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Fourier Analysis of AET (Aetna Inc. Common Stock)


AET (Aetna Inc. Common Stock) appears to have interesting cyclic behaviour every 208 weeks (4.4885*sine), 189 weeks (3.8612*sine), and 189 weeks (1.0678*cosine).

AET (Aetna Inc. Common Stock) has an average price of 19.66 (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 11/28/2016 for AET (Aetna Inc. Common Stock), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
019.65922   0 
116.54548 -17.96725 (1*2π)/20822,082 weeks
25.69736 -12.1888 (2*2π)/20821,041 weeks
36.38578 -6.86878 (3*2π)/2082694 weeks
48.31539 -10.26259 (4*2π)/2082521 weeks
51.54989 -11.47059 (5*2π)/2082416 weeks
6-.50869 -6.97804 (6*2π)/2082347 weeks
7.92319 -5.34678 (7*2π)/2082297 weeks
81.25658 -5.66707 (8*2π)/2082260 weeks
9.06943 -5.67842 (9*2π)/2082231 weeks
10-.63311 -4.48845 (10*2π)/2082208 weeks
11-1.06778 -3.86117 (11*2π)/2082189 weeks
12-.67421 -2.72472 (12*2π)/2082174 weeks
13.20877 -2.11772 (13*2π)/2082160 weeks
14.50401 -3.08162 (14*2π)/2082149 weeks
15-.57622 -3.1991 (15*2π)/2082139 weeks
16-.87833 -2.00396 (16*2π)/2082130 weeks
17.01798 -1.46256 (17*2π)/2082122 weeks
18.26032 -2.22166 (18*2π)/2082116 weeks
19-.59759 -2.34593 (19*2π)/2082110 weeks
20-.95436 -.99081 (20*2π)/2082104 weeks
21.08549 -.69321 (21*2π)/208299 weeks
22.78614 -.93349 (22*2π)/208295 weeks
23.59879 -1.79123 (23*2π)/208291 weeks
24.24622 -1.29425 (24*2π)/208287 weeks
25.55495 -1.58687 (25*2π)/208283 weeks
26.22103 -1.4954 (26*2π)/208280 weeks
27.3638 -1.48124 (27*2π)/208277 weeks
28.19851 -1.54977 (28*2π)/208274 weeks
29.20602 -1.44731 (29*2π)/208272 weeks
30.25106 -1.6155 (30*2π)/208269 weeks
31-.08195 -1.54698 (31*2π)/208267 weeks
32-.01883 -1.1407 (32*2π)/208265 weeks
33.22827 -1.37122 (33*2π)/208263 weeks
34.16262 -1.44045 (34*2π)/208261 weeks
35-.01199 -1.52001 (35*2π)/208259 weeks
36-.16297 -1.44636 (36*2π)/208258 weeks
37-.25901 -1.54623 (37*2π)/208256 weeks
38-.56153 -1.35512 (38*2π)/208255 weeks
39-.63781 -1.07404 (39*2π)/208253 weeks
40-.50271 -.58813 (40*2π)/208252 weeks
41-.09059 -.87404 (41*2π)/208251 weeks
42-.44438 -.85081 (42*2π)/208250 weeks
43-.20088 -.52682 (43*2π)/208248 weeks
44.00745 -.79838 (44*2π)/208247 weeks
45-.19575 -.92296 (45*2π)/208246 weeks
46-.5187 -.62409 (46*2π)/208245 weeks
47-.08528 -.31006 (47*2π)/208244 weeks
48.17233 -.55384 (48*2π)/208243 weeks
49-.04774 -.66848 (49*2π)/208242 weeks
50.0118 -.61336 (50*2π)/208242 weeks
51.09083 -.60538 (51*2π)/208241 weeks
