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Fourier Analysis of AET (Aetna Inc. Common Stock)


AET (Aetna Inc. Common Stock) appears to have interesting cyclic behaviour every 210 weeks (4.0729*sine), 150 weeks (3.3705*sine), and 191 weeks (3.2977*sine).

AET (Aetna Inc. Common Stock) has an average price of 20.61 (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 1/3/1977 to 4/24/2017 for AET (Aetna Inc. Common Stock), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
020.61008   0 
117.81599 -18.79124 (1*2π)/21032,103 weeks
26.62525 -12.94657 (2*2π)/21031,052 weeks
37.28895 -8.097 (3*2π)/2103701 weeks
48.07452 -11.92929 (4*2π)/2103526 weeks
5.63651 -11.89328 (5*2π)/2103421 weeks
6-.65769 -6.90089 (6*2π)/2103351 weeks
7.95742 -5.6995 (7*2π)/2103300 weeks
8.86775 -6.08224 (8*2π)/2103263 weeks
9-.49835 -5.57129 (9*2π)/2103234 weeks
10-.84341 -4.0729 (10*2π)/2103210 weeks
11-.96431 -3.29766 (11*2π)/2103191 weeks
12-.12727 -2.45086 (12*2π)/2103175 weeks
13.73658 -2.42814 (13*2π)/2103162 weeks
14.30335 -3.37046 (14*2π)/2103150 weeks
15-.71587 -2.72916 (15*2π)/2103140 weeks
16-.22262 -1.57018 (16*2π)/2103131 weeks
17.71126 -1.78846 (17*2π)/2103124 weeks
18.2571 -2.49427 (18*2π)/2103117 weeks
19-.42619 -1.88319 (19*2π)/2103111 weeks
20.3014 -.79517 (20*2π)/2103105 weeks
211.1608 -1.59291 (21*2π)/2103100 weeks
221.09271 -2.27724 (22*2π)/210396 weeks
23.16368 -2.55151 (23*2π)/210391 weeks
24.22395 -1.84095 (24*2π)/210388 weeks
25.13005 -2.22016 (25*2π)/210384 weeks
26-.08883 -1.80297 (26*2π)/210381 weeks
27-.03502 -1.8592 (27*2π)/210378 weeks
28-.23383 -1.69168 (28*2π)/210375 weeks
29-.16988 -1.59022 (29*2π)/210373 weeks
30-.30386 -1.60116 (30*2π)/210370 weeks
31-.34134 -1.21641 (31*2π)/210368 weeks
32.00184 -1.16149 (32*2π)/210366 weeks
33-.20889 -1.44456 (33*2π)/210364 weeks
34-.32211 -1.2224 (34*2π)/210362 weeks
35-.39549 -.99268 (35*2π)/210360 weeks
36-.28765 -.80152 (36*2π)/210358 weeks
37-.26624 -.73509 (37*2π)/210357 weeks
38-.00904 -.47871 (38*2π)/210355 weeks
39.3033 -.56993 (39*2π)/210354 weeks
40.57696 -.79738 (40*2π)/210353 weeks
41.19482 -1.20332 (41*2π)/210351 weeks
42.17291 -.80976 (42*2π)/210350 weeks
43.3966 -1.09472 (43*2π)/210349 weeks
44.01943 -1.18482 (44*2π)/210348 weeks
45.01644 -.88276 (45*2π)/210347 weeks
46.30838 -.78556 (46*2π)/210346 weeks
47.34693 -1.3056 (47*2π)/210345 weeks
48-.10016 -1.27377 (48*2π)/210344 weeks
49-.14868 -.92141 (49*2π)/210343 weeks
50-.0686 -1.00002 (50*2π)/210342 weeks
51-.11672 -.97064 (51*2π)/210341 weeks
52-.20489 -.83304 (52*2π)/210340 weeks
53-.11728 -.77246 (53*2π)/210340 weeks
54.00599 -.62962 (54*2π)/210339 weeks
55.16853 -.89435 (55*2π)/210338 weeks
