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Fourier Analysis of AIG (American International Group, I)


AIG (American International Group, I) appears to have interesting cyclic behaviour every 177 weeks (35.5192*sine), 165 weeks (33.6608*cosine), and 144 weeks (18.274*cosine).

AIG (American International Group, I) has an average price of 296.87 (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 1/2/1973 to 2/21/2017 for AIG (American International Group, I), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0296.8687   0 
1-239.7477 -374.8517 (1*2π)/23032,303 weeks
2-154.777 215.6563 (2*2π)/23031,152 weeks
3129.8308 40.44045 (3*2π)/2303768 weeks
414.89669 -26.85982 (4*2π)/2303576 weeks
542.16063 -32.28142 (5*2π)/2303461 weeks
6-49.38382 -63.36744 (6*2π)/2303384 weeks
7-50.49774 55.2399 (7*2π)/2303329 weeks
843.37651 31.38483 (8*2π)/2303288 weeks
921.57996 -26.30198 (9*2π)/2303256 weeks
10-2.2986 -14.96881 (10*2π)/2303230 weeks
11-9.93234 -14.69461 (11*2π)/2303209 weeks
12-30.80143 5.30574 (12*2π)/2303192 weeks
1313.22258 35.51919 (13*2π)/2303177 weeks
1433.66083 -10.75515 (14*2π)/2303165 weeks
15-9.75037 -31.29531 (15*2π)/2303154 weeks
16-18.27404 7.19613 (16*2π)/2303144 weeks
171.4578 8.23183 (17*2π)/2303135 weeks
182.47291 4.29728 (18*2π)/2303128 weeks
197.42417 -.82988 (19*2π)/2303121 weeks
201.9655 -5.47735 (20*2π)/2303115 weeks
21-2.8723 -8.62961 (21*2π)/2303110 weeks
22-8.79771 3.69854 (22*2π)/2303105 weeks
23-1.33679 8.58924 (23*2π)/2303100 weeks
2414.16009 2.38455 (24*2π)/230396 weeks
25-.0034 -14.96204 (25*2π)/230392 weeks
26-11.73342 1.30524 (26*2π)/230389 weeks
274.78408 7.1643 (27*2π)/230385 weeks
28-.37016 -5.15547 (28*2π)/230382 weeks
29.0113 3.94835 (29*2π)/230379 weeks
304.88586 -3.81511 (30*2π)/230377 weeks
31-2.89972 -2.18243 (31*2π)/230374 weeks
321.2318 -.1673 (32*2π)/230372 weeks
33-3.9094 -5.15773 (33*2π)/230370 weeks
34-3.06717 8.79926 (34*2π)/230368 weeks
3510.83885 .39165 (35*2π)/230366 weeks
36-2.16988 -10.93458 (36*2π)/230364 weeks
37-3.94926 3.81312 (37*2π)/230362 weeks
38.11209 -2.19803 (38*2π)/230361 weeks
39-1.93459 3.93171 (39*2π)/230359 weeks
407.54819 .48367 (40*2π)/230358 weeks
41-1.718 -7.87372 (41*2π)/230356 weeks
42-5.11774 1.75726 (42*2π)/230355 weeks
431.11587 2.73512 (43*2π)/230354 weeks
442.0493 -1.18866 (44*2π)/230352 weeks
45-1.21442 -1.1996 (45*2π)/230351 weeks
46.89636 .81781 (46*2π)/230350 weeks
47.72785 -2.1971 (47*2π)/230349 weeks
48-2.30918 -.18525 (48*2π)/230348 weeks
491.12458 .25834 (49*2π)/230347 weeks
50-3.28404 -.15374 (50*2π)/230346 weeks
514.56375 4.64224 (51*2π)/230345 weeks
523.24874 -8.10281 (52*2π)/230344 weeks
53-8.48376 -1.58638 (53*2π)/230343 weeks
542.6385 6.84273 (54*2π)/230343 weeks
551.06632 -3.07297 (55*2π)/230342 weeks
562.47787 .98034 (56*2π)/230341 weeks
57-1.43032 -6.03126 (57*2π)/230340 weeks
58-3.45855 4.36118 (58*2π)/230340 weeks
594.31487 -.4727 (59*2π)/230339 weeks
60-3.21142 -2.16532 (60*2π)/230338 weeks
612.07073 4.45414 (61*2π)/230338 weeks
622.37002 -5.55827 (62*2π)/230337 weeks
63-4.87 -.88902 (63*2π)/230337 weeks
64.2088 4.36416 (64*2π)/230336 weeks
653.03811 -.94601 (65*2π)/230335 weeks
