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Fourier Analysis of AON (Aon plc Class A Ordinary Shares)


AON (Aon plc Class A Ordinary Shares) appears to have interesting cyclic behaviour every 190 weeks (3.4664*sine), 127 weeks (2.8685*sine), and 136 weeks (2.5355*sine).

AON (Aon plc Class A Ordinary Shares) has an average price of 25.48 (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 6/2/1980 to 11/28/2016 for AON (Aon plc Class A Ordinary Shares), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
025.48102   0 
110.63451 -19.93236 (1*2π)/19041,904 weeks
29.63077 -13.21805 (2*2π)/1904952 weeks
31.99752 -10.4636 (3*2π)/1904635 weeks
45.35942 -8.911 (4*2π)/1904476 weeks
5-.01685 -9.76716 (5*2π)/1904381 weeks
6-.12523 -6.4119 (6*2π)/1904317 weeks
7-.32721 -4.51022 (7*2π)/1904272 weeks
8.13186 -4.98734 (8*2π)/1904238 weeks
9-.73996 -3.0956 (9*2π)/1904212 weeks
10-.19991 -3.46638 (10*2π)/1904190 weeks
11-.41755 -2.03218 (11*2π)/1904173 weeks
121.35239 -2.14427 (12*2π)/1904159 weeks
13.19174 -2.48731 (13*2π)/1904146 weeks
141.02757 -2.53546 (14*2π)/1904136 weeks
15-.22096 -2.8685 (15*2π)/1904127 weeks
16-.05954 -1.70511 (16*2π)/1904119 weeks
17.60858 -2.02136 (17*2π)/1904112 weeks
18-.27346 -2.25883 (18*2π)/1904106 weeks
19.1414 -1.2587 (19*2π)/1904100 weeks
20.72984 -1.74659 (20*2π)/190495 weeks
21.22618 -2.10089 (21*2π)/190491 weeks
22-.04163 -1.66679 (22*2π)/190487 weeks
23.29707 -1.55909 (23*2π)/190483 weeks
24.24505 -1.42372 (24*2π)/190479 weeks
25.27949 -1.65586 (25*2π)/190476 weeks
26.31476 -1.36872 (26*2π)/190473 weeks
27.66135 -1.91046 (27*2π)/190471 weeks
28-.40609 -2.27311 (28*2π)/190468 weeks
29-.37534 -1.20314 (29*2π)/190466 weeks
30-.13718 -1.70092 (30*2π)/190463 weeks
31-.25759 -1.01077 (31*2π)/190461 weeks
32-.07963 -1.50575 (32*2π)/190460 weeks
33-.33936 -1.16741 (33*2π)/190458 weeks
34-.42904 -1.26647 (34*2π)/190456 weeks
35-.399 -.84327 (35*2π)/190454 weeks
36-.36145 -1.02534 (36*2π)/190453 weeks
37-.15518 -.50107 (37*2π)/190451 weeks
38.0896 -.99255 (38*2π)/190450 weeks
39-.24606 -.84162 (39*2π)/190449 weeks
40.09368 -.90337 (40*2π)/190448 weeks
41-.31798 -1.01636 (41*2π)/190446 weeks
42-.39362 -.64204 (42*2π)/190445 weeks
43-.08039 -.45025 (43*2π)/190444 weeks
44.10781 -.70021 (44*2π)/190443 weeks
45.11526 -.57168 (45*2π)/190442 weeks
46-.09219 -.99881 (46*2π)/190441 weeks
47-.03816 -.50045 (47*2π)/190441 weeks
48-.14056 -.89033 (48*2π)/190440 weeks
49-.06677 -.54732 (49*2π)/190439 weeks
50-.05847 -.72424 (50*2π)/190438 weeks
51-.0039 -.48222 (51*2π)/190437 weeks
52.08903 -.72482 (52*2π)/190437 weeks
