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Fourier Analysis of AIG (American International Group, I)


AIG (American International Group, I) appears to have interesting cyclic behaviour every 178 weeks (31.3024*sine), 165 weeks (29.7994*cosine), and 165 weeks (19.0192*sine).

AIG (American International Group, I) has an average price of 294.45 (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 4/24/2017 for AIG (American International Group, I), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0294.4522   0 
1-243.7377 -368.1774 (1*2π)/23122,312 weeks
2-146.2488 219.7556 (2*2π)/23121,156 weeks
3132.3322 33.66744 (3*2π)/2312771 weeks
412.97482 -29.02464 (4*2π)/2312578 weeks
538.23729 -35.18277 (5*2π)/2312462 weeks
6-54.8919 -57.03227 (6*2π)/2312385 weeks
7-42.85951 60.84423 (7*2π)/2312330 weeks
847.9861 24.76236 (8*2π)/2312289 weeks
917.39133 -30.01062 (9*2π)/2312257 weeks
10-5.47797 -14.15911 (10*2π)/2312231 weeks
11-12.43582 -11.67603 (11*2π)/2312210 weeks
12-27.62657 11.42803 (12*2π)/2312193 weeks
1321.24436 31.30242 (13*2π)/2312178 weeks
1429.79935 -19.01923 (14*2π)/2312165 weeks
15-17.47798 -27.7245 (15*2π)/2312154 weeks
16-15.63901 12.62428 (16*2π)/2312145 weeks
174.65441 7.68207 (17*2π)/2312136 weeks
184.05128 2.72736 (18*2π)/2312128 weeks
196.8154 -3.46766 (19*2π)/2312122 weeks
20-.29839 -6.0524 (20*2π)/2312116 weeks
21-5.34128 -6.55682 (21*2π)/2312110 weeks
22-6.49105 6.9164 (22*2π)/2312105 weeks
232.83609 7.64836 (23*2π)/2312101 weeks
2413.69742 -3.66949 (24*2π)/231296 weeks
25-6.19031 -13.72401 (25*2π)/231292 weeks
26-9.81698 6.30154 (26*2π)/231289 weeks
277.80799 4.56692 (27*2π)/231286 weeks
28-2.04166 -5.17529 (28*2π)/231283 weeks
291.77465 3.24107 (29*2π)/231280 weeks
302.74741 -5.74963 (30*2π)/231277 weeks
31-3.74826 -.58963 (31*2π)/231275 weeks
321.0513 -.47863 (32*2π)/231272 weeks
33-4.98703 -2.35344 (33*2π)/231270 weeks
342.33985 8.63979 (34*2π)/231268 weeks
359.15349 -5.95149 (35*2π)/231266 weeks
36-7.82305 -7.97947 (36*2π)/231264 weeks
37-1.20466 6.12117 (37*2π)/231262 weeks
38-.10725 -2.01037 (38*2π)/231261 weeks
391.002 3.82372 (39*2π)/231259 weeks
406.04676 -4.16176 (40*2π)/231258 weeks
41-6.33035 -4.99983 (41*2π)/231256 weeks
42-2.46079 5.03241 (42*2π)/231255 weeks
433.20592 1.06805 (43*2π)/231254 weeks
44.91508 -2.5041 (44*2π)/231253 weeks
45-1.58849 -.27073 (45*2π)/231251 weeks
461.31375 .03267 (46*2π)/231250 weeks
47-.80772 -2.01663 (47*2π)/231249 weeks
48-1.59234 1.42066 (48*2π)/231248 weeks
491.44034 -.42728 (49*2π)/231247 weeks
50-1.90021 1.39691 (50*2π)/231246 weeks
516.06017 -.35242 (51*2π)/231245 weeks
52-3.87396 -7.62068 (52*2π)/231244 weeks
53-6.06255 5.53954 (53*2π)/231244 weeks
547.5541 2.55309 (54*2π)/231243 weeks
55-1.6245 -4.06709 (55*2π)/231242 weeks
561.78902 -.72187 (56*2π)/231241 weeks
57-4.90904 -2.49753 (57*2π)/231241 weeks
581.62997 5.56978 (58*2π)/231240 weeks
592.65709 -3.94457 (59*2π)/231239 weeks
60-3.49164 .93746 (60*2π)/231239 weeks
614.5141 .92918 (61*2π)/231238 weeks
62-3.17517 -5.12673 (62*2π)/231237 weeks
