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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 (4.3836*sine), 190 weeks (3.693*sine), and 190 weeks (1.0801*cosine).

AET (Aetna Inc. Common Stock) has an average price of 19.92 (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 1/9/2017 for AET (Aetna Inc. Common Stock), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
019.92261   0 
116.90248 -18.19084 (1*2π)/20882,088 weeks
25.96456 -12.39157 (2*2π)/20881,044 weeks
36.65819 -7.20593 (3*2π)/2088696 weeks
48.27169 -10.74413 (4*2π)/2088522 weeks
51.2941 -11.6124 (5*2π)/2088418 weeks
6-.55809 -6.9618 (6*2π)/2088348 weeks
7.93878 -5.44871 (7*2π)/2088298 weeks
81.15394 -5.80387 (8*2π)/2088261 weeks
9-.10631 -5.67567 (9*2π)/2088232 weeks
10-.72518 -4.38358 (10*2π)/2088209 weeks
11-1.08005 -3.69303 (11*2π)/2088190 weeks
12-.54507 -2.61095 (12*2π)/2088174 weeks
13.36995 -2.17213 (13*2π)/2088161 weeks
14.45645 -3.17537 (14*2π)/2088149 weeks
15-.66052 -3.07215 (15*2π)/2088139 weeks
16-.73659 -1.82504 (16*2π)/2088131 weeks
17.23085 -1.49204 (17*2π)/2088123 weeks
18.27337 -2.29012 (18*2π)/2088116 weeks
19-.60149 -2.18475 (19*2π)/2088110 weeks
20-.62198 -.79841 (20*2π)/2088104 weeks
21.4872 -.81268 (21*2π)/208899 weeks
221.03354 -1.26773 (22*2π)/208895 weeks
23.58472 -2.04627 (23*2π)/208891 weeks
24.32387 -1.46329 (24*2π)/208887 weeks
25.52602 -1.82282 (25*2π)/208884 weeks
26.18948 -1.63905 (26*2π)/208880 weeks
27.3099 -1.65827 (27*2π)/208877 weeks
28.10612 -1.67081 (28*2π)/208875 weeks
29.12388 -1.56785 (29*2π)/208872 weeks
30.0887 -1.71783 (30*2π)/208870 weeks
31-.21134 -1.51972 (31*2π)/208867 weeks
32-.0211 -1.17179 (32*2π)/208865 weeks
33.11002 -1.48532 (33*2π)/208863 weeks
34-.02633 -1.49874 (34*2π)/208861 weeks
35-.24019 -1.47858 (35*2π)/208860 weeks
36-.35987 -1.32575 (36*2π)/208858 weeks
37-.47292 -1.33816 (37*2π)/208856 weeks
38-.64605 -1.00675 (38*2π)/208855 weeks
39-.54282 -.71577 (39*2π)/208854 weeks
40-.2086 -.38892 (40*2π)/208852 weeks
41.03028 -.84499 (41*2π)/208851 weeks
42-.28898 -.6695 (42*2π)/208850 weeks
43.07456 -.51083 (43*2π)/208849 weeks
44.10221 -.85847 (44*2π)/208847 weeks
45-.15051 -.82841 (45*2π)/208846 weeks
46-.24739 -.43009 (46*2π)/208845 weeks
47.29299 -.41604 (47*2π)/208844 weeks
48.32885 -.77914 (48*2π)/208844 weeks
49.04463 -.76278 (49*2π)/208843 weeks
50.12724 -.73613 (50*2π)/208842 weeks
51.1652 -.7696 (51*2π)/208841 weeks
52.03872 -.85729 (52*2π)/208840 weeks
53-.00518 -.84521 (53*2π)/208839 weeks
54-.21903 -.68351 (54*2π)/208839 weeks
