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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 191 weeks (3.4479*sine), 127 weeks (2.8617*sine), and 136 weeks (2.7614*sine).

AON (Aon plc Class A Ordinary Shares) has an average price of 25.76 (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 1/9/2017 for AON (Aon plc Class A Ordinary Shares), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
025.75552   0 
110.9586 -20.15734 (1*2π)/19101,910 weeks
29.8001 -13.53642 (2*2π)/1910955 weeks
32.07984 -10.65003 (3*2π)/1910637 weeks
45.33851 -9.24485 (4*2π)/1910478 weeks
5-.21181 -9.81823 (5*2π)/1910382 weeks
6-.17354 -6.39021 (6*2π)/1910318 weeks
7-.28395 -4.49398 (7*2π)/1910273 weeks
8.09449 -4.98936 (8*2π)/1910239 weeks
9-.63557 -3.02383 (9*2π)/1910212 weeks
10-.13047 -3.44794 (10*2π)/1910191 weeks
11-.18628 -2.01784 (11*2π)/1910174 weeks
121.49853 -2.39351 (12*2π)/1910159 weeks
13.23189 -2.61031 (13*2π)/1910147 weeks
14.99624 -2.76145 (14*2π)/1910136 weeks
15-.32456 -2.86173 (15*2π)/1910127 weeks
16.04746 -1.73888 (16*2π)/1910119 weeks
17.60265 -2.19724 (17*2π)/1910112 weeks
18-.32271 -2.2408 (18*2π)/1910106 weeks
19.29439 -1.3611 (19*2π)/1910101 weeks
20.70359 -2.00356 (20*2π)/191096 weeks
21.07758 -2.20221 (21*2π)/191091 weeks
22-.07556 -1.69521 (22*2π)/191087 weeks
23.26906 -1.67947 (23*2π)/191083 weeks
24.20732 -1.55613 (24*2π)/191080 weeks
25.15589 -1.78965 (25*2π)/191076 weeks
26.22228 -1.53374 (26*2π)/191073 weeks
27.31179 -2.12301 (27*2π)/191071 weeks
28-.81488 -2.05185 (28*2π)/191068 weeks
29-.40414 -1.02296 (29*2π)/191066 weeks
30-.31509 -1.57897 (30*2π)/191064 weeks
31-.23518 -.88629 (31*2π)/191062 weeks
32-.23995 -1.41714 (32*2π)/191060 weeks
33-.3844 -.97455 (33*2π)/191058 weeks
34-.46468 -1.03128 (34*2π)/191056 weeks
35-.2659 -.65909 (35*2π)/191055 weeks
36-.26848 -.86319 (36*2π)/191053 weeks
37.09907 -.49662 (37*2π)/191052 weeks
38.08021 -1.063 (38*2π)/191050 weeks
39-.18296 -.7674 (39*2π)/191049 weeks
40.08447 -.94651 (40*2π)/191048 weeks
41-.33927 -.83697 (41*2π)/191047 weeks
42-.17992 -.48117 (42*2π)/191045 weeks
43.17971 -.52 (43*2π)/191044 weeks
44.18245 -.84164 (44*2π)/191043 weeks
45.17147 -.72032 (45*2π)/191042 weeks
46-.19904 -.97166 (46*2π)/191042 weeks
47.07925 -.54187 (47*2π)/191041 weeks
48-.18613 -.85277 (48*2π)/191040 weeks
49.05436 -.57302 (49*2π)/191039 weeks
50-.03386 -.74541 (50*2π)/191038 weeks
51.11092 -.57293 (51*2π)/191037 weeks
52.02654 -.82334 (52*2π)/191037 weeks
53-.12185 -.62318 (53*2π)/191036 weeks
54-.03799 -.62323 (54*2π)/191035 weeks