63-2.76241 4.01008 (63*2π)/231237 weeks
644.27666 1.69401 (64*2π)/231236 weeks
65.52823 -3.69304 (65*2π)/231236 weeks
66-2.24031 -.80332 (66*2π)/231235 weeks
67-.74084 1.95562 (67*2π)/231235 weeks
682.03565 -1.33717 (68*2π)/231234 weeks
69-1.67219 -.56463 (69*2π)/231234 weeks
70.26173 1.73943 (70*2π)/231233 weeks
711.91618 -1.46177 (71*2π)/231233 weeks
72-1.32827 -1.00712 (72*2π)/231232 weeks
73.26347 .30086 (73*2π)/231232 weeks
74-1.19397 -.76035 (74*2π)/231231 weeks
75-.71529 2.21893 (75*2π)/231231 weeks
763.36785 -.04404 (76*2π)/231230 weeks
77-.69964 -3.24373 (77*2π)/231230 weeks
78-2.61738 .29868 (78*2π)/231230 weeks
79.22537 2.09908 (79*2π)/231229 weeks
801.46139 .52793 (80*2π)/231229 weeks
811.15145 -3.42947 (81*2π)/231229 weeks
82-3.57479 .19936 (82*2π)/231228 weeks
83.6282 3.42771 (83*2π)/231228 weeks
842.58973 -3.23679 (84*2π)/231228 weeks
85-3.7917 -.62872 (85*2π)/231227 weeks
861.57719 3.688 (86*2π)/231227 weeks
872.56502 -3.85302 (87*2π)/231227 weeks
88-4.54136 -.29033 (88*2π)/231226 weeks
891.91234 3.68844 (89*2π)/231226 weeks
901.13457 -3.43111 (90*2π)/231226 weeks
91-1.16605 1.67315 (91*2π)/231225 weeks
921.51152 -1.48289 (92*2π)/231225 weeks
93-3.49146 .02446 (93*2π)/231225 weeks
943.42633 2.73457 (94*2π)/231225 weeks
95.77949 -4.27954 (95*2π)/231224 weeks
96-4.10094 1.18899 (96*2π)/231224 weeks
972.89062 2.38166 (97*2π)/231224 weeks
98.8239 -2.71695 (98*2π)/231224 weeks
99-1.66891 -1.0115 (99*2π)/231223 weeks
100-1.08745 1.29691 (100*2π)/231223 weeks
1011.75765 1.58413 (101*2π)/231223 weeks
102.93995 -2.838 (102*2π)/231223 weeks
103-2.5271 -.44065 (103*2π)/231222 weeks
104.32635 2.01686 (104*2π)/231222 weeks
1051.2489 -1.39703 (105*2π)/231222 weeks
106-1.61647 -.0775 (106*2π)/231222 weeks
1071.03167 .48964 (107*2π)/231222 weeks
108.04339 -.6728 (108*2π)/231221 weeks
109.04469 -1.29518 (109*2π)/231221 weeks
110-1.76442 .21127 (110*2π)/231221 weeks
111-.10865 1.75872 (111*2π)/231221 weeks
1122.37853 .16314 (112*2π)/231221 weeks
113-.23658 -2.72373 (113*2π)/231220 weeks
114-2.03008 .16918 (114*2π)/231220 weeks
115.1153 1.53394 (115*2π)/231220 weeks
116.52698 -.06718 (116*2π)/231220 weeks
1171.2252 .08698 (117*2π)/231220 weeks
118-.42268 -2.62278 (118*2π)/231220 weeks
119-2.83376 2.19228 (119*2π)/231219 weeks
1203.72159 .89056 (120*2π)/231219 weeks
121-1.5402 -3.63025 (121*2π)/231219 weeks
122-1.81351 3.9397 (122*2π)/231219 weeks
1233.77987 -1.10017 (123*2π)/231219 weeks
124-2.03964 -2.01446 (124*2π)/231219 weeks
125.44831 1.17393 (125*2π)/231218 weeks
126-1.31113 -.69341 (126*2π)/231218 weeks
1271.55425 2.31273 (127*2π)/231218 weeks
128.27678 -2.96533 (128*2π)/231218 weeks
129-.67534 1.8576 (129*2π)/231218 weeks
1301.48559 -2.31346 (130*2π)/231218 weeks
131-3.5381 .13368 (131*2π)/231218 weeks
1321.95213 2.81884 (132*2π)/231218 weeks
1331.411 -1.95812 (133*2π)/231217 weeks
134-.36575 -.50053 (134*2π)/231217 weeks
135-.38287 -1.18775 (135*2π)/231217 weeks
136-2.19182 .50429 (136*2π)/231217 weeks
1371.13048 2.27636 (137*2π)/231217 weeks
1382.23547 -1.42761 (138*2π)/231217 weeks