55.017 -.46677 (55*2π)/208838 weeks
56.12925 -.58338 (56*2π)/208837 weeks
57.2429 -.54623 (57*2π)/208837 weeks
58.18146 -.86255 (58*2π)/208836 weeks
59-.03202 -.8134 (59*2π)/208835 weeks
60-.09238 -.74094 (60*2π)/208835 weeks
61-.1303 -.5412 (61*2π)/208834 weeks
62.15497 -.57339 (62*2π)/208834 weeks
63-.02049 -.69497 (63*2π)/208833 weeks
64-.10809 -.53503 (64*2π)/208833 weeks
65.11347 -.35286 (65*2π)/208832 weeks
66.33048 -.6803 (66*2π)/208832 weeks
67.0159 -.85056 (67*2π)/208831 weeks
68-.08644 -.72662 (68*2π)/208831 weeks
69-.18144 -.48893 (69*2π)/208830 weeks
70.11127 -.44023 (70*2π)/208830 weeks
71.15529 -.70666 (71*2π)/208829 weeks
72-.11211 -.70638 (72*2π)/208829 weeks
73-.2056 -.49995 (73*2π)/208829 weeks
74-.03803 -.37072 (74*2π)/208828 weeks
75.17918 -.42323 (75*2π)/208828 weeks
76.11636 -.58975 (76*2π)/208827 weeks
77.03005 -.58824 (77*2π)/208827 weeks
78-.00478 -.54528 (78*2π)/208827 weeks
79.03767 -.47154 (79*2π)/208826 weeks
80.13991 -.55702 (80*2π)/208826 weeks
81.00099 -.6273 (81*2π)/208826 weeks
82.03232 -.61367 (82*2π)/208825 weeks
83-.04436 -.58615 (83*2π)/208825 weeks
84-.03813 -.47056 (84*2π)/208825 weeks
85.00477 -.55427 (85*2π)/208825 weeks
86-.0188 -.54765 (86*2π)/208824 weeks
87-.04577 -.59041 (87*2π)/208824 weeks
88-.14336 -.52913 (88*2π)/208824 weeks
89-.12615 -.44099 (89*2π)/208823 weeks
90-.01071 -.35171 (90*2π)/208823 weeks
91.06405 -.4559 (91*2π)/208823 weeks
92-.02081 -.48752 (92*2π)/208823 weeks
93-.01099 -.45534 (93*2π)/208822 weeks
94.00685 -.44445 (94*2π)/208822 weeks
95.03637 -.42046 (95*2π)/208822 weeks
96.12013 -.50543 (96*2π)/208822 weeks
97-.03269 -.64081 (97*2π)/208822 weeks
98-.16223 -.50813 (98*2π)/208821 weeks
99-.06358 -.34045 (99*2π)/208821 weeks
100.112 -.42823 (100*2π)/208821 weeks
101.03184 -.59225 (101*2π)/208821 weeks
102-.13486 -.58552 (102*2π)/208820 weeks
103-.14138 -.48248 (103*2π)/208820 weeks
104-.15095 -.45033 (104*2π)/208820 weeks
105-.12354 -.34108 (105*2π)/208820 weeks
106.03383 -.34651 (106*2π)/208820 weeks
107-.02567 -.51712 (107*2π)/208820 weeks
108-.0924 -.43003 (108*2π)/208819 weeks
109-.05386 -.39924 (109*2π)/208819 weeks
110-.00663 -.40911 (110*2π)/208819 weeks
111-.04342 -.52385 (111*2π)/208819 weeks
112-.16979 -.50096 (112*2π)/208819 weeks
113-.17628 -.35359 (113*2π)/208818 weeks
114-.04663 -.30617 (114*2π)/208818 weeks
115.05715 -.467 (115*2π)/208818 weeks
116-.12917 -.54524 (116*2π)/208818 weeks
117-.22475 -.4367 (117*2π)/208818 weeks
118-.19487 -.31117 (118*2π)/208818 weeks