55.03432 -.53758 (55*2π)/191035 weeks
56.06115 -.75868 (56*2π)/191034 weeks
57-.08094 -.55967 (57*2π)/191034 weeks
58.0788 -.69685 (58*2π)/191033 weeks
59-.0895 -.48164 (59*2π)/191032 weeks
60.33727 -.8265 (60*2π)/191032 weeks
61-.29895 -.86857 (61*2π)/191031 weeks
62-.02063 -.64582 (62*2π)/191031 weeks
63-.48783 -.60986 (63*2π)/191030 weeks
64.08516 -.24192 (64*2π)/191030 weeks
65-.02284 -.82574 (65*2π)/191029 weeks
66-.2845 -.46019 (66*2π)/191029 weeks
67-.09572 -.26955 (67*2π)/191029 weeks
68.03184 -.39613 (68*2π)/191028 weeks
69.09843 -.50559 (69*2π)/191028 weeks
70.07311 -.48794 (70*2π)/191027 weeks
71.06328 -.60249 (71*2π)/191027 weeks
72.06453 -.6084 (72*2π)/191027 weeks
73-.09274 -.69176 (73*2π)/191026 weeks
74-.14428 -.44216 (74*2π)/191026 weeks
75.0164 -.63775 (75*2π)/191025 weeks
76-.15826 -.53032 (76*2π)/191025 weeks
77-.02916 -.58818 (77*2π)/191025 weeks
78-.33115 -.4736 (78*2π)/191024 weeks
79-.1434 -.38984 (79*2π)/191024 weeks
80-.15529 -.41962 (80*2π)/191024 weeks
81-.0774 -.35447 (81*2π)/191024 weeks
82-.19354 -.42191 (82*2π)/191023 weeks
83-.10949 -.25008 (83*2π)/191023 weeks
84-.08113 -.37651 (84*2π)/191023 weeks
85.00632 -.24151 (85*2π)/191022 weeks
86-.01821 -.48836 (86*2π)/191022 weeks
87-.13906 -.25425 (87*2π)/191022 weeks
88.0765 -.35771 (88*2π)/191022 weeks
89-.09987 -.29703 (89*2π)/191021 weeks
90.02679 -.35682 (90*2π)/191021 weeks
91-.02013 -.24693 (91*2π)/191021 weeks
92.23458 -.38633 (92*2π)/191021 weeks
93-.09473 -.52195 (93*2π)/191021 weeks
94.06001 -.30031 (94*2π)/191020 weeks
95.00482 -.46953 (95*2π)/191020 weeks
96-.05144 -.34448 (96*2π)/191020 weeks
97.00406 -.41489 (97*2π)/191020 weeks
98-.05964 -.28819 (98*2π)/191019 weeks
99.13247 -.45498 (99*2π)/191019 weeks
100-.05243 -.39553 (100*2π)/191019 weeks
101.12366 -.52135 (101*2π)/191019 weeks
102-.21502 -.46131 (102*2π)/191019 weeks
103-.00118 -.40673 (103*2π)/191019 weeks
104-.1799 -.34393 (104*2π)/191018 weeks
105.09763 -.42906 (105*2π)/191018 weeks
106-.25465 -.49525 (106*2π)/191018 weeks
107-.08674 -.32077 (107*2π)/191018 weeks
108-.16808 -.40728 (108*2π)/191018 weeks
109-.09289 -.31758 (109*2π)/191018 weeks
110-.18827 -.39331 (110*2π)/191017 weeks
111-.25575 -.27129 (111*2π)/191017 weeks
112-.12505 -.11102 (112*2π)/191017 weeks
113.05059 -.24302 (113*2π)/191017 weeks
114-.07936 -.33293 (114*2π)/191017 weeks
115-.04737 -.28176 (115*2π)/191017 weeks
116-.17263 -.27762 (116*2π)/191016 weeks
117-.03735 -.14855 (117*2π)/191016 weeks
118.01163 -.30022 (118*2π)/191016 weeks
119-.04245 -.30728 (119*2π)/191016 weeks