139-1.02992 -1.85776 (139*2π)/231217 weeks
140-1.33917 .07479 (140*2π)/231217 weeks
141-.26773 .536 (141*2π)/231216 weeks
142.21601 1.24137 (142*2π)/231216 weeks
1431.74661 -.29249 (143*2π)/231216 weeks
144.08517 -2.26719 (144*2π)/231216 weeks
145-2.1126 .03741 (145*2π)/231216 weeks
146-.29431 1.51835 (146*2π)/231216 weeks
1471.36082 .44777 (147*2π)/231216 weeks
1481.09904 -.38001 (148*2π)/231216 weeks
149-.01073 -2.43655 (149*2π)/231216 weeks
150-2.67582 .40485 (150*2π)/231215 weeks
151.87431 2.09715 (151*2π)/231215 weeks
152.80104 -.91273 (152*2π)/231215 weeks
153.50847 .42423 (153*2π)/231215 weeks
154.69692 -2.50991 (154*2π)/231215 weeks
155-3.26933 .13891 (155*2π)/231215 weeks
156.80664 2.24349 (156*2π)/231215 weeks
1571.23001 -.28565 (157*2π)/231215 weeks
1581.05059 -.95993 (158*2π)/231215 weeks
159-1.39474 -1.8729 (159*2π)/231215 weeks
160-1.55358 1.31582 (160*2π)/231214 weeks
161.92753 1.08724 (161*2π)/231214 weeks
162.74832 -.33407 (162*2π)/231214 weeks
163.41137 -.9034 (163*2π)/231214 weeks
164-1.01819 -.60811 (164*2π)/231214 weeks
165-.57514 .11724 (165*2π)/231214 weeks
166.00119 .98044 (166*2π)/231214 weeks
167.78337 .43075 (167*2π)/231214 weeks
168.82823 -1.51668 (168*2π)/231214 weeks
169-1.07458 -.38607 (169*2π)/231214 weeks
170-.60154 .53431 (170*2π)/231214 weeks
171.62424 .77881 (171*2π)/231214 weeks
172.91821 -1.31345 (172*2π)/231213 weeks
173-1.60017 .09377 (173*2π)/231213 weeks
174.94724 .93211 (174*2π)/231213 weeks
175.23527 -1.33673 (175*2π)/231213 weeks
176-1.09244 .51567 (176*2π)/231213 weeks
177.58253 .40122 (177*2π)/231213 weeks
178.23692 -.55923 (178*2π)/231213 weeks
179-.02006 .1859 (179*2π)/231213 weeks
180-.14302 -.74022 (180*2π)/231213 weeks
181-.79195 .62173 (181*2π)/231213 weeks
182.75329 .46687 (182*2π)/231213 weeks
183.25426 -.54337 (183*2π)/231213 weeks
184-.13223 -.52478 (184*2π)/231213 weeks
185-.76401 .37932 (185*2π)/231212 weeks
1861.17883 .2546 (186*2π)/231212 weeks
187-.51736 -1.41836 (187*2π)/231212 weeks
188-1.02449 1.19523 (188*2π)/231212 weeks
1891.59768 .39256 (189*2π)/231212 weeks
190.11013 -1.69479 (190*2π)/231212 weeks
191-1.37907 -.04846 (191*2π)/231212 weeks
192-.19539 1.47552 (192*2π)/231212 weeks
1931.5522 -.47157 (193*2π)/231212 weeks
194-.84483 -1.1947 (194*2π)/231212 weeks
195-.76688 .69187 (195*2π)/231212 weeks
196.73419 .63156 (196*2π)/231212 weeks
197.44893 -1.21937 (197*2π)/231212 weeks
198-1.6749 -.00232 (198*2π)/231212 weeks
199.94818 1.73131 (199*2π)/231212 weeks
2001.51648 -1.50916 (200*2π)/231212 weeks
201-1.78794 -1.34193 (201*2π)/231212 weeks
202-.87437 2.22334 (202*2π)/231211 weeks
2032.23431 -.16834 (203*2π)/231211 weeks
204-.86652 -1.3998 (204*2π)/231211 weeks
205.18816 .38406 (205*2π)/231211 weeks
206-.47987 -1.02627 (206*2π)/231211 weeks
207-.96302 1.66812 (207*2π)/231211 weeks
2082.27037 -.40397 (208*2π)/231211 weeks
209-1.6802 -1.81648 (209*2π)/231211 weeks
210-.276 2.38444 (210*2π)/231211 weeks
2111.96763 -1.62858 (211*2π)/231211 weeks
212-2.36374 -.73076 (212*2π)/231211 weeks
213.46847 2.03308 (213*2π)/231211 weeks