119-.07925 -.27303 (119*2π)/208818 weeks
120-.0231 -.32811 (120*2π)/208817 weeks
121-.02795 -.46227 (121*2π)/208817 weeks
122-.1672 -.4404 (122*2π)/208817 weeks
123-.22903 -.29 (123*2π)/208817 weeks
124-.01109 -.18821 (124*2π)/208817 weeks
125.06678 -.43335 (125*2π)/208817 weeks
126-.14615 -.53754 (126*2π)/208817 weeks
127-.29057 -.30038 (127*2π)/208816 weeks
128-.09851 -.13763 (128*2π)/208816 weeks
129.09898 -.32064 (129*2π)/208816 weeks
130-.01808 -.51095 (130*2π)/208816 weeks
131-.19487 -.42896 (131*2π)/208816 weeks
132-.21093 -.32965 (132*2π)/208816 weeks
133-.13828 -.26174 (133*2π)/208816 weeks
134-.09553 -.30426 (134*2π)/208816 weeks
135-.10211 -.31351 (135*2π)/208815 weeks
136-.0982 -.37548 (136*2π)/208815 weeks
137-.22844 -.34678 (137*2π)/208815 weeks
138-.18359 -.20299 (138*2π)/208815 weeks
139-.12305 -.18803 (139*2π)/208815 weeks
140-.0215 -.21017 (140*2π)/208815 weeks
141-.0213 -.31155 (141*2π)/208815 weeks
142-.09761 -.33933 (142*2π)/208815 weeks
143-.12482 -.2953 (143*2π)/208815 weeks
144-.11895 -.26075 (144*2π)/208815 weeks
145-.11398 -.27124 (145*2π)/208814 weeks
146-.16658 -.21986 (146*2π)/208814 weeks
147-.04795 -.14743 (147*2π)/208814 weeks
148-.01936 -.25081 (148*2π)/208814 weeks
149-.03079 -.26396 (149*2π)/208814 weeks
150-.04872 -.23182 (150*2π)/208814 weeks
151.00154 -.21336 (151*2π)/208814 weeks
152.06065 -.32661 (152*2π)/208814 weeks
153-.02826 -.36176 (153*2π)/208814 weeks
154-.0498 -.33384 (154*2π)/208814 weeks
155-.02206 -.35813 (155*2π)/208813 weeks
156-.1206 -.40995 (156*2π)/208813 weeks
157-.10496 -.32406 (157*2π)/208813 weeks
158-.07836 -.35838 (158*2π)/208813 weeks
159-.07594 -.4486 (159*2π)/208813 weeks
160-.30652 -.45756 (160*2π)/208813 weeks
161-.27631 -.22732 (161*2π)/208813 weeks
162-.14703 -.2825 (162*2π)/208813 weeks
163-.25397 -.34583 (163*2π)/208813 weeks
164-.37098 -.21632 (164*2π)/208813 weeks
165-.21046 -.05193 (165*2π)/208813 weeks
166-.1352 -.17578 (166*2π)/208813 weeks
167-.17666 -.178 (167*2π)/208813 weeks
168-.18149 -.11571 (168*2π)/208812 weeks
169-.06927 -.1081 (169*2π)/208812 weeks
170-.0778 -.19657 (170*2π)/208812 weeks
171-.0821 -.18283 (171*2π)/208812 weeks
172-.10726 -.24688 (172*2π)/208812 weeks
173-.15653 -.19306 (173*2π)/208812 weeks
174-.13887 -.13575 (174*2π)/208812 weeks
175-.07593 -.16365 (175*2π)/208812 weeks
176-.0998 -.21827 (176*2π)/208812 weeks
177-.14259 -.20774 (177*2π)/208812 weeks
178-.17204 -.19881 (178*2π)/208812 weeks
179-.18924 -.10539 (179*2π)/208812 weeks
180-.10551 -.05869 (180*2π)/208812 weeks
