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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 (37.1147*sine), 164 weeks (34.8634*cosine), and 144 weeks (19.0188*cosine).

AIG (American International Group, I) has an average price of 297.48 (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 1/9/2017 for AIG (American International Group, I), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0297.475   0 
1-236.1975 -378.0259 (1*2π)/22972,297 weeks
2-159.9096 212.0015 (2*2π)/22971,149 weeks
3127.4958 44.74534 (3*2π)/2297766 weeks
415.98149 -25.23401 (4*2π)/2297574 weeks
544.50243 -29.98316 (5*2π)/2297459 weeks
6-45.13752 -67.0771 (6*2π)/2297383 weeks
7-55.04413 50.77021 (7*2π)/2297328 weeks
839.61357 35.28243 (8*2π)/2297287 weeks
923.87842 -23.38243 (9*2π)/2297255 weeks
10-.12568 -15.05591 (10*2π)/2297230 weeks
11-7.83475 -16.34341 (11*2π)/2297209 weeks
12-32.06803 .75914 (12*2π)/2297191 weeks
137.29505 37.11469 (13*2π)/2297177 weeks
1434.8634 -4.73554 (14*2π)/2297164 weeks
15-4.17685 -32.34719 (15*2π)/2297153 weeks
16-19.01883 3.29552 (16*2π)/2297144 weeks
17-.64664 7.94152 (17*2π)/2297135 weeks
181.08183 4.94464 (18*2π)/2297128 weeks
197.22626 .98863 (19*2π)/2297121 weeks
203.22894 -4.56784 (20*2π)/2297115 weeks
21-.78269 -9.40088 (21*2π)/2297109 weeks
22-9.49658 1.12024 (22*2π)/2297104 weeks
23-4.2773 8.08259 (23*2π)/2297100 weeks
2412.92005 6.36382 (24*2π)/229796 weeks
254.13463 -14.18144 (25*2π)/229792 weeks
26-11.6603 -2.25071 (26*2π)/229788 weeks
272.32234 7.99309 (27*2π)/229785 weeks
28.57394 -4.86235 (28*2π)/229782 weeks
29-1.39099 3.94753 (29*2π)/229779 weeks
305.61365 -2.02102 (30*2π)/229777 weeks
31-2.02055 -2.81663 (31*2π)/229774 weeks
321.31495 .21159 (32*2π)/229772 weeks
33-2.26702 -6.66315 (33*2π)/229770 weeks
34-6.47168 7.09462 (34*2π)/229768 weeks
359.64179 4.73107 (35*2π)/229766 weeks
362.01668 -10.7537 (36*2π)/229764 weeks
37-4.68967 1.81581 (37*2π)/229762 weeks
38.48498 -2.42766 (38*2π)/229760 weeks
39-3.83405 2.83273 (39*2π)/229759 weeks
406.60544 3.80187 (40*2π)/229757 weeks
411.90539 -7.67541 (41*2π)/229756 weeks
42-5.2273 -.96743 (42*2π)/229755 weeks
43-.61294 2.72755 (43*2π)/229753 weeks
442.0964 -.0836 (44*2π)/229752 weeks
45-.73602 -1.57252 (45*2π)/229751 weeks
46.30789 1.15324 (46*2π)/229750 weeks
471.65271 -1.60544 (47*2π)/229749 weeks
48-2.02228 -1.30624 (48*2π)/229748 weeks
49.85975 .50286 (49*2π)/229747 weeks
50-3.44158 -1.92296 (50*2π)/229746 weeks
511.27676 6.70521 (51*2π)/229745 weeks
527.0913 -4.93881 (52*2π)/229744 weeks
53-6.30643 -6.24578 (53*2π)/229743 weeks
54-1.53753 6.69568 (54*2π)/229743 weeks
551.60914 -1.79962 (55*2π)/229742 weeks
561.75176 2.59152 (56*2π)/229741 weeks
572.15158 -6.06901 (57*2π)/229740 weeks
58-5.27963 1.42266 (58*2π)/229740 weeks
593.56476 1.87278 (59*2π)/229739 weeks
60-1.68202 -3.71748 (60*2π)/229738 weeks
61-1.06641 5.0528 (61*2π)/229738 weeks
625.0996 -2.83239 (62*2π)/229737 weeks
63-3.04401 -4.0256 (63*2π)/229736 weeks
64-2.84826 3.19315 (64*2π)/229736 weeks
652.39902 1.35576 (65*2π)/229735 weeks
661.55843 -1.73054 (66*2π)/229735 weeks