2141.37943 -1.01952 (214*2π)/231211 weeks
215-.97302 -1.0044 (215*2π)/231211 weeks
216-.54997 .75897 (216*2π)/231211 weeks
217.5409 .11481 (217*2π)/231211 weeks
218-.21681 -.46652 (218*2π)/231211 weeks
219.04779 .35345 (219*2π)/231211 weeks
220.06469 -.22426 (220*2π)/231211 weeks
221-.09888 -.24301 (221*2π)/231210 weeks
222-.15703 .25016 (222*2π)/231210 weeks
223.28883 .03687 (223*2π)/231210 weeks
224-.27106 -.68241 (224*2π)/231210 weeks
225-.3124 1.26909 (225*2π)/231210 weeks
2261.64373 -.71283 (226*2π)/231210 weeks
227-1.62499 -1.31567 (227*2π)/231210 weeks
228-.15832 1.78584 (228*2π)/231210 weeks
229.83762 -.65864 (229*2π)/231210 weeks
230-.64753 .12148 (230*2π)/231210 weeks
231.86178 -.10608 (231*2π)/231210 weeks
232-.64433 -.51882 (232*2π)/231210 weeks
233.22793 .03608 (233*2π)/231210 weeks
234-1.18432 -.09384 (234*2π)/231210 weeks
235.83846 1.82778 (235*2π)/231210 weeks
2361.91287 -2.02447 (236*2π)/231210 weeks
237-2.88637 -1.04721 (237*2π)/231210 weeks
238.79057 2.59458 (238*2π)/231210 weeks
239.8854 -1.76368 (239*2π)/231210 weeks
240-1.26166 .46089 (240*2π)/231210 weeks
2411.49572 .52591 (241*2π)/231210 weeks
242-.52639 -2.16816 (242*2π)/231210 weeks
243-1.69871 1.47358 (243*2π)/231210 weeks
2441.79935 .64133 (244*2π)/23129 weeks
245-.20416 -.98725 (245*2π)/23129 weeks
246.10762 .1322 (246*2π)/23129 weeks
247-.40752 -.97016 (247*2π)/23129 weeks
248-.46783 1.1377 (248*2π)/23129 weeks
249.93077 -.45396 (249*2π)/23129 weeks
250-.98897 .09252 (250*2π)/23129 weeks
2511.43778 .40184 (251*2π)/23129 weeks
252-.52933 -2.15984 (252*2π)/23129 weeks
253-1.9278 1.64816 (253*2π)/23129 weeks
2542.16261 .63331 (254*2π)/23129 weeks
255-.44408 -1.43381 (255*2π)/23129 weeks
256-.13618 .50014 (256*2π)/23129 weeks
257.06528 -.88557 (257*2π)/23129 weeks
258-1.29309 .69594 (258*2π)/23129 weeks
2591.32918 .76165 (259*2π)/23129 weeks
260.10575 -1.25426 (260*2π)/23129 weeks
261-.62491 .06805 (261*2π)/23129 weeks
262-.02932 .09876 (262*2π)/23129 weeks
263-.02243 .072 (263*2π)/23129 weeks
264-.21475 .0845 (264*2π)/23129 weeks
265.6193 .56318 (265*2π)/23129 weeks
266.27197 -1.14394 (266*2π)/23129 weeks
267-.72327 -.27707 (267*2π)/23129 weeks
268-.27848 .75021 (268*2π)/23129 weeks
269.37531 -.13464 (269*2π)/23129 weeks
270.06904 .11907 (270*2π)/23129 weeks
271.51594 -.46081 (271*2π)/23129 weeks
272-1.013 -.71355 (272*2π)/23129 weeks
273-.38216 1.15047 (273*2π)/23128 weeks
274.96008 .16714 (274*2π)/23128 weeks
275.17514 -.8295 (275*2π)/23128 weeks
276-.52404 -.41242 (276*2π)/23128 weeks
277-.74414 .51681 (277*2π)/23128 weeks
278.7483 .55357 (278*2π)/23128 weeks
279.14197 -.62908 (279*2π)/23128 weeks
280-.30435 .01251 (280*2π)/23128 weeks
281-.11536 .13251 (281*2π)/23128 weeks
282.2208 -.01571 (282*2π)/23128 weeks
283-.0723 -.11876 (283*2π)/23128 weeks
284.05849 .12184 (284*2π)/23128 weeks
285.10913 -.12102 (285*2π)/23128 weeks
286-.05186 -.43238 (286*2π)/23128 weeks
287-.51087 .20832 (287*2π)/23128 weeks
288.51683 .38204 (288*2π)/23128 weeks
289.10854 -.7251 (289*2π)/23128 weeks
290-.5501 .26787