53-.12915 -.65713 (53*2π)/190436 weeks
54-.08569 -.62071 (54*2π)/190435 weeks
55-.07892 -.47757 (55*2π)/190435 weeks
56.09265 -.63764 (56*2π)/190434 weeks
57-.12717 -.55423 (57*2π)/190433 weeks
58.08689 -.57876 (58*2π)/190433 weeks
59-.20205 -.46717 (59*2π)/190432 weeks
60.40054 -.44639 (60*2π)/190432 weeks
61-.00106 -.88749 (61*2π)/190431 weeks
62.12337 -.60723 (62*2π)/190431 weeks
63-.3139 -.91958 (63*2π)/190430 weeks
64-.16948 -.25626 (64*2π)/190430 weeks
65.16561 -.72349 (65*2π)/190429 weeks
66-.22151 -.69353 (66*2π)/190429 weeks
67-.28804 -.4278 (67*2π)/190428 weeks
68-.16445 -.38472 (68*2π)/190428 weeks
69-.02669 -.39026 (69*2π)/190428 weeks
70-.03377 -.35453 (70*2π)/190427 weeks
71.05392 -.42304 (71*2π)/190427 weeks
72.11209 -.40517 (72*2π)/190426 weeks
73.11107 -.59722 (73*2π)/190426 weeks
74-.11787 -.47664 (74*2π)/190426 weeks
75.13716 -.49602 (75*2π)/190425 weeks
76-.02602 -.54727 (76*2π)/190425 weeks
77.15144 -.50135 (77*2π)/190425 weeks
78-.12522 -.67072 (78*2π)/190424 weeks
79-.10333 -.52201 (79*2π)/190424 weeks
80-.10039 -.55328 (80*2π)/190424 weeks
81-.08894 -.43842 (81*2π)/190424 weeks
82-.11409 -.58581 (82*2π)/190423 weeks
83-.21765 -.4273 (83*2π)/190423 weeks
84-.13303 -.48975 (84*2π)/190423 weeks
85-.19394 -.30107 (85*2π)/190422 weeks
86.01105 -.4562 (86*2π)/190422 weeks
87-.24593 -.43673 (87*2π)/190422 weeks
88-.04874 -.319 (88*2π)/190422 weeks
89-.20453 -.40019 (89*2π)/190421 weeks
90-.0968 -.35818 (90*2π)/190421 weeks
91-.25534 -.32305 (91*2π)/190421 weeks
92.00413 -.11376 (92*2π)/190421 weeks
93-.00933 -.4504 (93*2π)/190420 weeks
94-.09676 -.22477 (94*2π)/190420 weeks
95.02289 -.33077 (95*2π)/190420 weeks
96-.0996 -.32123 (96*2π)/190420 weeks
97-.00985 -.32187 (97*2π)/190420 weeks
98-.19096 -.30825 (98*2π)/190419 weeks
99.04593 -.20065 (99*2π)/190419 weeks
100-.08688 -.29235 (100*2π)/190419 weeks
101.16296 -.16581 (101*2π)/190419 weeks
102-.00637 -.43813 (102*2π)/190419 weeks
103.06813 -.27118 (103*2π)/190418 weeks
104-.11044 -.39778 (104*2π)/190418 weeks
105.10285 -.148 (105*2π)/190418 weeks
106.06156 -.48307 (106*2π)/190418 weeks
107-.00667 -.31157 (107*2π)/190418 weeks
108.03032 -.42376 (108*2π)/190418 weeks
109.00295 -.3168 (109*2π)/190417 weeks
110.06577 -.4308 (110*2π)/190417 weeks
111-.04286 -.53671 (111*2π)/190417 weeks
112-.22414 -.41618 (112*2π)/190417 weeks
113-.10261 -.24343 (113*2π)/190417 weeks
114-.0431 -.34939 (114*2π)/190417 weeks
115-.03403 -.29294 (115*2π)/190417 weeks
116-.07262 -.44622 (116*2π)/190416 weeks
117-.1982 -.30912 (117*2π)/190416 weeks
118-.0767 -.26929 (118*2π)/190416 weeks