120-.12139 -.30584 (120*2π)/191016 weeks
121-.08496 -.1261 (121*2π)/191016 weeks
122.07414 -.20996 (122*2π)/191016 weeks
123-.00505 -.30328 (123*2π)/191016 weeks
124-.04066 -.19734 (124*2π)/191015 weeks
125.09824 -.24564 (125*2π)/191015 weeks
126.07107 -.32601 (126*2π)/191015 weeks
127.00819 -.3791 (127*2π)/191015 weeks
128-.02423 -.3486 (128*2π)/191015 weeks
129-.08247 -.3762 (129*2π)/191015 weeks
130-.1244 -.25485 (130*2π)/191015 weeks
131.01199 -.30866 (131*2π)/191015 weeks
132-.05569 -.30383 (132*2π)/191014 weeks
133-.06074 -.33985 (133*2π)/191014 weeks
134-.1093 -.26225 (134*2π)/191014 weeks
135-.07906 -.28112 (135*2π)/191014 weeks
136-.04598 -.21323 (136*2π)/191014 weeks
137-.07167 -.29305 (137*2π)/191014 weeks
138-.08747 -.20424 (138*2π)/191014 weeks
139.04856 -.22148 (139*2π)/191014 weeks
140.0367 -.31558 (140*2π)/191014 weeks
141-.01272 -.38033 (141*2π)/191014 weeks
142-.11371 -.3967 (142*2π)/191013 weeks
143-.17281 -.29222 (143*2π)/191013 weeks
144-.13145 -.29791 (144*2π)/191013 weeks
145-.17473 -.24617 (145*2π)/191013 weeks
146-.13585 -.29573 (146*2π)/191013 weeks
147-.27772 -.11372 (147*2π)/191013 weeks
148.02626 -.0949 (148*2π)/191013 weeks
149-.11798 -.27001 (149*2π)/191013 weeks
150-.09445 -.12755 (150*2π)/191013 weeks
151-.04412 -.12696 (151*2π)/191013 weeks
152.00807 -.17754 (152*2π)/191013 weeks
153-.04897 -.16598 (153*2π)/191012 weeks
154.10332 -.20562 (154*2π)/191012 weeks
155-.04052 -.26205 (155*2π)/191012 weeks
156.00203 -.2665 (156*2π)/191012 weeks
157-.01673 -.2569 (157*2π)/191012 weeks
158-.03096 -.288 (158*2π)/191012 weeks
159-.14111 -.27603 (159*2π)/191012 weeks
160-.02256 -.23709 (160*2π)/191012 weeks
161-.08914 -.27289 (161*2π)/191012 weeks
162-.1389 -.25038 (162*2π)/191012 weeks
163-.06964 -.17786 (163*2π)/191012 weeks
164-.12856 -.32029 (164*2π)/191012 weeks
165-.20418 -.0973 (165*2π)/191012 weeks
166-.0183 -.11925 (166*2π)/191012 weeks
167-.04963 -.14652 (167*2π)/191011 weeks
168-.00492 -.17893 (168*2π)/191011 weeks
169-.01899 -.16633 (169*2π)/191011 weeks
170-.00281 -.26905 (170*2π)/191011 weeks
171-.09043 -.18263 (171*2π)/191011 weeks
172-.00894 -.19832 (172*2π)/191011 weeks
173-.04357 -.207 (173*2π)/191011 weeks
174-.03383 -.20516 (174*2π)/191011 weeks
175-.02566 -.22928 (175*2π)/191011 weeks
176-.02219 -.22405 (176*2π)/191011 weeks
177-.09302 -.27295 (177*2π)/191011 weeks
178-.03514 -.17278 (178*2π)/191011 weeks
179-.08207 -.28145 (179*2π)/191011 weeks
180-.05758 -.17264 (180*2π)/191011 weeks
181-.07559 -.32762 (181*2π)/191011 weeks
182-.1607 -.18447 (182*2π)/191010 weeks
