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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 (33.7777*sine), 165 weeks (32.1192*cosine), and 144 weeks (17.2577*cosine).

AIG (American International Group, I) has an average price of 294.96 (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 3/20/2017 for AIG (American International Group, I), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0294.9589   0
1-240.8588 -370.8341 (1*2π)/23072,307 weeks
2-150.5621 216.9091 (2*2π)/23071,154 weeks
3130.6251 37.33636 (3*2π)/2307769 weeks
414.03358 -27.76593 (4*2π)/2307577 weeks
540.32767 -33.53462 (5*2π)/2307461 weeks
6-51.78044 -60.4399 (6*2π)/2307385 weeks
7-47.04293 57.6949 (7*2π)/2307330 weeks
845.42442 28.44194 (8*2π)/2307288 weeks
919.74865 -27.9587 (9*2π)/2307256 weeks
10-3.71987 -14.65527 (10*2π)/2307231 weeks
11-11.10716 -13.37507 (11*2π)/2307210 weeks
12-29.46028 8.1187 (12*2π)/2307192 weeks
1316.88375 33.77774 (13*2π)/2307177 weeks
1432.11917 -14.5229 (14*2π)/2307165 weeks
15-13.2651 -29.88383 (15*2π)/2307154 weeks
16-17.25767 9.66501 (16*2π)/2307144 weeks
172.8833 8.1054 (17*2π)/2307136 weeks
183.25101 3.66223 (18*2π)/2307128 weeks
197.25835 -2.02876 (19*2π)/2307121 weeks
20.99058 -5.83656 (20*2π)/2307115 weeks
21-4.07309 -7.79745 (21*2π)/2307110 weeks
22-7.9115 5.23578 (22*2π)/2307105 weeks
23.59493 8.38099 (23*2π)/2307100 weeks
2414.24357 -.35252 (24*2π)/230796 weeks
25-2.80901 -14.71217 (25*2π)/230792 weeks
26-11.1312 3.6164 (26*2π)/230789 weeks
276.24197 6.17153 (27*2π)/230785 weeks
28-1.0778 -5.21881 (28*2π)/230782 weeks
29.85885 3.7097 (29*2π)/230780 weeks
304.05028 -4.80071 (30*2π)/230777 weeks
31-3.35817 -1.55088 (31*2π)/230774 weeks
321.14313 -.33745 (32*2π)/230772 weeks
33-4.58265 -3.92896 (33*2π)/230770 weeks
34-.61309 9.09362 (34*2π)/230768 weeks
3510.54945 -2.56626 (35*2π)/230766 weeks
36-4.87444 -10.03793 (36*2π)/230764 weeks
37-2.94351 4.98925 (37*2π)/230762 weeks
38-.01613 -2.06551 (38*2π)/230761 weeks
39-.57156 4.1157 (39*2π)/230759 weeks
407.25645 -1.73826 (40*2π)/230758 weeks
41-4.00531 -6.99776 (41*2π)/230756 weeks
42-4.25353 3.42974 (42*2π)/230755 weeks
432.18818 2.21205 (43*2π)/230754 weeks
441.68272 -1.86586 (44*2π)/230752 weeks
45-1.44313 -.82893 (45*2π)/230751 weeks
461.15068 .48768 (46*2π)/230750 weeks
47.01699 -2.26558 (47*2π)/230749 weeks
48-2.14717 .59227 (48*2π)/230748 weeks
491.29507 .00806 (49*2π)/230747 weeks
50-2.75459 .72657 (50*2π)/230746 weeks
515.77337 2.5069 (51*2π)/230745 weeks
52.00829 -8.6665 (52*2π)/230744 weeks
53-8.20199 1.85015 (53*2π)/230744 weeks
545.24199 5.51155 (54*2π)/230743 weeks
55.11006 -3.76709 (55*2π)/230742 weeks
562.34058 .02662 (56*2π)/230741 weeks
57-3.4164 -4.82448 (57*2π)/230740 weeks
58-1.36195 5.47202 (58*2π)/230740 weeks
593.97753 -2.15742 (59*2π)/230739 weeks
60-3.6427 -.80671 (60*2π)/230738 weeks
613.58855 3.11617 (61*2π)/230738 weeks
62-.15595 -6.06252 (62*2π)/230737 weeks
63-4.61589 1.56098 (63*2π)/230737 weeks
642.37016 3.76278 (64*2π)/230736 weeks
652.36739 -2.49832 (65*2π)/230735 weeks
66-1.28063 -2.05581 (66*2π)/230735 weeks
67-1.92156 1.15872 (67*2π)/230734 weeks
682.24501 -.15717 (68*2π)/230734 weeks
69-1.09918 -1.49077 (69*2π)/230733 weeks
70-1.00945 1.55358 (70*2π)/230733 weeks
712.27177 -.07468 (71*2π)/230732 weeks
72-.44891 -1.54017 (72*2π)/230732 weeks
73.18642 .25166 (73*2π)/230732 weeks
74-.57735 -1.55382 (74*2π)/230731 weeks
75-2.27761 1.23403 (75*2π)/230731 weeks
762.50647 2.21163 (76*2π)/230730 weeks
771.61989 -2.74453 (77*2π)/230730 weeks