67-2.11504 -1.53655 (67*2π)/229734 weeks
68.89535 1.61676 (68*2π)/229734 weeks
691.0031 -1.65066 (69*2π)/229733 weeks
70-2.11265 -.79357 (70*2π)/229733 weeks
71.45516 1.84719 (71*2π)/229732 weeks
72.97072 -.81057 (72*2π)/229732 weeks
73-.04594 .54816 (73*2π)/229731 weeks
741.64727 -1.05908 (74*2π)/229731 weeks
75-1.86267 -2.56653 (75*2π)/229731 weeks
76-2.11337 2.62293 (76*2π)/229730 weeks
772.38802 1.44102 (77*2π)/229730 weeks
781.60142 -2.03315 (78*2π)/229729 weeks
79-1.23465 -1.43547 (79*2π)/229729 weeks
80-2.70085 .16089 (80*2π)/229729 weeks
812.05072 3.05115 (81*2π)/229728 weeks
822.40443 -2.43211 (82*2π)/229728 weeks
83-3.72735 -2.09205 (83*2π)/229728 weeks
84.75133 3.54946 (84*2π)/229727 weeks
853.11431 -2.76181 (85*2π)/229727 weeks
86-4.13019 -1.8107 (86*2π)/229727 weeks
87.8902 4.35324 (87*2π)/229726 weeks
883.44508 -2.99435 (88*2π)/229726 weeks
89-3.81651 -1.41907 (89*2π)/229726 weeks
901.81383 1.76315 (90*2π)/229726 weeks
91-1.1407 -1.71107 (91*2π)/229725 weeks
92-.03198 2.65019 (92*2π)/229725 weeks
932.82925 -3.45956 (93*2π)/229725 weeks
94-4.36294 -.59277 (94*2π)/229724 weeks
951.32062 3.97653 (95*2π)/229724 weeks
962.66914 -3.25093 (96*2π)/229724 weeks
97-3.19446 -1.0076 (97*2π)/229724 weeks
98-.54226 1.79495 (98*2π)/229723 weeks
991.59627 .71812 (99*2π)/229723 weeks
1001.37564 -1.69478 (100*2π)/229723 weeks
101-2.71531 -1.4369 (101*2π)/229723 weeks
102-.53473 2.44919 (102*2π)/229723 weeks
1032.26098 -.19956 (103*2π)/229722 weeks
104-.97304 -1.88438 (104*2π)/229722 weeks
105-.60317 1.38302 (105*2π)/229722 weeks
1061.0908 -.99365 (106*2π)/229722 weeks
107-.81109 -.38127 (107*2π)/229721 weeks
108-.72712 -.34783 (108*2π)/229721 weeks
109-.09564 1.61843 (109*2π)/229721 weeks
1101.75711 .22567 (110*2π)/229721 weeks
111.89325 -2.25545 (111*2π)/229721 weeks
112-2.58172 -.90901 (112*2π)/229721 weeks
113-.3765 2.03723 (113*2π)/229720 weeks
1141.71048 .39428 (114*2π)/229720 weeks
115.24264 -.99009 (115*2π)/229720 weeks
116.50534 -.91034 (116*2π)/229720 weeks
117-2.1059 -1.00931 (117*2π)/229720 weeks
118.20561 3.34501 (118*2π)/229719 weeks
1193.13501 -2.49942 (119*2π)/229719 weeks
120-3.6778 -1.23046 (120*2π)/229719 weeks
1211.73191 3.88788 (121*2π)/229719 weeks
1221.89879 -3.85474 (122*2π)/229719 weeks
123-3.05302 .0026 (123*2π)/229719 weeks
1241.33822 .85241 (124*2π)/229719 weeks
125-1.19088 .01381 (125*2π)/229718 weeks
1262.56564 .69666 (126*2π)/229718 weeks
127-1.57035 -2.74626 (127*2π)/229718 weeks
128.36855 1.98158 (128*2π)/229718 weeks
129-.02098 -2.68609 (129*2π)/229718 weeks
130-2.68759 2.08058 (130*2π)/229718 weeks
1313.39844 1.17004 (131*2π)/229718 weeks
132.08117 -2.70155 (132*2π)/229717 weeks
133-.78281 -.15872 (133*2π)/229717 weeks
134-.86318 -.71593 (134*2π)/229717 weeks
135-1.51856 1.43976 (135*2π)/229717 weeks
1362.16854 1.38596 (136*2π)/229717 weeks
1371.3795 -2.40393 (137*2π)/229717 weeks
138-1.811 -1.28042 (138*2π)/229717 weeks
139-1.14235 .66714 (139*2π)/229717 weeks
140.10536 .63135 (140*2π)/229716 weeks
141.66823 1.00357 (141*2π)/229716 weeks
1421.57534 -.90794 (142*2π)/229716 weeks
143-.58216 -2.19797 (143*2π)/229716 weeks