119-.04282 -.28555 (119*2π)/190416 weeks
120-.01559 -.4002 (120*2π)/190416 weeks
121-.20776 -.37359 (121*2π)/190416 weeks
122-.15576 -.21943 (122*2π)/190416 weeks
123-.06672 -.27707 (123*2π)/190415 weeks
124-.18993 -.31211 (124*2π)/190415 weeks
125-.16394 -.17807 (125*2π)/190415 weeks
126-.10356 -.1445 (126*2π)/190415 weeks
127-.03262 -.17774 (127*2π)/190415 weeks
128-.03085 -.17717 (128*2π)/190415 weeks
129.03356 -.24328 (129*2π)/190415 weeks
130-.0946 -.31041 (130*2π)/190415 weeks
131-.03477 -.19915 (131*2π)/190415 weeks
132-.04602 -.22045 (132*2π)/190414 weeks
133.02187 -.22787 (133*2π)/190414 weeks
134-.04276 -.27118 (134*2π)/190414 weeks
135-.01614 -.28127 (135*2π)/190414 weeks
136-.09095 -.22816 (136*2π)/190414 weeks
137-.01903 -.26218 (137*2π)/190414 weeks
138-.11444 -.31422 (138*2π)/190414 weeks
139-.1462 -.18335 (139*2π)/190414 weeks
140-.09534 -.12421 (140*2π)/190414 weeks
141-.01106 -.09833 (141*2π)/190414 weeks
142.07987 -.16122 (142*2π)/190413 weeks
143.02242 -.23583 (143*2π)/190413 weeks
144.05431 -.21937 (144*2π)/190413 weeks
145.00868 -.27021 (145*2π)/190413 weeks
146.13211 -.2385 (146*2π)/190413 weeks
147-.03001 -.47457 (147*2π)/190413 weeks
148-.13234 -.2139 (148*2π)/190413 weeks
149.02735 -.30995 (149*2π)/190413 weeks
150-.06445 -.32861 (150*2π)/190413 weeks
151-.12077 -.31285 (151*2π)/190413 weeks
152-.10119 -.24547 (152*2π)/190413 weeks
153-.14612 -.32557 (153*2π)/190412 weeks
154-.1471 -.13876 (154*2π)/190412 weeks
155-.10829 -.21667 (155*2π)/190412 weeks
156-.08459 -.1769 (156*2π)/190412 weeks
157-.09277 -.15942 (157*2π)/190412 weeks
158-.05217 -.11452 (158*2π)/190412 weeks
159-.02571 -.24592 (159*2π)/190412 weeks
160-.05875 -.14734 (160*2π)/190412 weeks
161-.01532 -.15551 (161*2π)/190412 weeks
162.01606 -.2302 (162*2π)/190412 weeks
163-.08718 -.1715 (163*2π)/190412 weeks
164.11963 -.17815 (164*2π)/190412 weeks
165-.01191 -.35904 (165*2π)/190412 weeks
166-.0668 -.25466 (166*2π)/190411 weeks
167-.08875 -.27446 (167*2π)/190411 weeks
168-.0824 -.22718 (168*2π)/190411 weeks
169-.14206 -.22626 (169*2π)/190411 weeks
170-.03742 -.15139 (170*2π)/190411 weeks
171-.07201 -.24647 (171*2π)/190411 weeks
172-.08448 -.18731 (172*2π)/190411 weeks
173-.08032 -.20017 (173*2π)/190411 weeks
174-.09585 -.19673 (174*2π)/190411 weeks
175-.08233 -.17746 (175*2π)/190411 weeks
176-.10739 -.13197 (176*2π)/190411 weeks
177-.00971 -.18243 (177*2π)/190411 weeks
178-.12263 -.14856 (178*2π)/190411 weeks
179-.00807 -.15595 (179*2π)/190411 weeks
180-.1364 -.15179 (180*2π)/190411 weeks
181.02672 -.07447 (181*2π)/190411 weeks
182-.01311 -.17036 (182*2π)/190410 weeks