52.0531 -.74348 (52*2π)/208240 weeks
53.04443 -.78993 (53*2π)/208239 weeks
54-.24004 -.79983 (54*2π)/208239 weeks
55-.19879 -.49348 (55*2π)/208238 weeks
56-.06161 -.4941 (56*2π)/208237 weeks
57.03671 -.33902 (57*2π)/208237 weeks
58.20479 -.60505 (58*2π)/208236 weeks
59.05327 -.71198 (59*2π)/208235 weeks
60-.02955 -.73456 (60*2π)/208235 weeks
61-.21377 -.61107 (61*2π)/208234 weeks
62.03083 -.44842 (62*2π)/208234 weeks
63-.0056 -.6352 (63*2π)/208233 weeks
64-.19012 -.59893 (64*2π)/208233 weeks
65-.1826 -.27955 (65*2π)/208232 weeks
66.21589 -.32065 (66*2π)/208232 weeks
67.15998 -.64219 (67*2π)/208231 weeks
68.04974 -.68205 (68*2π)/208231 weeks
69-.21755 -.59449 (69*2π)/208230 weeks
70-.07946 -.33721 (70*2π)/208230 weeks
71.17442 -.45633 (71*2π)/208229 weeks
72.04282 -.65646 (72*2π)/208229 weeks
73-.18799 -.63051 (73*2π)/208229 weeks
74-.22389 -.43984 (74*2π)/208228 weeks
75-.05023 -.2715 (75*2π)/208228 weeks
76.04928 -.38186 (76*2π)/208227 weeks
77.02184 -.44321 (77*2π)/208227 weeks
78-.02803 -.45528 (78*2π)/208227 weeks
79-.07152 -.36584 (79*2π)/208226 weeks
80.06916 -.31291 (80*2π)/208226 weeks
81.04745 -.44452 (81*2π)/208226 weeks
82.0912 -.43158 (82*2π)/208225 weeks
83.04588 -.48267 (83*2π)/208225 weeks
84-.04706 -.39823 (84*2π)/208225 weeks
85.03166 -.40946 (85*2π)/208224 weeks
86.03107 -.41049 (86*2π)/208224 weeks
87.07622 -.46292 (87*2π)/208224 weeks
88-.01402 -.52927 (88*2π)/208224 weeks
89-.09338 -.50834 (89*2π)/208223 weeks
90-.13102 -.35584 (90*2π)/208223 weeks
91-.01278 -.31715 (91*2π)/208223 weeks
92-.02146 -.3864 (92*2π)/208223 weeks
93-.03747 -.36928 (93*2π)/208222 weeks
94-.04126 -.34691 (94*2π)/208222 weeks
95-.06449 -.28673 (95*2π)/208222 weeks
96.06371 -.20727 (96*2π)/208222 weeks
97.15311 -.3906 (97*2π)/208221 weeks
98.01048 -.49125 (98*2π)/208221 weeks
99-.12934 -.3515 (99*2π)/208221 weeks
100-.00176 -.18973 (100*2π)/208221 weeks
101.14067 -.27307 (101*2π)/208221 weeks
102.10974 -.42808 (102*2π)/208220 weeks
103.0438 -.42721 (103*2π)/208220 weeks
104.01126 -.45949 (104*2π)/208220 weeks
105-.10485 -.41311 (105*2π)/208220 weeks
106-.06814 -.23829 (106*2π)/208220 weeks
107.06875 -.33288 (107*2π)/208219 weeks
108-.00304 -.36223 (108*2π)/208219 weeks
109-.02738 -.3221 (109*2π)/208219 weeks
110-.01215 -.24507 (110*2π)/208219 weeks
111.10367 -.2918 (111*2π)/208219 weeks
112.08824 -.4227 (112*2π)/208219 weeks
113-.05222 -.42738 (113*2π)/208218 weeks
114-.1144 -.29152 (114*2π)/208218 weeks
115.07206 -.18632 (115*2π)/208218 weeks
116.14866 -.3457 (116*2π)/208218 weeks