56-.05628 -.9712 (56*2π)/210338 weeks
57-.08679 -.93458 (57*2π)/210337 weeks
58-.36561 -.80806 (58*2π)/210336 weeks
59-.19764 -.57039 (59*2π)/210336 weeks
60-.07061 -.59679 (60*2π)/210335 weeks
61.05494 -.63816 (61*2π)/210334 weeks
62-.04729 -.86676 (62*2π)/210334 weeks
63-.16589 -.61615 (63*2π)/210333 weeks
64.00307 -.62108 (64*2π)/210333 weeks
65.00378 -.82831 (65*2π)/210332 weeks
66-.36052 -.81399 (66*2π)/210332 weeks
67-.30958 -.40431 (67*2π)/210331 weeks
68-.03623 -.44325 (68*2π)/210331 weeks
69.09166 -.50945 (69*2π)/210330 weeks
70-.05439 -.76508 (70*2π)/210330 weeks
71-.26805 -.58422 (71*2π)/210330 weeks
72-.07278 -.35641 (72*2π)/210329 weeks
73.09483 -.49597 (73*2π)/210329 weeks
74.00965 -.71379 (74*2π)/210328 weeks
75-.17443 -.71771 (75*2π)/210328 weeks
76-.24647 -.47926 (76*2π)/210328 weeks
77-.12418 -.42321 (77*2π)/210327 weeks
78-.07368 -.4543 (78*2π)/210327 weeks
79-.07629 -.50216 (79*2π)/210327 weeks
80-.17641 -.47535 (80*2π)/210326 weeks
81-.1135 -.32009 (81*2π)/210326 weeks
82-.0451 -.41067 (82*2π)/210326 weeks
83.01354 -.37341 (83*2π)/210325 weeks
84.03578 -.44078 (84*2π)/210325 weeks
85-.0816 -.42134 (85*2π)/210325 weeks
86-.01385 -.39284 (86*2π)/210324 weeks
87-.00441 -.3859 (87*2π)/210324 weeks
88.07655 -.41095 (88*2π)/210324 weeks
89.03916 -.51766 (89*2π)/210324 weeks
90-.03958 -.55311 (90*2π)/210323 weeks
91-.13681 -.43055 (91*2π)/210323 weeks
92-.04159 -.34857 (92*2π)/210323 weeks
93-.02507 -.41149 (93*2π)/210323 weeks
94-.03975 -.40238 (94*2π)/210322 weeks
95-.04518 -.38345 (95*2π)/210322 weeks
96-.07688 -.32694 (96*2π)/210322 weeks
97.0458 -.22819 (97*2π)/210322 weeks
98.16157 -.40482 (98*2π)/210321 weeks
99.02899 -.52326 (99*2π)/210321 weeks
100-.11401 -.39123 (100*2π)/210321 weeks
101.01941 -.23531 (101*2π)/210321 weeks
102.16005 -.3356 (102*2π)/210321 weeks
103.11205 -.49558 (103*2π)/210320 weeks
104.03977 -.49004 (104*2π)/210320 weeks
105-.00285 -.51442 (105*2π)/210320 weeks
106-.10456 -.44209 (106*2π)/210320 weeks
107-.02232 -.29042 (107*2π)/210320 weeks
108.08143 -.42779 (108*2π)/210319 weeks
109-.00508 -.43453 (109*2π)/210319 weeks
110-.01209 -.39002 (110*2π)/210319 weeks
111.03013 -.34166 (111*2π)/210319 weeks
112.10212 -.44584 (112*2π)/210319 weeks
113.00934 -.54565 (113*2π)/210319 weeks
114-.1132 -.46417 (114*2π)/210318 weeks
115-.07425 -.3275 (115*2π)/210318 weeks
116.12448 -.36825 (116*2π)/210318 weeks
117.05328 -.54938 (117*2π)/210318 weeks
118-.09065 -.55225 (118*2π)/210318 weeks
119-.16389 -.44413 (119*2π)/210318 weeks
120-.10603 -.33628 (120*2π)/210318 weeks
121-.03011 -.32921 (121*2π)/210317 weeks
122.04582 -.44987 (122*2π)/210317 weeks