66-.09611 -2.42644 (66*2π)/230335 weeks
67-2.40442 .1196 (67*2π)/230334 weeks
681.95593 .73942 (68*2π)/230334 weeks
69-.30864 -1.8903 (69*2π)/230333 weeks
70-1.81683 .83775 (70*2π)/230333 weeks
711.88276 1.00061 (71*2π)/230332 weeks
72.2954 -1.48305 (72*2π)/230332 weeks
73.17328 .31629 (73*2π)/230332 weeks
74.3111 -1.79025 (74*2π)/230331 weeks
75-2.82884 -.26151 (75*2π)/230331 weeks
76.80347 3.24583 (76*2π)/230330 weeks
772.77582 -1.25439 (77*2π)/230330 weeks
78-.69409 -2.60075 (78*2π)/230330 weeks
79-1.96781 .29072 (79*2π)/230329 weeks
80-1.06114 1.80247 (80*2π)/230329 weeks
813.73611 .21708 (81*2π)/230328 weeks
82-.68629 -3.46005 (82*2π)/230328 weeks
83-3.74796 1.36431 (83*2π)/230328 weeks
843.46953 1.53187 (84*2π)/230327 weeks
85-.2247 -4.13185 (85*2π)/230327 weeks
86-3.68573 2.11891 (86*2π)/230327 weeks
874.16118 1.76081 (87*2π)/230326 weeks
88-.42166 -4.6535 (88*2π)/230326 weeks
89-3.43105 2.22386 (89*2π)/230326 weeks
902.98254 -.10874 (90*2π)/230326 weeks
91-1.94604 -.41888 (91*2π)/230325 weeks
921.91617 1.32143 (92*2π)/230325 weeks
93-.95178 -4.12479 (93*2π)/230325 weeks
94-2.64222 3.44776 (94*2π)/230325 weeks
954.17695 .7445 (95*2π)/230324 weeks
96-1.40107 -4.12554 (96*2π)/230324 weeks
97-2.44345 2.48227 (97*2π)/230324 weeks
981.87158 1.02996 (98*2π)/230324 weeks
991.32321 -1.42085 (99*2π)/230323 weeks
100-1.00398 -1.73741 (100*2π)/230323 weeks
101-2.277 1.65599 (101*2π)/230323 weeks
1022.2971 1.2867 (102*2π)/230323 weeks
103.78747 -2.3858 (103*2π)/230322 weeks
104-2.11064 -.07596 (104*2π)/230322 weeks
1051.06673 1.12013 (105*2π)/230322 weeks
106-.17322 -1.64958 (106*2π)/230322 weeks
107-.63852 .64866 (107*2π)/230322 weeks
108-.05713 .20845 (108*2π)/230321 weeks
1091.51758 .39853 (109*2π)/230321 weeks
110.55606 -1.8246 (110*2π)/230321 weeks
111-1.78182 -1.33835 (111*2π)/230321 weeks
112-1.37808 2.09742 (112*2π)/230321 weeks
1132.24657 .6725 (113*2π)/230320 weeks
114.80611 -1.84604 (114*2π)/230320 weeks
115-1.17849 -.65871 (115*2π)/230320 weeks
116-.47278 -.37703 (116*2π)/230320 weeks
117-1.12002 1.37589 (117*2π)/230320 weeks
1183.04931 .54928 (118*2π)/230320 weeks
119-1.3456 -3.79994 (119*2π)/230319 weeks
120-2.14651 3.0384 (120*2π)/230319 weeks
1214.11334 -.51471 (121*2π)/230319 weeks
122-3.27486 -3.12864 (122*2π)/230319 weeks
123-.6533 3.21 (123*2π)/230319 weeks
1241.86432 -1.19466 (124*2π)/230319 weeks
125-.66146 .56582 (125*2π)/230318 weeks
1261.25165 -1.94246 (126*2π)/230318 weeks
127-3.10239 .60056 (127*2π)/230318 weeks
1282.25398 .60001 (128*2π)/230318 weeks
129-2.15311 -.92537 (129*2π)/230318 weeks
1301.54065 2.62428 (130*2π)/230318 weeks
1311.72061 -3.42358 (131*2π)/230318 weeks
132-3.06203 -.34882 (132*2π)/230317 weeks
133.14775 1.31218 (133*2π)/230317 weeks
134-.22618 .48286 (134*2π)/230317 weeks
1351.30599 1.00023 (135*2π)/230317 weeks
1361.30507 -2.33603 (136*2π)/230317 weeks
137-2.46442 -1.32657 (137*2π)/230317 weeks
138-1.01662 2.04506 (138*2π)/230317 weeks
1391.23968 .77291 (139*2π)/230317 weeks
140.91328 -.70846 (140*2π)/230316 weeks
141.61756 -.80559 (141*2π)/230316 weeks
142-1.06907 -1.41925 (142*2π)/230316 weeks