117.07247 -.45047 (117*2π)/208218 weeks
118-.04791 -.44419 (118*2π)/208218 weeks
119-.09504 -.33596 (119*2π)/208217 weeks
120-.07309 -.25401 (120*2π)/208217 weeks
121.08106 -.25529 (121*2π)/208217 weeks
122.09522 -.37915 (122*2π)/208217 weeks
123-.06774 -.47461 (123*2π)/208217 weeks
124-.18855 -.24485 (124*2π)/208217 weeks
125.03523 -.13841 (125*2π)/208217 weeks
126.1938 -.33174 (126*2π)/208217 weeks
127-.01021 -.49987 (127*2π)/208216 weeks
128-.22138 -.34544 (128*2π)/208216 weeks
129-.08765 -.12787 (129*2π)/208216 weeks
130.12775 -.18277 (130*2π)/208216 weeks
131.10401 -.32661 (131*2π)/208216 weeks
132.03053 -.38657 (132*2π)/208216 weeks
133-.04405 -.33508 (133*2π)/208216 weeks
134-.02156 -.29605 (134*2π)/208216 weeks
135-.02539 -.27955 (135*2π)/208215 weeks
136.06932 -.25757 (136*2π)/208215 weeks
137.07714 -.40292 (137*2π)/208215 weeks
138-.04177 -.39712 (138*2π)/208215 weeks
139-.10632 -.37617 (139*2π)/208215 weeks
140-.12505 -.26444 (140*2π)/208215 weeks
141-.04232 -.2192 (141*2π)/208215 weeks
142.01107 -.26761 (142*2π)/208215 weeks
143.00156 -.29797 (143*2π)/208215 weeks
144-.02495 -.2984 (144*2π)/208214 weeks
145.00284 -.2981 (145*2π)/208214 weeks
146-.04579 -.39153 (146*2π)/208214 weeks
147-.15054 -.29788 (147*2π)/208214 weeks
148-.0956 -.26078 (148*2π)/208214 weeks
149-.06798 -.25249 (149*2π)/208214 weeks
150-.10373 -.27187 (150*2π)/208214 weeks
151-.1783 -.22389 (151*2π)/208214 weeks
152-.09652 -.12183 (152*2π)/208214 weeks
153-.04388 -.15326 (153*2π)/208214 weeks
154-.06049 -.16356 (154*2π)/208214 weeks
155-.03808 -.09303 (155*2π)/208213 weeks
156.04179 -.17339 (156*2π)/208213 weeks
157-.019 -.16714 (157*2π)/208213 weeks
158-.02125 -.1202 (158*2π)/208213 weeks
159.10171 -.01459 (159*2π)/208213 weeks
160.23607 -.22469 (160*2π)/208213 weeks
161.06282 -.29007 (161*2π)/208213 weeks
162.07589 -.16235 (162*2π)/208213 weeks
163.20372 -.20668 (163*2π)/208213 weeks
164.18127 -.4126 (164*2π)/208213 weeks
165-.02017 -.36742 (165*2π)/208213 weeks
166.02614 -.29373 (166*2π)/208213 weeks
167.05312 -.31983 (167*2π)/208212 weeks
168-.00807 -.38175 (168*2π)/208212 weeks
169-.07981 -.29412 (169*2π)/208212 weeks
170-.03012 -.26761 (170*2π)/208212 weeks
171-.05485 -.23673 (171*2π)/208212 weeks
172.02779 -.22354 (172*2π)/208212 weeks
173.03389 -.27326 (173*2π)/208212 weeks
174-.02965 -.30201 (174*2π)/208212 weeks
175-.05227 -.24062 (175*2π)/208212 weeks
176-.00337 -.21552 (176*2π)/208212 weeks
177.02188 -.22954 (177*2π)/208212 weeks
178.07929 -.2633 (178*2π)/208212 weeks