183.02778 -.15937 (183*2π)/190410 weeks
184-.03206 -.21389 (184*2π)/190410 weeks
185-.01238 -.10998 (185*2π)/190410 weeks
186.07736 -.25087 (186*2π)/190410 weeks
187-.07553 -.23755 (187*2π)/190410 weeks
188-.02052 -.2284 (188*2π)/190410 weeks
189-.13113 -.19191 (189*2π)/190410 weeks
190.01347 -.15571 (190*2π)/190410 weeks
191-.10886 -.24692 (191*2π)/190410 weeks
192-.05036 -.12066 (192*2π)/190410 weeks
193-.08963 -.18817 (193*2π)/190410 weeks
194.00182 -.01153 (194*2π)/190410 weeks
195.08086 -.27053 (195*2π)/190410 weeks
196-.05563 -.17526 (196*2π)/190410 weeks
197-.0101 -.25526 (197*2π)/190410 weeks
198-.07488 -.2014 (198*2π)/190410 weeks
199-.01055 -.20564 (199*2π)/190410 weeks
200-.08374 -.22752 (200*2π)/190410 weeks
201-.06749 -.19619 (201*2π)/19049 weeks
202-.10656 -.19616 (202*2π)/19049 weeks
203-.05253 -.14438 (203*2π)/19049 weeks
204-.09114 -.2079 (204*2π)/19049 weeks
205-.0613 -.12357 (205*2π)/19049 weeks
206-.08821 -.18782 (206*2π)/19049 weeks
207-.03788 -.07404 (207*2π)/19049 weeks
208-.00804 -.23692 (208*2π)/19049 weeks
209-.09998 -.13113 (209*2π)/19049 weeks
210-.00763 -.19516 (210*2π)/19049 weeks
211-.13836 -.15112 (211*2π)/19049 weeks
212.00804 -.1088 (212*2π)/19049 weeks
213-.07832 -.16139 (213*2π)/19049 weeks
214.04551 -.11855 (214*2π)/19049 weeks
215-.02594 -.21449 (215*2π)/19049 weeks
216-.00973 -.20071 (216*2π)/19049 weeks
217-.10221 -.23975 (217*2π)/19049 weeks
218-.10017 -.13132 (218*2π)/19049 weeks
219-.07819 -.12123 (219*2π)/19049 weeks
220-.01172 -.15417 (220*2π)/19049 weeks
221-.07903 -.16995 (221*2π)/19049 weeks
222-.0203 -.16149 (222*2π)/19049 weeks
223-.09371 -.14282 (223*2π)/19049 weeks
224.03436 -.11319 (224*2π)/19049 weeks
225-.0627 -.19499 (225*2π)/19048 weeks
226.01447 -.10971 (226*2π)/19048 weeks
227-.00634 -.22212 (227*2π)/19048 weeks
228-.00211 -.18801 (228*2π)/19048 weeks
229-.07839 -.27222 (229*2π)/19048 weeks
230-.07754 -.16097 (230*2π)/19048 weeks
231-.06887 -.26628 (231*2π)/19048 weeks
232-.189 -.16145 (232*2π)/19048 weeks
233-.0903 -.14896 (233*2π)/19048 weeks
234-.11915 -.10716 (234*2π)/19048 weeks
235-.05076 -.13408 (235*2π)/19048 weeks
236-.06557 -.10452 (236*2π)/19048 weeks
237-.05028 -.16832 (237*2π)/19048 weeks
238-.10974 -.13858 (238*2π)/19048 weeks
239-.05141 -.13432 (239*2π)/19048 weeks
240-.07831 -.1225 (240*2π)/19048 weeks
241-.0519 -.16004 (241*2π)/19048 weeks
242-.09307 -.11785 (242*2π)/19048 weeks
243-.03247 -.06949 (243*2π)/19048 weeks
244-.02039 -.1604 (244*2π)/19048 weeks
245-.03925 -.15009 (245*2π)/19048 weeks
246-.07961 -.18784 (246*2π)/19048 weeks
247-.12264 -.06879 (247*2π)/19048 weeks