143-1.72344 .8237 (143*2π)/230316 weeks
1441.1232 1.90014 (144*2π)/230316 weeks
1451.59789 -.8846 (145*2π)/230316 weeks
146-.21709 -1.7256 (146*2π)/230316 weeks
147-1.014 -.40156 (147*2π)/230316 weeks
148-1.75493 .64045 (148*2π)/230316 weeks
1491.2903 2.29354 (149*2π)/230315 weeks
1502.01527 -1.67812 (150*2π)/230315 weeks
151-1.49552 -1.11091 (151*2π)/230315 weeks
152.07862 .0367 (152*2π)/230315 weeks
153-1.91049 -.32299 (153*2π)/230315 weeks
154.71136 2.99075 (154*2π)/230315 weeks
1552.4935 -1.6382 (155*2π)/230315 weeks
156-.97778 -1.52369 (156*2π)/230315 weeks
157-1.02162 -.40918 (157*2π)/230315 weeks
158-1.38568 1.43461 (158*2π)/230315 weeks
1591.8101 1.23583 (159*2π)/230314 weeks
1601.06631 -1.46821 (160*2π)/230314 weeks
161-.72301 -.872 (161*2π)/230314 weeks
162-.81198 -.19848 (162*2π)/230314 weeks
163-.48034 .97028 (163*2π)/230314 weeks
164.58688 .22386 (164*2π)/230314 weeks
1651.0067 -.18996 (165*2π)/230314 weeks
166.12077 -.96052 (166*2π)/230314 weeks
167-1.2616 -.96381 (167*2π)/230314 weeks
168-.32463 1.26534 (168*2π)/230314 weeks
169.70878 .3666 (169*2π)/230314 weeks
170.77374 -.69794 (170*2π)/230314 weeks
171-.93939 -1.10581 (171*2π)/230313 weeks
172-.28094 1.57171 (172*2π)/230313 weeks
1731.26752 -.78684 (173*2π)/230313 weeks
174-1.18546 -.64057 (174*2π)/230313 weeks
175.23916 1.2094 (175*2π)/230313 weeks
176.65835 -.69735 (176*2π)/230313 weeks
177-.4569 -.4806 (177*2π)/230313 weeks
178.1066 .21748 (178*2π)/230313 weeks
179-.5513 -.19439 (179*2π)/230313 weeks
180.3757 .82962 (180*2π)/230313 weeks
181.71878 -.74117 (181*2π)/230313 weeks
182-.56112 -.53245 (182*2π)/230313 weeks
183-.41579 -.00568 (183*2π)/230313 weeks
184.07214 .66992 (184*2π)/230313 weeks
185.76919 -.94162 (185*2π)/230312 weeks
186-1.41142 -.19015 (186*2π)/230312 weeks
187.68498 1.35711 (187*2π)/230312 weeks
1881.04985 -1.38126 (188*2π)/230312 weeks
189-1.50864 -.80368 (189*2π)/230312 weeks
190-.49627 1.33098 (190*2π)/230312 weeks
1911.22848 .65776 (191*2π)/230312 weeks
192.36334 -1.69117 (192*2π)/230312 weeks
193-1.50674 .12142 (193*2π)/230312 weeks
194.36198 .99338 (194*2π)/230312 weeks
195.91918 -.41974 (195*2π)/230312 weeks
196-.71841 -1.05781 (196*2π)/230312 weeks
197-.83423 1.24192 (197*2π)/230312 weeks
1981.98083 .13111 (198*2π)/230312 weeks
199-.41392 -2.14831 (199*2π)/230312 weeks
200-2.05724 .70583 (200*2π)/230312 weeks
2011.28669 1.95454 (201*2π)/230311 weeks
2021.33594 -2.00517 (202*2π)/230311 weeks
203-1.79421 -.38363 (203*2π)/230311 weeks
204.4764 .3299 (204*2π)/230311 weeks
205-.86693 -.35161 (205*2π)/230311 weeks
206.50572 1.69697 (206*2π)/230311 weeks
2071.35449 -1.92201 (207*2π)/230311 weeks
208-2.44179 -.19363 (208*2π)/230311 weeks
2091.41651 1.93859 (209*2π)/230311 weeks
210.46552 -2.57324 (210*2π)/230311 weeks
211-2.25656 1.01617 (211*2π)/230311 weeks
2121.81041 1.22239 (212*2π)/230311 weeks
213.3857 -1.80835 (213*2π)/230311 weeks
214-1.41996 -.1174 (214*2π)/230311 weeks
215.13216 .97673 (215*2π)/230311 weeks
216.57899 -.30154 (216*2π)/230311 weeks
217-.40298 -.3139 (217*2π)/230311 weeks
218.25762 .27977 (218*2π)/230311 weeks
219-.04762 -.28568 (219*2π)/230311 weeks
220-.1598 -.14629</