π)/19427 weeks
260-.13042 -.0789 (260*2π)/19427 weeks
261-.04882 -.07387 (261*2π)/19427 weeks
262-.06225 -.12953 (262*2π)/19427 weeks
263-.09264 -.13577 (263*2π)/19427 weeks
264-.08153 -.09483 (264*2π)/19427 weeks
265-.07378 -.08997 (265*2π)/19427 weeks
266-.04166 -.0975 (266*2π)/19427 weeks
267-.05277 -.13806 (267*2π)/19427 weeks
268-.05389 -.14338 (268*2π)/19427 weeks
269-.08962 -.14938 (269*2π)/19427 weeks
270-.0981 -.12661 (270*2π)/19427 weeks
271-.12507 -.12119 (271*2π)/19427 weeks
272-.12954 -.05525 (272*2π)/19427 weeks
273-.0648 -.06224 (273*2π)/19427 weeks
274-.04333 -.0564 (274*2π)/19427 weeks
275-.02444 -.10847 (275*2π)/19427 weeks
276-.06899 -.10818 (276*2π)/19427 weeks
277-.06995 -.09105 (277*2π)/19427 weeks
278-.04584 -.07575 (278*2π)/19427 weeks
279-.01526 -.07986 (279*2π)/19427 weeks
280.00848 -.12598 (280*2π)/19427 weeks
281-.05182 -.17716 (281*2π)/19427 weeks
282-.08115 -.12609 (282*2π)/19427 weeks
283-.06563 -.13075 (283*2π)/19427 weeks
284-.05271 -.11785 (284*2π)/19427 weeks
285-.08397 -.15088 (285*2π)/19427 weeks
286-.12001 -.11296 (286*2π)/19427 weeks
287-.08469 -.07105 (287*2π)/19427 weeks
288-.05005 -.09535 (288*2π)/19427 weeks
289-.06576 -.14313 (289*2π)/19427 weeks
290-.12448 -.11603 (290*2π)/19427 weeks
291-.11916 -.0513 (291*2π)/19427 weeks
292-.06234 -.0681 (292*2π)/19427 weeks
293-.07453 -.0662 (293*2π)/19427 weeks
294-.05498 -.06708 (294*2π)/19427 weeks
295-.05279 -.06056 (295*2π)/19427 weeks
296-.02244 -.08779 (296*2π)/19427 weeks
297-.04239 -.11144 (297*2π)/19427 weeks
298-.08282 -.13262 (298*2π)/19427 weeks
299-.10873 -.06818 (299*2π)/19426 weeks
300-.06806 -.03421 (300*2π)/19426 weeks
301-.02911 -.05572 (301*2π)/19426 weeks
302-.03972 -.10941 (302*2π)/19426 weeks
303-.06284 -.08996 (303*2π)/19426 weeks
304-.07208 -.07915 (304*2π)/19426 weeks
305-.06168 -.05857 (305*2π)/19426 weeks
306-.06126 -.0842 (306*2π)/19426 weeks
307-.07588 -.0463 (307*2π)/19426 weeks
308-.04492 -.052 (308*2π)/19426 weeks
309-.0409 -.01749 (309*2π)/19426 weeks
310.0139 -.0428 (310*2π)/19426 weeks
311.00278 -.09149 (311*2π)/19426 weeks
312-.01966 -.11305 (312*2π)/19426 weeks
313-.03988 -.09426 (313*2π)/19426 weeks
314-.02149 -.08347 (314*2π)/19426 weeks
315-.03276 -.10077 (315*2π)/19426 weeks
316-.03744 -.11412 (316*2π)/19426 weeks
317-.06055 -.09373 (317*2π)/19426 weeks
318-.03321 -.07163 (318*2π)/19426 weeks
319-.02162 -.10159 (319*2π)/19426 weeks
320-.03062 -.11098 (320*2π)/19426 weeks
321-.06444 -.10373 (321*2π)/19426 weeks
322-.05306 -.07792 (322*2π)/19426 weeks
323-.02615 -.07147 (323*2π)/19426 weeks
324-.0348 -.07459 (324*2π)/19426 weeks
325-.01155 -.0804 (325*2π)/19426 weeks
326-.02913 -.09199 (326*2π)/19426 weeks
327-.01529 -.07029 (327*2π)/19426 weeks
328.01839 -.083 (328*2π)/19426 weeks
329.03825 -.12195 (329*2π)/19426 weeks
330.01834 -.17983 (330*2π)/19426 weeks
331-.03461 -.17792 (331*2π)/19426 weeks
332-.0583 -.16024 (332*2π)/19426 weeks
333-.04944 -.12366 (333*2π)/19426 weeks
334-.03021 -.16062 (334*2π)/19426 weeks
335-.04638 -.17762 (335*2π)/19426 weeks
336-.09458 -.17927 (336*2π)/19426 weeks
337-.11086 -.15919 (337*2π)/19426 weeks
338-.1416 -.13723 (338*2π)/19426 weeks
339-.12509 -.10791 (339*2π)/19426 weeks
340-.11301 -.09481 (340*2π)/19426 weeks
341-.10157 -.1061 (341*2π)/19426 weeks
342-.11851 -.09266 (342*2π)/19426 weeks
343-.10041 -.07858 (343*2π)/19426 weeks
344-.10221 -.09457 (344*2π)/19426 weeks
345-.09704 -.08924 (345*2π)/19426 weeks
346-.11452 -.08925 (346*2π)/19426 weeks
347-.1236 -.07062 (347*2π)/19426 weeks
348-.12346 -.05273 (348*2π)/19426 weeks
349-.10546 -.05356 (349*2π)/19426 weeks
350-.12139 -.03369 (350*2π)/19426 weeks
351-.10619 -.01985 (351*2π)/19426 weeks
352-.09361 .01207 (352*2π)/19426 weeks
353-.04121 -.01696 (353*2π)/19426 weeks
354-.04538 -.0446 (354*2π)/19425 weeks
355-.06941 -.03495 (355*2π)/19425 weeks
356-.05058 -.00856 (356*2π)/19425 weeks
357-.02688 -.01738 (357*2π)/19425 weeks
358-.0229 -.04317 (358*2π)/19425 weeks
359-.01588 -.0557 (359*2π)/19425 weeks
360-.0281 -.06051 (360*2π)/19425 weeks
361-.02524 -.05257 (361*2π)/19425 weeks
362-.0203