123-.07716 -.51235 (123*2π)/210317 weeks
124-.22302 -.41295 (124*2π)/210317 weeks
125-.08016 -.21019 (125*2π)/210317 weeks
126.10109 -.38759 (126*2π)/210317 weeks
127-.04352 -.58198 (127*2π)/210317 weeks
128-.27565 -.42298 (128*2π)/210316 weeks
129-.1664 -.19154 (129*2π)/210316 weeks
130.08106 -.29137 (130*2π)/210316 weeks
131.03404 -.51081 (131*2π)/210316 weeks
132-.15738 -.48449 (132*2π)/210316 weeks
133-.20751 -.392 (133*2π)/210316 weeks
134-.15527 -.30542 (134*2π)/210316 weeks
135-.10813 -.33405 (135*2π)/210316 weeks
136-.11321 -.34038 (136*2π)/210315 weeks
137-.10468 -.40048 (137*2π)/210315 weeks
138-.23968 -.37852 (138*2π)/210315 weeks
139-.20374 -.22778 (139*2π)/210315 weeks
140-.14184 -.20614 (140*2π)/210315 weeks
141-.03892 -.22743 (141*2π)/210315 weeks
142-.04305 -.32796 (142*2π)/210315 weeks
143-.12278 -.34793 (143*2π)/210315 weeks
144-.14643 -.29717 (144*2π)/210315 weeks
145-.13588 -.26048 (145*2π)/210315 weeks
146-.13105 -.2678 (146*2π)/210314 weeks
147-.16848 -.20724 (147*2π)/210314 weeks
148-.03618 -.16319 (148*2π)/210314 weeks
149-.03334 -.27476 (149*2π)/210314 weeks
150-.05164 -.28084 (150*2π)/210314 weeks
151-.06185 -.24674 (151*2π)/210314 weeks
152-.01339 -.25216 (152*2π)/210314 weeks
153-.00582 -.37575 (153*2π)/210314 weeks
154-.11235 -.36713 (154*2π)/210314 weeks
155-.12401 -.32574 (155*2π)/210314 weeks
156-.11632 -.35011 (156*2π)/210313 weeks
157-.22487 -.34417 (157*2π)/210313 weeks
158-.16981 -.26319 (158*2π)/210313 weeks
159-.16921 -.30272 (159*2π)/210313 weeks
160-.21936 -.35069 (160*2π)/210313 weeks
161-.39433 -.21534 (161*2π)/210313 weeks
162-.21481 -.04022 (162*2π)/210313 weeks
163-.13885 -.16592 (163*2π)/210313 weeks
164-.25408 -.13664 (164*2π)/210313 weeks
165-.22597 .02794 (165*2π)/210313 weeks
166.00965 .02222 (166*2π)/210313 weeks
167-.02821 -.14049 (167*2π)/210313 weeks
168-.06055 -.10468 (168*2π)/210313 weeks
169-.01543 -.07298 (169*2π)/210312 weeks
170.05406 -.15693 (170*2π)/210312 weeks
171-.03174 -.20649 (171*2π)/210312 weeks
172-.02991 -.17708 (172*2π)/210312 weeks
173-.08267 -.18991 (173*2π)/210312 weeks
174-.05606 -.11274 (174*2π)/210312 weeks
175.00007 -.11366 (175*2π)/210312 weeks
176.00265 -.18586 (176*2π)/210312 weeks
177-.05682 -.18244 (177*2π)/210312 weeks
178-.05399 -.13296 (178*2π)/210312 weeks
179-.03404 -.11382 (179*2π)/210312 weeks
180.04434 -.08239 (180*2π)/210312 weeks
181.10027 -.16802 (181*2π)/210312 weeks
182.05706 -.2552 (182*2π)/210312 weeks
183-.02602 -.25651 (183*2π)/210311 weeks
184-.04737 -.16136 (184*2π)/210311 weeks
185.02264 -.17609 (185*2π)/210311 weeks
186.00974 -.21427 (186*2π)/210311 weeks
187-.03683 -.21912 (187*2π)/210311 weeks
