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Fourier Analysis of AET (Aetna Inc. Common Stock)


AET (Aetna Inc. Common Stock) appears to have interesting cyclic behaviour every 209 weeks (4.2711*sine), 190 weeks (3.5319*sine), and 95 weeks (1.1412*cosine).

AET (Aetna Inc. Common Stock) has an average price of 20.22 (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 2/21/2017 for AET (Aetna Inc. Common Stock), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
020.21818   0 
117.27485 -18.45603 (1*2π)/20942,094 weeks
26.22137 -12.62714 (2*2π)/20941,047 weeks
36.91161 -7.56705 (3*2π)/2094698 weeks
48.20233 -11.2408 (4*2π)/2094524 weeks
51.01567 -11.75714 (5*2π)/2094419 weeks
6-.62308 -6.95178 (6*2π)/2094349 weeks
7.93145 -5.55833 (7*2π)/2094299 weeks
81.02566 -5.93521 (8*2π)/2094262 weeks
9-.29288 -5.65789 (9*2π)/2094233 weeks
10-.81348 -4.27106 (10*2π)/2094209 weeks
11-1.07963 -3.53187 (11*2π)/2094190 weeks
12-.41186 -2.5259 (12*2π)/2094175 weeks
13.50661 -2.25616 (13*2π)/2094161 weeks
14.38154 -3.26352 (14*2π)/2094150 weeks
15-.72998 -2.93768 (15*2π)/2094140 weeks
16-.57324 -1.68616 (16*2π)/2094131 weeks
17.41963 -1.57345 (17*2π)/2094123 weeks
18.25826 -2.36803 (18*2π)/2094116 weeks
19-.57824 -2.04167 (19*2π)/2094110 weeks
20-.27135 -.71196 (20*2π)/2094105 weeks
21.81263 -1.05439 (21*2π)/2094100 weeks
221.14118 -1.66346 (22*2π)/209495 weeks
23.45825 -2.28835 (23*2π)/209491 weeks
24.31073 -1.63488 (24*2π)/209487 weeks
25.39413 -2.02836 (25*2π)/209484 weeks
26.08136 -1.74653 (26*2π)/209481 weeks
27.17458 -1.78773 (27*2π)/209478 weeks
28-.04726 -1.73038 (28*2π)/209475 weeks
29-.01547 -1.62508 (29*2π)/209472 weeks
30-.11151 -1.72915 (30*2π)/209470 weeks
31-.33089 -1.42386 (31*2π)/209468 weeks
32-.04507 -1.17467 (32*2π)/209465 weeks
33-.05381 -1.5183 (33*2π)/209463 weeks
34-.22139 -1.44049 (34*2π)/209462 weeks
35-.41657 -1.31339 (35*2π)/209460 weeks
36-.4597 -1.10589 (36*2π)/209458 weeks
37-.53538 -1.05034 (37*2π)/209457 weeks
38-.52417 -.6707 (38*2π)/209455 weeks
39-.26619 -.48192 (39*2π)/209454 weeks
40.14754 -.38902 (40*2π)/209452 weeks
41.14286 -.92038 (41*2π)/209451 weeks
42-.08553 -.62165 (42*2π)/209450 weeks
43.29661 -.66369 (43*2π)/209449 weeks
44.12506 -.98171 (44*2π)/209448 weeks
45-.08075 -.79863 (45*2π)/209447 weeks
46.04607 -.44758 (46*2π)/209446 weeks
47.4961 -.74201 (47*2π)/209445 weeks
48.27038 -1.06027 (48*2π)/209444 weeks
49.00716 -.88023 (49*2π)/209443 weeks
50.10025 -.89087 (50*2π)/209442 weeks
51.08572 -.92272 (51*2π)/209441 weeks