248.02351 -.12211 (248*2π)/19048 weeks
249-.0671 -.14316 (249*2π)/19048 weeks
250-.00914 -.13914 (250*2π)/19048 weeks
251-.06264 -.19261 (251*2π)/19048 weeks
252-.06697 -.16606 (252*2π)/19048 weeks
253-.09151 -.14402 (253*2π)/19048 weeks
254-.04937 -.14245 (254*2π)/19047 weeks
255-.14135 -.17292 (255*2π)/19047 weeks
256-.09321 -.05714 (256*2π)/19047 weeks
257-.06107 -.10543 (257*2π)/19047 weeks
258-.05922 -.10005 (258*2π)/19047 weeks
259-.04576 -.14769 (259*2π)/19047 weeks
260-.0823 -.06874 (260*2π)/19047 weeks
261-.0437 -.09109 (261*2π)/19047 weeks
262-.01043 -.03838 (262*2π)/19047 weeks
263.09276 -.17994 (263*2π)/19047 weeks
264-.04967 -.19251 (264*2π)/19047 weeks
265-.04307 -.18943 (265*2π)/19047 weeks
266-.13656 -.13634 (266*2π)/19047 weeks
267-.03531 -.11048 (267*2π)/19047 weeks
268-.12353 -.1549 (268*2π)/19047 weeks
269-.03921 -.0558 (269*2π)/19047 weeks
270-.02311 -.13633 (270*2π)/19047 weeks
271.0036 -.11397 (271*2π)/19047 weeks
272-.04695 -.23001 (272*2π)/19047 weeks
273-.12474 -.12767 (273*2π)/19047 weeks
274-.07029 -.10363 (274*2π)/19047 weeks
275-.06186 -.07855 (275*2π)/19047 weeks
276-.0061 -.11665 (276*2π)/19047 weeks
277-.03634 -.13755 (277*2π)/19047 weeks
278-.02683 -.1692 (278*2π)/19047 weeks
279-.08963 -.15034 (279*2π)/19047 weeks
280-.07481 -.11683 (280*2π)/19047 weeks
281-.04861 -.111 (281*2π)/19047 weeks
282-.04685 -.15266 (282*2π)/19047 weeks
283-.0904 -.09027 (283*2π)/19047 weeks
284-.00101 -.12199 (284*2π)/19047 weeks
285-.06811 -.1587 (285*2π)/19047 weeks
286-.03649 -.11603 (286*2π)/19047 weeks
287-.05047 -.20414 (287*2π)/19047 weeks
288-.10495 -.10676 (288*2π)/19047 weeks
289-.02777 -.17154 (289*2π)/19047 weeks
290-.12335 -.11644 (290*2π)/19047 weeks
291-.05647 -.16693 (291*2π)/19047 weeks
292-.19614 -.13211 (292*2π)/19047 weeks
293-.04787 -.02 (293*2π)/19046 weeks
294-.05095 -.1152 (294*2π)/19046 weeks
295-.06801 -.11162 (295*2π)/19046 weeks
296-.08726 -.09384 (296*2π)/19046 weeks
297-.04101 -.0678 (297*2π)/19046 weeks
298-.03382 -.11046 (298*2π)/19046 weeks
299-.01663 -.09642 (299*2π)/19046 weeks
300-.0388 -.17244 (300*2π)/19046 weeks
301-.09123 -.10321 (301*2π)/19046 weeks
302-.03923 -.13923 (302*2π)/19046 weeks
303-.0799 -.11363 (303*2π)/19046 weeks
304-.06237 -.13955 (304*2π)/19046 weeks
305-.08425 -.08774 (305*2π)/19046 weeks
306-.00976 -.11748 (306*2π)/19046 weeks
307-.09285 -.14749 (307*2π)/19046 weeks
308-.02831 -.08292 (308*2π)/19046 weeks
309-.04915 -.18346 (309*2π)/19046 weeks
310-.10635 -.11576 (310*2π)/19046 weeks
311-.08657 -.14752 (311*2π)/19046 weeks
312-.11412 -.08099 (312*2π)/19046 weeks