183-.11626 -.20792 (183*2π)/191010 weeks
184-.12052 -.13883 (184*2π)/191010 weeks
185-.05861 -.19648 (185*2π)/191010 weeks
186-.18714 -.1708 (186*2π)/191010 weeks
187-.04829 -.0573 (187*2π)/191010 weeks
188-.0524 -.16904 (188*2π)/191010 weeks
189-.01115 -.11859 (189*2π)/191010 weeks
190-.06251 -.247 (190*2π)/191010 weeks
191-.07722 -.09862 (191*2π)/191010 weeks
192-.00111 -.23327 (192*2π)/191010 weeks
193-.09055 -.16865 (193*2π)/191010 weeks
194-.03922 -.26132 (194*2π)/191010 weeks
195-.25153 -.13044 (195*2π)/191010 weeks
196-.01208 -.06871 (196*2π)/191010 weeks
197-.10605 -.13059 (197*2π)/191010 weeks
198-.00755 -.11762 (198*2π)/191010 weeks
199-.05525 -.16816 (199*2π)/191010 weeks
200-.02704 -.10252 (200*2π)/191010 weeks
201-.0144 -.16827 (201*2π)/191010 weeks
202-.02073 -.15337 (202*2π)/19109 weeks
203-.02924 -.21016 (203*2π)/19109 weeks
204-.06474 -.14432 (204*2π)/19109 weeks
205-.01814 -.20996 (205*2π)/19109 weeks
206-.08086 -.15462 (206*2π)/19109 weeks
207-.0385 -.22092 (207*2π)/19109 weeks
208-.1499 -.12516 (208*2π)/19109 weeks
209.01209 -.14033 (209*2π)/19109 weeks
210-.10609 -.18198 (210*2π)/19109 weeks
211-.00452 -.12513 (211*2π)/19109 weeks
212-.09453 -.2428 (212*2π)/19109 weeks
213-.08476 -.10267 (213*2π)/19109 weeks
214-.09684 -.19673 (214*2π)/19109 weeks
215-.0852 -.05279 (215*2π)/19109 weeks
216-.03217 -.12354 (216*2π)/19109 weeks
217-.00499 -.0899 (217*2π)/19109 weeks
218.01619 -.20194 (218*2π)/19109 weeks
219-.06847 -.18112 (219*2π)/19109 weeks
220-.10349 -.16629 (220*2π)/19109 weeks
221-.04811 -.11281 (221*2π)/19109 weeks
222-.06799 -.17468 (222*2π)/19109 weeks
223-.03232 -.12778 (223*2π)/19109 weeks
224-.09711 -.19043 (224*2π)/19109 weeks
225-.06137 -.05407 (225*2π)/19108 weeks
226-.04768 -.16854 (226*2π)/19108 weeks
227-.07853 -.05089 (227*2π)/19108 weeks
228.00032 -.1082 (228*2π)/19108 weeks
229.00107 -.06555 (229*2π)/19108 weeks
230.04623 -.1841 (230*2π)/19108 weeks
231-.03278 -.12732 (231*2π)/19108 weeks
232.07544 -.18729 (232*2π)/19108 weeks
233-.0711 -.24808 (233*2π)/19108 weeks
234-.03786 -.19223 (234*2π)/19108 weeks
235-.10434 -.1867 (235*2π)/19108 weeks
236-.05151 -.15288 (236*2π)/19108 weeks
237-.08639 -.12609 (237*2π)/19108 weeks
238-.02494 -.14841 (238*2π)/19108 weeks
239-.08401 -.18183 (239*2π)/19108 weeks
240-.05228 -.14355 (240*2π)/19108 weeks
241-.08294 -.14672 (241*2π)/19108 weeks
242-.03361 -.15852 (242*2π)/19108 weeks
243-.09017 -.16983 (243*2π)/19108 weeks
244-.10105 -.08107 (244*2π)/19108 weeks
245-.02953 -.11859 (245*2π)/19108 weeks