52-.0766 -.91306 (52*2π)/209440 weeks
53-.09122 -.84233 (53*2π)/209440 weeks
54-.15448 -.60675 (54*2π)/209439 weeks
55.16705 -.59216 (55*2π)/209438 weeks
56.15706 -.78043 (56*2π)/209437 weeks
57.20305 -.80516 (57*2π)/209437 weeks
58-.05692 -.99909 (58*2π)/209436 weeks
59-.18772 -.7833 (59*2π)/209435 weeks
60-.15277 -.68033 (60*2π)/209435 weeks
61-.05033 -.53358 (61*2π)/209434 weeks
62.13233 -.73785 (62*2π)/209434 weeks
63-.10735 -.71054 (63*2π)/209433 weeks
64-.048 -.54417 (64*2π)/209433 weeks
65.19894 -.59189 (65*2π)/209432 weeks
66.08558 -.95822 (66*2π)/209432 weeks
67-.27187 -.81098 (67*2π)/209431 weeks
68-.20526 -.6095 (68*2π)/209431 weeks
69-.09868 -.4203 (69*2π)/209430 weeks
70.12079 -.6216 (70*2π)/209430 weeks
71-.0761 -.8036 (71*2π)/209429 weeks
72-.24976 -.57041 (72*2π)/209429 weeks
73-.12088 -.39321 (73*2π)/209429 weeks
74.08653 -.47991 (74*2π)/209428 weeks
75.13382 -.67298 (75*2π)/209428 weeks
76-.0756 -.7103 (76*2π)/209428 weeks
77-.12469 -.61406 (77*2π)/209427 weeks
78-.10301 -.55998 (78*2π)/209427 weeks
79-.03565 -.55573 (79*2π)/209427 weeks
80-.06206 -.671 (80*2π)/209426 weeks
81-.21178 -.59075 (81*2π)/209426 weeks
82-.15265 -.57599 (82*2π)/209426 weeks
83-.17463 -.48901 (83*2π)/209425 weeks
84-.09236 -.43763 (84*2π)/209425 weeks
85-.13824 -.53404 (85*2π)/209425 weeks
86-.15224 -.48852 (86*2π)/209424 weeks
87-.18643 -.47701 (87*2π)/209424 weeks
88-.17137 -.36747 (88*2π)/209424 weeks
89-.07055 -.36522 (89*2π)/209424 weeks
90.03114 -.42864 (90*2π)/209423 weeks
91-.05463 -.53765 (91*2π)/209423 weeks
92-.13695 -.46336 (92*2π)/209423 weeks
93-.09504 -.45064 (93*2π)/209423 weeks
94-.08767 -.45951 (94*2π)/209422 weeks
95-.08101 -.46915 (95*2π)/209422 weeks
96-.13648 -.54546 (96*2π)/209422 weeks
97-.30298 -.44266 (97*2π)/209422 weeks
98-.19333 -.27532 (98*2π)/209421 weeks
99-.01727 -.32917 (99*2π)/209421 weeks
100-.07156 -.51144 (100*2π)/209421 weeks
101-.26552 -.45473 (101*2π)/209421 weeks
102-.27852 -.28653 (102*2π)/209421 weeks
103-.14593 -.25468 (103*2π)/209420 weeks
104-.11303 -.26575 (104*2π)/209420 weeks
105-.02503 -.27506 (105*2π)/209420 weeks
106-.01794 -.4122 (106*2π)/209420 weeks
107-.20433 -.39712 (107*2π)/209420 weeks
108-.12556 -.27959 (108*2π)/209419 weeks
109-.09057 -.31897 (109*2π)/209419 weeks
110-.11032 -.34849 (110*2π)/209419 weeks
111-.21522 -.33008 (111*2π)/209419 weeks
112-.18719 -.20318 (112*2π)/209419 weeks
113-.04125 -.19147 (113*2π)/209419 weeks
114-.00661 -.32152 (114*2π)/209418 weeks
115-.14621 -.41081 (115*2π)/209418 weeks