181-.02469 -.10531 (181*2π)/208812 weeks
182-.02112 -.18874 (182*2π)/208811 weeks
183-.1164 -.18719 (183*2π)/208811 weeks
184-.0946 -.13102 (184*2π)/208811 weeks
185-.06055 -.1372 (185*2π)/208811 weeks
186-.05857 -.18952 (186*2π)/208811 weeks
187-.1234 -.19454 (187*2π)/208811 weeks
188-.12491 -.11368 (188*2π)/208811 weeks
189-.06294 -.10245 (189*2π)/208811 weeks
190-.03029 -.13867 (190*2π)/208811 weeks
191-.05747 -.19866 (191*2π)/208811 weeks
192-.11858 -.15144 (192*2π)/208811 weeks
193-.07231 -.0992 (193*2π)/208811 weeks
194-.00468 -.11371 (194*2π)/208811 weeks
195-.01691 -.21681 (195*2π)/208811 weeks
196-.1017 -.1836 (196*2π)/208811 weeks
197-.08454 -.11912 (197*2π)/208811 weeks
198-.04267 -.12967 (198*2π)/208811 weeks
199-.04009 -.14417 (199*2π)/208810 weeks
200-.01925 -.12717 (200*2π)/208810 weeks
201-.00697 -.18195 (201*2π)/208810 weeks
202-.02906 -.16681 (202*2π)/208810 weeks
203-.01217 -.21353 (203*2π)/208810 weeks
204-.05013 -.20471 (204*2π)/208810 weeks
205-.03059 -.22737 (205*2π)/208810 weeks
206-.10675 -.24438 (206*2π)/208810 weeks
207-.09645 -.18101 (207*2π)/208810 weeks
208-.08237 -.21497 (208*2π)/208810 weeks
209-.12157 -.18783 (209*2π)/208810 weeks
210-.10908 -.18672 (210*2π)/208810 weeks
211-.10338 -.16509 (211*2π)/208810 weeks
212-.13541 -.22996 (212*2π)/208810 weeks
213-.21235 -.1466 (213*2π)/208810 weeks
214-.17568 -.07577 (214*2π)/208810 weeks
215-.13315 -.04309 (215*2π)/208810 weeks
216-.0561 -.05476 (216*2π)/208810 weeks
217-.05356 -.08375 (217*2π)/208810 weeks
218-.06463 -.12224 (218*2π)/208810 weeks
219-.06062 -.10883 (219*2π)/208810 weeks
220-.10738 -.1361 (220*2π)/20889 weeks
221-.13447 -.02257 (221*2π)/20889 weeks
222.00492 .02057 (222*2π)/20889 weeks
223.04327 -.06959 (223*2π)/20889 weeks
224.02247 -.14675 (224*2π)/20889 weeks
225-.00823 -.1058 (225*2π)/20889 weeks
226.02334 -.14226 (226*2π)/20889 weeks
227.00941 -.16122 (227*2π)/20889 weeks
228.00003 -.17862 (228*2π)/20889 weeks
229-.04732 -.21385 (229*2π)/20889 weeks
230-.0913 -.15164 (230*2π)/20889 weeks
231-.04655 -.14301 (231*2π)/20889 weeks
232-.07578 -.1532 (232*2π)/20889 weeks
233-.06881 -.11528 (233*2π)/20889 weeks
234-.03866 -.1258 (234*2π)/20889 weeks
235-.05476 -.12654 (235*2π)/20889 weeks
236-.03469 -.12324 (236*2π)/20889 weeks
237-.03963 -.11134 (237*2π)/20889 weeks
238.00901 -.15658 (238*2π)/20889 weeks
239-.07218 -.17341 (239*2π)/20889 weeks
240-.05272 -.12728 (240*2π)/20889 weeks
241-.0479 -.15184 (241*2π)/20889 weeks
242-.02928 -.14526 (242*2π)/20889 weeks