246-.03138 -.11865 (246*2π)/19108 weeks
247-.01919 -.18835 (247*2π)/19108 weeks
248-.1524 -.14518 (248*2π)/19108 weeks
249-.02174 -.07337 (249*2π)/19108 weeks
250-.06597 -.13445 (250*2π)/19108 weeks
251-.02177 -.08916 (251*2π)/19108 weeks
252-.0161 -.16189 (252*2π)/19108 weeks
253-.02553 -.15822 (253*2π)/19108 weeks
254-.06126 -.16253 (254*2π)/19108 weeks
255-.02438 -.13214 (255*2π)/19107 weeks
256-.07624 -.22796 (256*2π)/19107 weeks
257-.12332 -.11809 (257*2π)/19107 weeks
258-.08256 -.12473 (258*2π)/19107 weeks
259-.08561 -.11272 (259*2π)/19107 weeks
260-.04011 -.14908 (260*2π)/19107 weeks
261-.11628 -.10708 (261*2π)/19107 weeks
262-.08762 -.10218 (262*2π)/19107 weeks
263-.10281 -.02003 (263*2π)/19107 weeks
264.07916 -.06044 (264*2π)/19107 weeks
265-.00308 -.14806 (265*2π)/19107 weeks
266.01174 -.15973 (266*2π)/19107 weeks
267-.10323 -.17511 (267*2π)/19107 weeks
268-.03784 -.10185 (268*2π)/19107 weeks
269-.09714 -.18896 (269*2π)/19107 weeks
270-.08341 -.06215 (270*2π)/19107 weeks
271-.03249 -.11147 (271*2π)/19107 weeks
272-.00749 -.06877 (272*2π)/19107 weeks
273.01668 -.2007 (273*2π)/19107 weeks
274-.09876 -.16419 (274*2π)/19107 weeks
275-.07485 -.1215 (275*2π)/19107 weeks
276-.08557 -.08658 (276*2π)/19107 weeks
277-.018 -.08829 (277*2π)/19107 weeks
278-.02946 -.11515 (278*2π)/19107 weeks
279-.00003 -.14443 (279*2π)/19107 weeks
280-.0624 -.15933 (280*2π)/19107 weeks
281-.06904 -.12664 (281*2π)/19107 weeks
282-.04954 -.10676 (282*2π)/19107 weeks
283-.02857 -.14633 (283*2π)/19107 weeks
284-.09576 -.10359 (284*2π)/19107 weeks
285-.00156 -.09633 (285*2π)/19107 weeks
286-.04685 -.15403 (286*2π)/19107 weeks
287-.03085 -.10318 (287*2π)/19107 weeks
288-.01125 -.19523 (288*2π)/19107 weeks
289-.09499 -.1233 (289*2π)/19107 weeks
290-.00195 -.1628 (290*2π)/19107 weeks
291-.10778 -.13757 (291*2π)/19107 weeks
292-.03036 -.17061 (292*2π)/19107 weeks
293-.18091 -.18224 (293*2π)/19107 weeks
294-.07602 -.03168 (294*2π)/19106 weeks
295-.05162 -.11476 (295*2π)/19106 weeks
296-.06626 -.1179 (296*2π)/19106 weeks
297-.09164 -.10564 (297*2π)/19106 weeks
298-.05361 -.06689 (298*2π)/19106 weeks
299-.036 -.10437 (299*2π)/19106 weeks
300-.01817 -.08564 (300*2π)/19106 weeks
301-.02249 -.16674 (301*2π)/19106 weeks
302-.08739 -.11028 (302*2π)/19106 weeks
303-.03174 -.13729 (303*2π)/19106 weeks
304-.07513 -.11857 (304*2π)/19106 weeks
305-.05546 -.14278 (305*2π)/19106 weeks
306-.08537 -.09387 (306*2π)/19106 weeks
307-.00675 -.11261 (307*2π)/19106 weeks
308-.08534 -.15294 (308*2π)/19106 weeks
309-.02825 -.08173 (309*2π)/19106 weeks