116-.23994 -.21252 (116*2π)/209418 weeks
117-.10211 -.12487 (117*2π)/209418 weeks
118.01857 -.17755 (118*2π)/209418 weeks
119.0343 -.29495 (119*2π)/209418 weeks
120-.05513 -.33623 (120*2π)/209417 weeks
121-.16004 -.31898 (121*2π)/209417 weeks
122-.12443 -.16514 (122*2π)/209417 weeks
123.01122 -.14206 (123*2π)/209417 weeks
124.08699 -.342 (124*2π)/209417 weeks
125-.16902 -.39995 (125*2π)/209417 weeks
126-.22436 -.16497 (126*2π)/209417 weeks
127.02157 -.05185 (127*2π)/209416 weeks
128.13269 -.28247 (128*2π)/209416 weeks
129-.08214 -.44442 (129*2π)/209416 weeks
130-.23888 -.26212 (130*2π)/209416 weeks
131-.10962 -.08007 (131*2π)/209416 weeks
132.00431 -.12701 (132*2π)/209416 weeks
133.04578 -.21738 (133*2π)/209416 weeks
134-.02173 -.25779 (134*2π)/209416 weeks
135-.0378 -.23007 (135*2π)/209416 weeks
136-.06718 -.22506 (136*2π)/209415 weeks
137-.02098 -.1217 (137*2π)/209415 weeks
138.11227 -.2006 (138*2π)/209415 weeks
139.06115 -.28413 (139*2π)/209415 weeks
140.00723 -.34617 (140*2π)/209415 weeks
141-.09344 -.29822 (141*2π)/209415 weeks
142-.08248 -.20775 (142*2π)/209415 weeks
143-.01395 -.19726 (143*2π)/209415 weeks
144.0098 -.21947 (144*2π)/209415 weeks
145-.0046 -.23473 (145*2π)/209414 weeks
146.02765 -.21325 (146*2π)/209414 weeks
147.055 -.32825 (147*2π)/209414 weeks
148-.08098 -.32366 (148*2π)/209414 weeks
149-.06824 -.27501 (149*2π)/209414 weeks
150-.04652 -.25171 (150*2π)/209414 weeks
151-.06404 -.28837 (151*2π)/209414 weeks
152-.16391 -.29175 (152*2π)/209414 weeks
153-.15028 -.16402 (153*2π)/209414 weeks
154-.09323 -.15687 (154*2π)/209414 weeks
155-.10306 -.16971 (155*2π)/209414 weeks
156-.11257 -.08685 (156*2π)/209413 weeks
157-.00568 -.12643 (157*2π)/209413 weeks
158-.05592 -.1422 (158*2π)/209413 weeks
159-.07953 -.10093 (159*2π)/209413 weeks
160.00532 .05362 (160*2π)/209413 weeks
161.21139 -.09894 (161*2π)/209413 weeks
162.07923 -.21838 (162*2π)/209413 weeks
163.06034 -.09845 (163*2π)/209413 weeks
164.2016 -.10723 (164*2π)/209413 weeks
165.23657 -.32233 (165*2π)/209413 weeks
166.03351 -.33067 (166*2π)/209413 weeks
167.06041 -.25873 (167*2π)/209413 weeks
168.09088 -.2839 (168*2π)/209412 weeks
169.03673 -.3597 (169*2π)/209412 weeks
170-.04775 -.28503 (170*2π)/209412 weeks
171-.00444 -.25616 (171*2π)/209412 weeks
172-.03251 -.2275 (172*2π)/209412 weeks
173.04866 -.21253 (173*2π)/209412 weeks
174.05547 -.26476 (174*2π)/209412 weeks
175-.00966 -.29584 (175*2π)/209412 weeks
176-.03215 -.23564 (176*2π)/209412 weeks
177.0173 -.21512 (177*2π)/209412 weeks