313-.05747 -.15911 (313*2π)/19046 weeks
314-.15109 -.06619 (314*2π)/19046 weeks
315-.04396 -.07695 (315*2π)/19046 weeks
316-.1019 -.0817 (316*2π)/19046 weeks
317.00818 -.08905 (317*2π)/19046 weeks
318-.09851 -.13361 (318*2π)/19046 weeks
319-.06117 -.09671 (319*2π)/19046 weeks
320-.07439 -.10683 (320*2π)/19046 weeks
321-.05851 -.11672 (321*2π)/19046 weeks
322-.10007 -.14095 (322*2π)/19046 weeks
323-.09237 -.10263 (323*2π)/19046 weeks
324-.12035 -.07769 (324*2π)/19046 weeks
325-.06229 -.05304 (325*2π)/19046 weeks
326-.05682 -.10534 (326*2π)/19046 weeks
327-.09327 -.07566 (327*2π)/19046 weeks
328-.04616 -.0824 (328*2π)/19046 weeks
329-.07252 -.0868 (329*2π)/19046 weeks
330-.05968 -.07658 (330*2π)/19046 weeks
331-.05549 -.1183 (331*2π)/19046 weeks
332-.09178 -.07968 (332*2π)/19046 weeks
333-.05293 -.10313 (333*2π)/19046 weeks
334-.10446 -.08244 (334*2π)/19046 weeks
335-.06133 -.08203 (335*2π)/19046 weeks
336-.10414 -.06981 (336*2π)/19046 weeks
337-.07419 -.06358 (337*2π)/19046 weeks
338-.04339 -.05039 (338*2π)/19046 weeks
339-.04585 -.11174 (339*2π)/19046 weeks
340-.10082 -.05355 (340*2π)/19046 weeks
341-.02025 -.093 (341*2π)/19046 weeks
342-.0921 -.09801 (342*2π)/19046 weeks
343-.07846 -.0518 (343*2π)/19046 weeks
344-.08266 -.04559 (344*2π)/19046 weeks
345-.05485 -.03706 (345*2π)/19046 weeks
346-.0217 -.0264 (346*2π)/19046 weeks
347-.00958 -.07819 (347*2π)/19045 weeks
348-.01299 -.0663 (348*2π)/19045 weeks
349-.0043 -.10656 (349*2π)/19045 weeks
350-.05281 -.07012 (350*2π)/19045 weeks
351-.00076 -.11652 (351*2π)/19045 weeks
352-.05472 -.11305 (352*2π)/19045 weeks
353-.02457 -.10312 (353*2π)/19045 weeks
354-.05732 -.1171 (354*2π)/19045 weeks
355-.04818 -.1153 (355*2π)/19045 weeks
356-.0846 -.09105 (356*2π)/19045 weeks
357-.05035 -.11925 (357*2π)/19045 weeks
358-.09585 -.08689 (358*2π)/19045 weeks
359-.0687 -.08407 (359*2π)/19045 weeks
360-.07287 -.02848 (360*2π)/19045 weeks
361-.03338 -.09246 (361*2π)/19045 weeks
362-.05637 -.03802 (362*2π)/19045 weeks
363.00093 -.09151 (363*2π)/19045 weeks
364-.02811 -.06521 (364*2π)/19045 weeks
365.02865 -.14787 (365*2π)/19045 weeks
366-.08081 -.12849 (366*2π)/19045 weeks
367-.02906 -.11641 (367*2π)/19045 weeks
368-.06611 -.14479 (368*2π)/19045 weeks
369-.0675 -.14754 (369*2π)/19045 weeks
370-.15321 -.12302 (370*2π)/19045 weeks
371-.07066 -.0654 (371*2π)/19045 weeks
372-.10736 -.10357 (372*2π)/19045 weeks
373-.09194 -.04939 (373*2π)/19045 weeks
374-.06894 -.09946 (374*2π)/19045 weeks
375-.08672 -.05792 (375*2π)/19045 weeks
376-.091 -.04977 (376*2π)/19045 weeks
377-.03778 -.02466 (377*2π)/19045 weeks
378-.01069 -.09021