179.03825 -.35028 (179*2π)/208212 weeks
180-.05384 -.35736 (180*2π)/208212 weeks
181-.1007 -.28578 (181*2π)/208212 weeks
182-.0504 -.20062 (182*2π)/208211 weeks
183-.00118 -.25875 (183*2π)/208211 weeks
184-.03854 -.27689 (184*2π)/208211 weeks
185-.07452 -.25174 (185*2π)/208211 weeks
186-.04166 -.20207 (186*2π)/208211 weeks
187.0253 -.23929 (187*2π)/208211 weeks
188-.01236 -.2984 (188*2π)/208211 weeks
189-.06453 -.28819 (189*2π)/208211 weeks
190-.09052 -.23877 (190*2π)/208211 weeks
191-.02293 -.20203 (191*2π)/208211 weeks
192-.00081 -.2717 (192*2π)/208211 weeks
193-.05346 -.30204 (193*2π)/208211 weeks
194-.12819 -.2506 (194*2π)/208211 weeks
195-.05466 -.17412 (195*2π)/208211 weeks
196-.00496 -.22523 (196*2π)/208211 weeks
197-.04293 -.26529 (197*2π)/208211 weeks
198-.06395 -.25149 (198*2π)/208211 weeks
199-.05819 -.2535 (199*2π)/208210 weeks
200-.10925 -.24986 (200*2π)/208210 weeks
201-.08878 -.20952 (201*2π)/208210 weeks
202-.11766 -.22213 (202*2π)/208210 weeks
203-.09725 -.17242 (203*2π)/208210 weeks
204-.09919 -.18753 (204*2π)/208210 weeks
205-.0991 -.12309 (205*2π)/208210 weeks
206-.02609 -.14687 (206*2π)/208210 weeks
207-.06089 -.16856 (207*2π)/208210 weeks
208-.03457 -.12879 (208*2π)/208210 weeks
209-.02765 -.15618 (209*2π)/208210 weeks
210-.01395 -.15083 (210*2π)/208210 weeks
211-.05769 -.13607 (211*2π)/208210 weeks
212.03373 -.07843 (212*2π)/208210 weeks
213.08736 -.15452 (213*2π)/208210 weeks
214.07953 -.2094 (214*2π)/208210 weeks
215.04722 -.26858 (215*2π)/208210 weeks
216-.00418 -.24588 (216*2π)/208210 weeks
217-.03319 -.23154 (217*2π)/208210 weeks
218-.008 -.21707 (218*2π)/208210 weeks
219-.02731 -.1891 (219*2π)/208210 weeks
220.06857 -.17296 (220*2π)/20829 weeks
221.08512 -.30708 (221*2π)/20829 weeks
222-.04127 -.32697 (222*2π)/20829 weeks
223-.09952 -.28722 (223*2π)/20829 weeks
224-.05856 -.23045 (224*2π)/20829 weeks
225-.08265 -.26666 (225*2π)/20829 weeks
226-.09879 -.23509 (226*2π)/20829 weeks
227-.10644 -.21526 (227*2π)/20829 weeks
228-.12594 -.17741 (228*2π)/20829 weeks
229-.06373 -.13225 (229*2π)/20829 weeks
230-.04188 -.18588 (230*2π)/20829 weeks
231-.06351 -.16487 (231*2π)/20829 weeks
232-.02591 -.16764 (232*2π)/20829 weeks
233-.034 -.20059 (233*2π)/20829 weeks
234-.04664 -.18324 (234*2π)/20829 weeks
235-.03663 -.19854 (235*2π)/20829 weeks
236-.04173 -.18962 (236*2π)/20829 weeks
237-.06375 -.23374 (237*2π)/20829 weeks
238-.10308 -.15741 (238*2π)/20829 weeks
239-.04195 -.16314 (239*2π)/20829 weeks
240-.0666 -.18181 (240*2π)/20829 weeks
241-.05609 -.17907 (241*2π)/20829 weeks