310-.03823 -.18399 (310*2π)/19106 weeks
311-.1015 -.12272 (311*2π)/19106 weeks
312-.08127 -.15294 (312*2π)/19106 weeks
313-.11369 -.08738 (313*2π)/19106 weeks
314-.05366 -.16232 (314*2π)/19106 weeks
315-.15127 -.07291 (315*2π)/19106 weeks
316-.04426 -.07921 (316*2π)/19106 weeks
317-.10151 -.08449 (317*2π)/19106 weeks
318.00871 -.09094 (318*2π)/19106 weeks
319-.09795 -.13532 (319*2π)/19106 weeks
320-.0604 -.09856 (320*2π)/19106 weeks
321-.07396 -.10834 (321*2π)/19106 weeks
322-.05894 -.11846 (322*2π)/19106 weeks
323-.10172 -.13969 (323*2π)/19106 weeks
324-.09175 -.10036 (324*2π)/19106 weeks
325-.11662 -.07342 (325*2π)/19106 weeks
326-.05598 -.0542 (326*2π)/19106 weeks
327-.05592 -.10682 (327*2π)/19106 weeks
328-.08873 -.0733 (328*2π)/19106 weeks
329-.04237 -.08531 (329*2π)/19106 weeks
330-.06972 -.08672 (330*2π)/19106 weeks
331-.05556 -.07896 (331*2π)/19106 weeks
332-.05808 -.11954 (332*2π)/19106 weeks
333-.08765 -.07518 (333*2π)/19106 weeks
334-.05283 -.10379 (334*2π)/19106 weeks
335-.09938 -.07412 (335*2π)/19106 weeks
336-.05564 -.08105 (336*2π)/19106 weeks
337-.09421 -.06173 (337*2π)/19106 weeks
338-.06019 -.06298 (338*2π)/19106 weeks
339-.02952 -.05942 (339*2π)/19106 weeks
340-.04824 -.11663 (340*2π)/19106 weeks
341-.08581 -.0476 (341*2π)/19106 weeks
342-.01742 -.10566 (342*2π)/19106 weeks
343-.08937 -.08835 (343*2π)/19106 weeks
344-.05948 -.0475 (344*2π)/19106 weeks
345-.05884 -.04531 (345*2π)/19106 weeks
346-.02741 -.04926 (346*2π)/19106 weeks
347.00368 -.05485 (347*2π)/19106 weeks
348-.00518 -.10932 (348*2π)/19105 weeks
349-.00929 -.09593 (349*2π)/19105 weeks
350-.01817 -.13378 (350*2π)/19105 weeks
351-.05253 -.08454 (351*2π)/19105 weeks
352-.02057 -.14513 (352*2π)/19105 weeks
353-.07153 -.118 (353*2π)/19105 weeks
354-.03978 -.11781 (354*2π)/19105 weeks
355-.07676 -.11708 (355*2π)/19105 weeks
356-.06599 -.11438 (356*2π)/19105 weeks
357-.08802 -.0798 (357*2π)/19105 weeks
358-.06486 -.11688 (358*2π)/19105 weeks
359-.09047 -.06707 (359*2π)/19105 weeks
360-.05844 -.07791 (360*2π)/19105 weeks
361-.04075 -.03558 (361*2π)/19105 weeks
362-.03457 -.11395 (362*2π)/19105 weeks
363-.03453 -.058 (363*2π)/19105 weeks
364-.01311 -.13438 (364*2π)/19105 weeks
365-.0366 -.0982 (365*2π)/19105 weeks
366-.03473 -.18768 (366*2π)/19105 weeks
367-.12036 -.10627 (367*2π)/19105 weeks
368-.06414 -.12079 (368*2π)/19105 weeks
369-.11281 -.12083 (369*2π)/19105 weeks
370-.11004 -.11015 (370*2π)/19105 weeks
371-.15332 -.04549 (371*2π)/19105 weeks
372-.0463 -.04824 (372*2π)/19105 weeks
373-.10025 -.06456 (373*2π)/19105 weeks
374-.0538 -.03381