243-.08887 -.20708 (243*2π)/20889 weeks
244-.12186 -.11495 (244*2π)/20889 weeks
245-.0708 -.12357 (245*2π)/20889 weeks
246-.07659 -.11058 (246*2π)/20888 weeks
247-.07027 -.14744 (247*2π)/20888 weeks
248-.1491 -.1242 (248*2π)/20888 weeks
249-.12765 -.02901 (249*2π)/20888 weeks
250-.08628 .00142 (250*2π)/20888 weeks
251-.01539 .01741 (251*2π)/20888 weeks
252.0586 -.01605 (252*2π)/20888 weeks
253.07993 -.09365 (253*2π)/20888 weeks
254.03127 -.14667 (254*2π)/20888 weeks
255.00468 -.12127 (255*2π)/20888 weeks
256.02521 -.14249 (256*2π)/20888 weeks
257-.01821 -.17961 (257*2π)/20888 weeks
258-.0669 -.14369 (258*2π)/20888 weeks
259-.05167 -.08404 (259*2π)/20888 weeks
260.01748 -.07102 (260*2π)/20888 weeks
261.04288 -.14342 (261*2π)/20888 weeks
262-.00522 -.16723 (262*2π)/20888 weeks
263-.02668 -.15638 (263*2π)/20888 weeks
264-.05542 -.15119 (264*2π)/20888 weeks
265-.06314 -.10181 (265*2π)/20888 weeks
266-.01521 -.08453 (266*2π)/20888 weeks
267.02785 -.13628 (267*2π)/20888 weeks
268-.0345 -.13996 (268*2π)/20888 weeks
269-.00302 -.12086 (269*2π)/20888 weeks
270-.00739 -.14567 (270*2π)/20888 weeks
271-.03363 -.14818 (271*2π)/20888 weeks
272-.03679 -.11706 (272*2π)/20888 weeks
273-.00813 -.10472 (273*2π)/20888 weeks
274-.00922 -.14261 (274*2π)/20888 weeks
275-.02371 -.11667 (275*2π)/20888 weeks
276-.00751 -.10332 (276*2π)/20888 weeks
277.04235 -.10049 (277*2π)/20888 weeks
278.06097 -.18822 (278*2π)/20888 weeks
279-.01987 -.20831 (279*2π)/20887 weeks
280-.07131 -.15762 (280*2π)/20887 weeks
281-.03361 -.08946 (281*2π)/20887 weeks
282.03911 -.10736 (282*2π)/20887 weeks
283.05259 -.18707 (283*2π)/20887 weeks
284.00007 -.2152 (284*2π)/20887 weeks
285-.03794 -.19222 (285*2π)/20887 weeks
286-.02457 -.21063 (286*2π)/20887 weeks
287-.06809 -.1823 (287*2π)/20887 weeks
288-.04781 -.16739 (288*2π)/20887 weeks
289-.06438 -.17445 (289*2π)/20887 weeks
290-.04909 -.17438 (290*2π)/20887 weeks
291-.08098 -.14757 (291*2π)/20887 weeks
292-.02223 -.13886 (292*2π)/20887 weeks
293-.0304 -.19628 (293*2π)/20887 weeks
294-.07678 -.23068 (294*2π)/20887 weeks
295-.15553 -.1712 (295*2π)/20887 weeks
296-.11058 -.09628 (296*2π)/20887 weeks
297-.08642 -.11798 (297*2π)/20887 weeks
298-.07079 -.11944 (298*2π)/20887 weeks
299-.09335 -.12104 (299*2π)/20887 weeks
300-.10111 -.08301 (300*2π)/20887 weeks
301-.06232 -.04901 (301*2π)/20887 weeks
302.00465 -.07265 (302*2π)/20887 weeks
303-.00354 -.12628 (303*2π)/20887 weeks
304-.00955 -.14958 (304*2π)/20887 weeks
305-.06235 -.14524 (305*2π)/20887 weeks
306-.034