242-.11825 -.15131 (242*2π)/20829 weeks
243-.03465 -.09211 (243*2π)/20829 weeks
244-.02075 -.15909 (244*2π)/20829 weeks
245-.02419 -.14318 (245*2π)/20828 weeks
246-.04563 -.15997 (246*2π)/20828 weeks
247-.04422 -.08821 (247*2π)/20828 weeks
248.05445 -.08978 (248*2π)/20828 weeks
249.07694 -.14366 (249*2π)/20828 weeks
250.09405 -.20777 (250*2π)/20828 weeks
251.06479 -.2752 (251*2π)/20828 weeks
252-.01237 -.30074 (252*2π)/20828 weeks
253-.07601 -.25899 (253*2π)/20828 weeks
254-.05833 -.21284 (254*2π)/20828 weeks
255-.06157 -.23477 (255*2π)/20828 weeks
256-.1043 -.2074 (256*2π)/20828 weeks
257-.08058 -.15036 (257*2π)/20828 weeks
258-.01865 -.14891 (258*2π)/20828 weeks
259.0115 -.20639 (259*2π)/20828 weeks
260-.04753 -.25463 (260*2π)/20828 weeks
261-.0917 -.21024 (261*2π)/20828 weeks
262-.08338 -.18033 (262*2π)/20828 weeks
263-.08416 -.15908 (263*2π)/20828 weeks
264-.0445 -.1355 (264*2π)/20828 weeks
265-.00931 -.17519 (265*2π)/20828 weeks
266-.03161 -.23034 (266*2π)/20828 weeks
267-.07679 -.17838 (267*2π)/20828 weeks
268-.03661 -.18834 (268*2π)/20828 weeks
269-.06177 -.1979 (269*2π)/20828 weeks
270-.07444 -.17654 (270*2π)/20828 weeks
271-.04883 -.15701 (271*2π)/20828 weeks
272-.02612 -.17469 (272*2π)/20828 weeks
273-.05505 -.19898 (273*2π)/20828 weeks
274-.04549 -.16801 (274*2π)/20828 weeks
275-.02629 -.17811 (275*2π)/20828 weeks
276-.0034 -.21143 (276*2π)/20828 weeks
277-.05958 -.27128 (277*2π)/20828 weeks
278-.12516 -.2105 (278*2π)/20827 weeks
279-.10878 -.14217 (279*2π)/20827 weeks
280-.032 -.13396 (280*2π)/20827 weeks
281-.00548 -.205 (281*2π)/20827 weeks
282-.06022 -.26176 (282*2π)/20827 weeks
283-.11714 -.23125 (283*2π)/20827 weeks
284-.1231 -.18559 (284*2π)/20827 weeks
285-.11366 -.20356 (285*2π)/20827 weeks
286-.12686 -.15352 (286*2π)/20827 weeks
287-.09676 -.15755 (287*2π)/20827 weeks
288-.11262 -.15719 (288*2π)/20827 weeks
289-.09583 -.16257 (289*2π)/20827 weeks
290-.10588 -.12784 (290*2π)/20827 weeks
291-.05603 -.15737 (291*2π)/20827 weeks
292-.10284 -.19548 (292*2π)/20827 weeks
293-.15284 -.1832 (293*2π)/20827 weeks
294-.17085 -.08987 (294*2π)/20827 weeks
295-.08447 -.06286 (295*2π)/20827 weeks
296-.07736 -.10554 (296*2π)/20827 weeks
297-.06764 -.11346 (297*2π)/20827 weeks
298-.0872 -.10403 (298*2π)/20827 weeks
299-.07048 -.07282 (299*2π)/20827 weeks
300-.02126 -.07372 (300*2π)/20827 weeks
301.01545 -.13159 (301*2π)/20827 weeks
302-.02698 -.17223 (302*2π)/20827 weeks
303-.04564 -.18001 (303*2π)/20827 weeks
304-.08749 -.14952 (304*2π)/20827 weeks
305-.04249 -.12881