178.04054 -.23474 (178*2π)/209412 weeks
179.09041 -.2772 (179*2π)/209412 weeks
180.03386 -.36049 (180*2π)/209412 weeks
181-.06211 -.3522 (181*2π)/209412 weeks
182-.09637 -.27151 (182*2π)/209412 weeks
183-.03192 -.1996 (183*2π)/209411 weeks
184.00237 -.26961 (184*2π)/209411 weeks
185-.04235 -.27814 (185*2π)/209411 weeks
186-.07006 -.24481 (186*2π)/209411 weeks
187-.02495 -.20949 (187*2π)/209411 weeks
188.02262 -.26719 (188*2π)/209411 weeks
189-.03879 -.30943 (189*2π)/209411 weeks
190-.08539 -.27663 (190*2π)/209411 weeks
191-.08795 -.22215 (191*2π)/209411 weeks
192-.01403 -.21734 (192*2π)/209411 weeks
193-.02873 -.29029 (193*2π)/209411 weeks
194-.09283 -.28619 (194*2π)/209411 weeks
195-.12962 -.20624 (195*2π)/209411 weeks
196-.02701 -.17653 (196*2π)/209411 weeks
197-.01714 -.25004 (197*2π)/209411 weeks
198-.07639 -.26133 (198*2π)/209411 weeks
199-.08664 -.23243 (199*2π)/209411 weeks
200-.08242 -.23097 (200*2π)/209410 weeks
201-.11866 -.19919 (201*2π)/209410 weeks
202-.07452 -.17517 (202*2π)/209410 weeks
203-.09874 -.17427 (203*2π)/209410 weeks
204-.04901 -.14759 (204*2π)/209410 weeks
205-.05495 -.16534 (205*2π)/209410 weeks
206-.01581 -.12633 (206*2π)/209410 weeks
207.01964 -.19871 (207*2π)/209410 weeks
208-.02679 -.19368 (208*2π)/209410 weeks
209.01562 -.18404 (209*2π)/209410 weeks
210-.00398 -.21623 (210*2π)/209410 weeks
211.00463 -.21788 (211*2π)/209410 weeks
212-.01575 -.19201 (212*2π)/209410 weeks
213.07333 -.2318 (213*2π)/209410 weeks
214.01942 -.32265 (214*2π)/209410 weeks
215-.04772 -.32902 (215*2π)/209410 weeks
216-.11022 -.31557 (216*2π)/209410 weeks
217-.11607 -.24435 (217*2π)/209410 weeks
218-.11093 -.22026 (218*2π)/209410 weeks
219-.07847 -.23248 (219*2π)/209410 weeks
220-.07633 -.21196 (220*2π)/209410 weeks
221-.03666 -.27799 (221*2π)/20949 weeks
222-.15849 -.32429 (222*2π)/20949 weeks
223-.22068 -.1914 (223*2π)/20949 weeks
224-.17451 -.13237 (224*2π)/20949 weeks
225-.09692 -.14714 (225*2π)/20949 weeks
226-.13809 -.14888 (226*2π)/20949 weeks
227-.1014 -.12026 (227*2π)/20949 weeks
228-.07957 -.11679 (228*2π)/20949 weeks
229-.05212 -.10793 (229*2π)/20949 weeks
230-.00491 -.16116 (230*2π)/20949 weeks
231-.06299 -.19775 (231*2π)/20949 weeks
232-.05663 -.16343 (232*2π)/20949 weeks
233-.05478 -.19753 (233*2π)/20949 weeks
234-.09098 -.18814 (234*2π)/20949 weeks
235-.07633 -.16418 (235*2π)/20949 weeks
236-.08557 -.17613 (236*2π)/20949 weeks
237-.0808 -.15806 (237*2π)/20949 weeks
238-.1085 -.14888 (238*2π)/20949 weeks
239-.04046 -.10724 (239*2π)/20949 weeks