188-.03768 -.16074 (188*2π)/210311 weeks
189.04184 -.16161 (189*2π)/210311 weeks
190.03992 -.23361 (190*2π)/210311 weeks
191-.01032 -.25389 (191*2π)/210311 weeks
192-.05784 -.22144 (192*2π)/210311 weeks
193-.0069 -.16609 (193*2π)/210311 weeks
194.03471 -.22782 (194*2π)/210311 weeks
195-.00827 -.27575 (195*2π)/210311 weeks
196-.09625 -.24265 (196*2π)/210311 weeks
197-.0383 -.15652 (197*2π)/210311 weeks
198.01708 -.20145 (198*2π)/210311 weeks
199-.01836 -.24631 (199*2π)/210311 weeks
200-.04221 -.23506 (200*2π)/210311 weeks
201-.03935 -.23748 (201*2π)/210310 weeks
202-.09166 -.23049 (202*2π)/210310 weeks
203-.06911 -.19039 (203*2π)/210310 weeks
204-.09755 -.19779 (204*2π)/210310 weeks
205-.068 -.15068 (205*2π)/210310 weeks
206-.06888 -.1649 (206*2π)/210310 weeks
207-.04986 -.10626 (207*2π)/210310 weeks
208.01552 -.15317 (208*2π)/210310 weeks
209-.02396 -.16665 (209*2π)/210310 weeks
210.01438 -.14215 (210*2π)/210310 weeks
211.01065 -.17715 (211*2π)/210310 weeks
212.02277 -.17939 (212*2π)/210310 weeks
213-.00566 -.15841 (213*2π)/210310 weeks
214.09615 -.16586 (214*2π)/210310 weeks
215.08272 -.27036 (215*2π)/210310 weeks
216.02525 -.30622 (216*2π)/210310 weeks
217-.0423 -.32049 (217*2π)/210310 weeks
218-.07144 -.25858 (218*2π)/210310 weeks
219-.07838 -.23213 (219*2π)/210310 weeks
220-.04728 -.23666 (220*2π)/210310 weeks
221-.04919 -.21395 (221*2π)/210310 weeks
222.00476 -.27209 (222*2π)/21039 weeks
223-.10668 -.34487 (223*2π)/21039 weeks
224-.19549 -.22711 (224*2π)/21039 weeks
225-.16571 -.15754 (225*2π)/21039 weeks
226-.08793 -.15866 (226*2π)/21039 weeks
227-.12804 -.16233 (227*2π)/21039 weeks
228-.0949 -.1288 (228*2π)/21039 weeks
229-.07251 -.12155 (229*2π)/21039 weeks
230-.04425 -.10947 (230*2π)/21039 weeks
231.00708 -.1602 (231*2π)/21039 weeks
232-.04881 -.19945 (232*2π)/21039 weeks
233-.04329 -.16572 (233*2π)/21039 weeks
234-.04163 -.1998 (234*2π)/21039 weeks
235-.07789 -.18978 (235*2π)/21039 weeks
236-.06277 -.16597 (236*2π)/21039 weeks
237-.07233 -.17709 (237*2π)/21039 weeks
238-.06648 -.1588 (238*2π)/21039 weeks
239-.09172 -.1476 (239*2π)/21039 weeks
240-.02026 -.11371 (240*2π)/21039 weeks
241-.03361 -.18744 (241*2π)/21039 weeks
242-.05949 -.15583 (242*2π)/21039 weeks
243-.04199 -.16448 (243*2π)/21039 weeks
244-.0251 -.13243 (244*2π)/21039 weeks
245.00226 -.2249 (245*2π)/21039 weeks
246-.08767 -.21208 (246*2π)/21039 weeks
247-.06115 -.18719 (247*2π)/21039 weeks
248-.07527 -.17497 (248*2π)/21038 weeks
249-.03519 -.19721 (249*2π)/21038 weeks
250-.1022 -.2559 (250*2π)/21038 weeks
251-.16983 -.19113 (251*2π)/21038 weeks
252-.19049 -.13681 (252*2π)/21038 weeks
253-.17004 -.06086 (253*2π)/21038 weeks
254-.09667 -.00888 (254*2π)/21038 weeks