144-2.052 .61842 (144*2π)/229716 weeks
145.14633 1.54806 (145*2π)/229716 weeks
1461.48905 .11846 (146*2π)/229716 weeks
147.97793 -.63228 (147*2π)/229716 weeks
148-.37344 -2.41817 (148*2π)/229716 weeks
149-2.63277 .72289 (149*2π)/229715 weeks
1501.08282 2.03023 (150*2π)/229715 weeks
151.7722 -1.00077 (151*2π)/229715 weeks
152.51501 .39095 (152*2π)/229715 weeks
153.69253 -2.55349 (153*2π)/229715 weeks
154-3.31466 .04664 (154*2π)/229715 weeks
155.67552 2.28524 (155*2π)/229715 weeks
1561.23675 -.17164 (156*2π)/229715 weeks
1571.19006 -.85087 (157*2π)/229715 weeks
158-1.14263 -2.09868 (158*2π)/229715 weeks
159-1.78776 1.00536 (159*2π)/229714 weeks
160.64653 1.23733 (160*2π)/229714 weeks
161.77257 -.11713 (161*2π)/229714 weeks
162.64976 -.78297 (162*2π)/229714 weeks
163-.82126 -.87851 (163*2π)/229714 weeks
164-.65437 -.16049 (164*2π)/229714 weeks
165-.38455 .90117 (165*2π)/229714 weeks
166.50848 .77496 (166*2π)/229714 weeks
1671.31757 -1.12499 (167*2π)/229714 weeks
168-.77505 -.82181 (168*2π)/229714 weeks
169-.85801 .14542 (169*2π)/229714 weeks
170.1184 1.01381 (170*2π)/229714 weeks
1711.4345 -.80227 (171*2π)/229713 weeks
172-1.48069 -.69143 (172*2π)/229713 weeks
173.30797 1.25701 (173*2π)/229713 weeks
174.87893 -1.04533 (174*2π)/229713 weeks
175-1.20087 -.18232 (175*2π)/229713 weeks
176.12849 .61461 (176*2π)/229713 weeks
177.4425 -.32905 (177*2π)/229713 weeks
178-.08452 .20477 (178*2π)/229713 weeks
179.35183 -.75591 (179*2π)/229713 weeks
180-1.07612 -.11013 (180*2π)/229713 weeks
181.10193 .82339 (181*2π)/229713 weeks
182.44042 -.10891 (182*2π)/229713 weeks
183.32721 -.49484 (183*2π)/229713 weeks
184-.95868 -.33287 (184*2π)/229712 weeks
185.57128 1.07831 (185*2π)/229712 weeks
186.74882 -1.37102 (186*2π)/229712 weeks
187-1.67491 -.14725 (187*2π)/229712 weeks
188.45353 1.54592 (188*2π)/229712 weeks
1891.46555 -.75518 (189*2π)/229712 weeks
190-.51664 -1.29817 (190*2π)/229712 weeks
191-1.55811 .52155 (191*2π)/229712 weeks
1921.04025 1.13175 (192*2π)/229712 weeks
193.63072 -1.21191 (193*2π)/229712 weeks
194-.94489 -.53006 (194*2π)/229712 weeks
195-.45122 .93558 (195*2π)/229712 weeks
1961.31251 -.05194 (196*2π)/229712 weeks
197-.73123 -1.76345 (197*2π)/229712 weeks
198-1.50943 1.39929 (198*2π)/229712 weeks
1991.75795 1.13652 (199*2π)/229712 weeks
200.94198 -2.12794 (200*2π)/229711 weeks
201-2.49013 -.39802 (201*2π)/229711 weeks
202.48368 1.99381 (202*2π)/229711 weeks
203.74402 -1.00764 (203*2π)/229711 weeks
204-.15969 .44447 (204*2π)/229711 weeks
2051.12689 -.90128 (205*2π)/229711 weeks
206-2.09356 -.76752 (206*2π)/229711 weeks
207.61196 2.22309 (207*2π)/229711 weeks
2081.53912 -1.97248 (208*2π)/229711 weeks
209-2.54594 .00177 (209*2π)/229711 weeks
2101.69871 1.79493 (210*2π)/229711 weeks
211.65479 -2.36727 (211*2π)/229711 weeks
212-2.00136 .22933 (212*2π)/229711 weeks
213.60829 1.3435 (213*2π)/229711 weeks
2141.01932 -.7347 (214*2π)/229711 weeks
215-.57742 -.66909 (215*2π)/229711 weeks
216-.24036 .36995 (216*2π)/229711 weeks
217.36591 -.33315 (217*2π)/229711 weeks
218-.34645 -.00408 (218*2π)/229711 weeks
219.02678 .02221 (219*2π)/2297