240-.04526 -.18115 (240*2π)/20949 weeks
241-.07448 -.15323 (241*2π)/20949 weeks
242-.05693 -.15939 (242*2π)/20949 weeks
243-.04416 -.12159 (243*2π)/20949 weeks
244.0018 -.20788 (244*2π)/20949 weeks
245-.08642 -.21422 (245*2π)/20949 weeks
246-.06571 -.1876 (246*2π)/20949 weeks
247-.08192 -.17738 (247*2π)/20948 weeks
248-.03347 -.18953 (248*2π)/20948 weeks
249-.07815 -.26882 (249*2π)/20948 weeks
250-.15962 -.23449 (250*2π)/20948 weeks
251-.20306 -.19656 (251*2π)/20948 weeks
252-.21794 -.12206 (252*2π)/20948 weeks
253-.17591 -.04482 (253*2π)/20948 weeks
254-.09618 -.02792 (254*2π)/20948 weeks
255-.05731 -.07988 (255*2π)/20948 weeks
256-.08114 -.08419 (256*2π)/20948 weeks
257-.04457 -.07065 (257*2π)/20948 weeks
258-.01981 -.12632 (258*2π)/20948 weeks
259-.06555 -.16483 (259*2π)/20948 weeks
260-.11868 -.13461 (260*2π)/20948 weeks
261-.10721 -.05984 (261*2π)/20948 weeks
262-.03112 -.06126 (262*2π)/20948 weeks
263-.02232 -.10514 (263*2π)/20948 weeks
264-.03 -.11988 (264*2π)/20948 weeks
265-.04697 -.15098 (265*2π)/20948 weeks
266-.09812 -.13736 (266*2π)/20948 weeks
267-.0985 -.08686 (267*2π)/20948 weeks
268-.02612 -.07692 (268*2π)/20948 weeks
269-.05785 -.12112 (269*2π)/20948 weeks
270-.0497 -.08798 (270*2π)/20948 weeks
271-.02985 -.10233 (271*2π)/20948 weeks
272-.0399 -.12837 (272*2π)/20948 weeks
273-.06647 -.11591 (273*2π)/20948 weeks
274-.06057 -.08186 (274*2π)/20948 weeks
275-.03406 -.10782 (275*2π)/20948 weeks
276-.06005 -.10199 (276*2π)/20948 weeks
277-.06724 -.0808 (277*2π)/20948 weeks
278-.03743 -.02872 (278*2π)/20948 weeks
279.05063 -.06688 (279*2π)/20948 weeks
280.02842 -.1406 (280*2π)/20947 weeks
281-.04339 -.15674 (281*2π)/20947 weeks
282-.07648 -.08578 (282*2π)/20947 weeks
283-.02049 -.0352 (283*2π)/20947 weeks
284.05221 -.07285 (284*2π)/20947 weeks
285.04869 -.12831 (285*2π)/20947 weeks
286.01013 -.14012 (286*2π)/20947 weeks
287.03691 -.15696 (287*2π)/20947 weeks
288-.01149 -.16612 (288*2π)/20947 weeks
289-.00642 -.14649 (289*2π)/20947 weeks
290-.01867 -.16286 (290*2π)/20947 weeks
291-.0036 -.1606 (291*2π)/20947 weeks
292-.04958 -.15719 (292*2π)/20947 weeks
293-.00851 -.11271 (293*2π)/20947 weeks
294.02434 -.15759 (294*2π)/20947 weeks
295.01806 -.22351 (295*2π)/20947 weeks
296-.08229 -.23252 (296*2π)/20947 weeks
297-.09676 -.15087 (297*2π)/20947 weeks
298-.07498 -.152 (298*2π)/20947 weeks
299-.0594 -.14464 (299*2π)/20947 weeks
300-.07861 -.159 (300*2π)/20947 weeks
301-.11144 -.13259 (301*2π)/20947 weeks
302-.10513 -.07842 (302*2π)/20947 weeks
303-.03605