255-.01534 -.03071 (255*2π)/21038 weeks
256-.00112 -.09792 (256*2π)/21038 weeks
257-.02703 -.09567 (257*2π)/21038 weeks
258.00958 -.10082 (258*2π)/21038 weeks
259.00451 -.1615 (259*2π)/21038 weeks
260-.05443 -.17021 (260*2π)/21038 weeks
261-.08122 -.11578 (261*2π)/21038 weeks
262-.03084 -.06152 (262*2π)/21038 weeks
263.03344 -.10695 (263*2π)/21038 weeks
264.01172 -.15246 (264*2π)/21038 weeks
265-.0081 -.15855 (265*2π)/21038 weeks
266-.03806 -.17129 (266*2π)/21038 weeks
267-.06815 -.13058 (267*2π)/21038 weeks
268-.03273 -.09436 (268*2π)/21038 weeks
269.02923 -.12937 (269*2π)/21038 weeks
270-.02567 -.15225 (270*2π)/21038 weeks
271-.00017 -.12876 (271*2π)/21038 weeks
272.00343 -.15512 (272*2π)/21038 weeks
273-.02144 -.16658 (273*2π)/21038 weeks
274-.03138 -.13876 (274*2π)/21038 weeks
275-.00486 -.12226 (275*2π)/21038 weeks
276-.00053 -.16146 (276*2π)/21038 weeks
277-.01728 -.13963 (277*2π)/21038 weeks
278-.00233 -.1265 (278*2π)/21038 weeks
279.04808 -.12353 (279*2π)/21038 weeks
280.06824 -.21428 (280*2π)/21038 weeks
281-.01491 -.23709 (281*2π)/21037 weeks
282-.06639 -.18583 (282*2π)/21037 weeks
283-.02495 -.12206 (283*2π)/21037 weeks
284.04449 -.15055 (284*2π)/21037 weeks
285.04413 -.23437 (285*2π)/21037 weeks
286-.01749 -.25483 (286*2π)/21037 weeks
287-.05448 -.22549 (287*2π)/21037 weeks
288-.0474 -.24329 (288*2π)/21037 weeks
289-.08642 -.20492 (289*2π)/21037 weeks
290-.06432 -.19462 (290*2π)/21037 weeks
291-.08345 -.19716 (291*2π)/21037 weeks
292-.07016 -.1979 (292*2π)/21037 weeks
293-.09258 -.16397 (293*2π)/21037 weeks
294-.03827 -.17727 (294*2π)/21037 weeks
295-.07521 -.22483 (295*2π)/21037 weeks
296-.13169 -.22421 (296*2π)/21037 weeks
297-.16847 -.13116 (297*2π)/21037 weeks
298-.08712 -.08906 (298*2π)/21037 weeks
299-.07512 -.12738 (299*2π)/21037 weeks
300-.06428 -.13406 (300*2π)/21037 weeks
301-.0827 -.12371 (301*2π)/21037 weeks
302-.063 -.09341 (302*2π)/21037 weeks
303-.013 -.10095 (303*2π)/21037 weeks
304.01397 -.16557 (304*2π)/21037 weeks
305-.03856 -.19988 (305*2π)/21037 weeks
306-.06166 -.20049 (306*2π)/21037 weeks
307-.09571 -.1604 (307*2π)/21037 weeks
308-.04838 -.15289 (308*2π)/21037 weeks
309-.06103 -.199 (309*2π)/21037 weeks
310-.11172 -.17339 (310*2π)/21037 weeks
311-.10813 -.13219 (311*2π)/21037 weeks
312-.07159 -.12856 (312*2π)/21037 weeks
313-.05982 -.15995 (313*2π)/21037 weeks
314-.08964 -.18709 (314*2π)/21037 weeks
315-.13321 -.13188 (315*2π)/21037 weeks
316-.0951 -.09833 (316*2π)/21037 weeks
317-.06128 -.11197 (317*2π)/21037 weeks
318-.0607 -.12723 (318*2π)/21037 weeks
319-.06647 -.13708 (319*2π)/21037 weeks
320-.07235 -.12671 (320*2π)/21037 weeks
321-.07243 -.14876 (321*2π)/21037 weeks
322-.08152 -.11615 (322*2π)/21037 weeks
323-.04037 -.12086 (323*2π)/21037 weeks
324-.04774 -.15973 (324*2π)/21036 weeks
325-.10117 -.18386 (325*2π)/21036 weeks
326-.12593 -.10245 (326*2π)/21036 weeks
327-.03826 -.08268 (327*2π)/21036 weeks
328-.02907 -.15387 (328*2π)/21036 weeks
329-.06388 -.1863 (329*2π)/21036 weeks
330-.1059 -.16831 (330*2π)/21036 weeks
331-.11342 -.16112 (331*2π)/21036 weeks
332-.12933 -.12309 (332*2π)/21036 weeks
333-.10269 -.13597 (333*2π)/21036 weeks
334-.12537 -.13959 (334*2π)/21036 weeks
335-.14661 -.1067 (335*2π)/21036 weeks
336-.12628 -.06783 (336*2π)/21036 weeks
337-.12216 -.07913 (337*2π)/21036 weeks
338-.09443 -.03646 (338*2π)/21036 weeks
339-.05888 -.0783 (339*2π)/21036 weeks
340-.10423 -.0771 (340*2π)/21036 weeks
341-.08318 -.06773 (341*2π)/21036 weeks
342-.08114 -.01799 (342*2π)/21036 weeks
343-.00898 -.0672 (343*2π)/21036 weeks
344-.06785 -.08465 (344*2π)/21036 weeks
345-.03981 -.06155 (345*2π)/21036 weeks
346-.05105 -.06228 (346*2π)/21036 weeks
347-.00982 -.05214 (347*2π)/21036 weeks
348-.01481 -.07005 (348*2π)/21036 weeks
349.01175 -.08211 (349*2π)/21036 weeks
350.01417 -.09402 (350*2π)/21036 weeks
351.02891 -.14238 (351*2π)/21036 weeks
352-.01468 -.16054 (352*2π)/21036 weeks
353-.01722 -.174 (353*2π)/21036 weeks
354-.06851 -.17057 (354*2π)/21036 weeks
355-.06412 -.14672 (355*2π)/21036 weeks
356-.07405 -.1424 (356*2π)/21036 weeks
357-.05616 -.12688 (357*2π)/21036 weeks
358-.08369 -.15662 (358*2π)/21036 weeks
359-.1052 -.11803 (359*2π)/21036 weeks
360-.09369 -.10042 (360*2π)/21036 weeks
361-.08213 -.09363 (361*2π)/21036 weeks
362-.07692 -.0876 (362*2π)/21036 weeks
363-.06666 -.08158 (363*2π)/21036 weeks
364-.0465 -.07868 (364*2π)/21036 weeks
365-.01657 -.09994 (365*2π)/21036 weeks
366-.05507 -.13781 (366*2π)/21036 weeks
367-.07815 -.09303 (367*2π)/21036 weeks
368-.04001 -.08613 (368*2π)/21036 weeks
369-.03712 -.10485 (369*2π)/21036 weeks
370-.04521 -.11302 (370*2π)/21036 weeks
371-.04377 -.0969 (371*2π)/21036 weeks
372-.01602 -.11718 (372*2π)/21036 weeks
373-.03562 -.1292 (373*2π)/21036 weeks
374-.04643 -.14034 (374*2π)/21036 weeks
375-.04757 -.13059 (375*2π)/21036 weeks
376-.05936 -.13234 (376*2π)/21036 weeks
377-.03429 -.13904 (377*2π)/21036 weeks
378-.05964 -.18114 (378*2π)/21036 weeks
379-.11015 -.15582 (379*2π)/21036 weeks
380-.11538 -.1315 (380*2π)/21036 weeks
381-.10944 -.12328 (381*2π)/21036 weeks
382-.12551 -.11831 (382*2π)/21036 weeks
383-.11278 -.077 (383*2π)/21035 weeks
384-.10826 -.09578 (384*2π)/21035 weeks
385-.13294 -.04128 (385*2π)/21035 weeks
386-.05938 -.02767 (386*2π)/21035 weeks
387-.0297 -.04972 (387*2π)/21035 weeks
388-.04072 -.08939