78-2.07052 -1.69845 (78*2π)/230730 weeks
79-1.37525 1.48786 (79*2π)/230729 weeks
80.36504 1.71896 (80*2π)/230729 weeks
813.20965 -1.88629 (81*2π)/230728 weeks
82-2.63172 -2.39123 (82*2π)/230728 weeks
83-2.16023 3.05037 (83*2π)/230728 weeks
843.88043 -.71654 (84*2π)/230727 weeks
85-2.43413 -3.20046 (85*2π)/230727 weeks
86-1.61998 3.75835 (86*2π)/230727 weeks
874.45721 -1.01761 (87*2π)/230727 weeks
88-3.04562 -3.49455 (88*2π)/230726 weeks
89-1.38922 3.83723 (89*2π)/230726 weeks
902.75479 -1.7781 (90*2π)/230726 weeks
91-1.88182 .59269 (91*2π)/230725 weeks
922.20008 -.06436 (92*2π)/230725 weeks
93-2.88859 -2.66634 (93*2π)/230725 weeks
94.19435 4.32458 (94*2π)/230725 weeks
953.7085 -2.15492 (95*2π)/230724 weeks
96-3.65175 -2.34234 (96*2π)/230724 weeks
97-.12838 3.56137 (97*2π)/230724 weeks
982.31383 -.77826 (98*2π)/230724 weeks
99-.06802 -1.98992 (99*2π)/230723 weeks
100-1.80048 -.40241 (100*2π)/230723 weeks
101-.42747 2.55383 (101*2π)/230723 weeks
1022.67235 -.82169 (102*2π)/230723 weeks
103-1.0911 -2.33685 (103*2π)/230722 weeks
104-1.53881 1.35707 (104*2π)/230722 weeks
1051.6683 .08378 (105*2π)/230722 weeks
106-1.10509 -1.25903 (106*2π)/230722 weeks
107.09686 .95582 (107*2π)/230722 weeks
108.31422 -.1283 (108*2π)/230721 weeks
1091.26533 -.82085 (109*2π)/230721 weeks
110-1.04341 -1.58235 (110*2π)/230721 weeks
111-1.91629 .53121 (111*2π)/230721 weeks
112.81689 2.25378 (112*2π)/230721 weeks
1132.11443 -1.45469 (113*2π)/230720 weeks
114-.96883 -1.82382 (114*2π)/230720 weeks
115-1.30886 .57812 (115*2π)/230720 weeks
116-.18753 .19734 (116*2π)/230720 weeks
117.40285 1.41327 (117*2π)/230720 weeks
1182.27417 -1.85068 (118*2π)/230720 weeks
119-3.55931 -1.51618 (119*2π)/230719 weeks
120.94087 3.58232 (120*2π)/230719 weeks
1212.35625 -3.30947 (121*2π)/230719 weeks
122-4.46485 .34949 (122*2π)/230719 weeks
1232.34212 2.62509 (123*2π)/230719 weeks
124.56485 -2.49764 (124*2π)/230719 weeks
125-.36872 .856 (125*2π)/230718 weeks
126-.39922 -1.92992 (126*2π)/230718 weeks
127-1.47785 2.61866 (127*2π)/230718 weeks
1282.30532 -1.27385 (128*2π)/230718 weeks
129-1.99954 .67309 (129*2π)/230718 weeks
1302.88058 .28841 (130*2π)/230718 weeks
131-1.6675 -3.39858 (131*2π)/230718 weeks
132-1.98853 2.52184 (132*2π)/230717 weeks
1331.70016 .59132 (133*2π)/230717 weeks
134.3354 -.00811 (134*2π)/230717 weeks
1351.29012 -.72262 (135*2π)/230717 weeks
136-1.26653 -2.2522 (136*2π)/230717 weeks
137-2.1766 1.5031 (137*2π)/230717 weeks
1381.58538 1.7928 (138*2π)/230717 weeks
1391.39561 -1.12565 (139*2π)/230717 weeks
140-.25476 -1.33796 (140*2π)/230716 weeks
141-.46619 -.64629 (141*2π)/230716 weeks
142-1.51714 .3252 (142*2π)/230716 weeks
143.27292 1.71162 (143*2π)/230716 weeks
1442.26867 -.30239 (144*2π)/230716 weeks
145-.25662 -2.00295 (145*2π)/230716 weeks
146-1.60938 -.41952 (146*2π)/230716 weeks
147-.50694 1.02466 (147*2π)/230716 weeks
148.13664 1.43655 (148*2π)/230716 weeks
1492.57314 -.35146 (149*2π)/230715 weeks
150-.73223 -2.6315 (150*2π)/230715 weeks
151-1.82086 .96639 (151*2π)/230715 weeks
152.49458 .21898 (152*2π)/230715 weeks
153-.75471 1.09181 (153*2π)/230715 weeks
1542.87106 .40314 (154*2π)/230715 weeks
155-.55784 -3.19528 (155*2π)/230715 weeks
156-1.95405 .57628 (156*2π)/230715 weeks
157-.2399 .90651 (157*2π)/230715 weeks
158.92435 1.40907 (158*2π)/230715 weeks
1591.81614 -1.48441 (159*2π)/230715 weeks
160-1.18648 -1.58581 (160*2π)/230714 weeks
161-1.08308 .58218 (161*2π)/230714 weeks
162-.11339 .64404 (162*2π)/230714 weeks
163.83078 .5578 (163*2π)/230714 weeks
164.46603 -.87448 (164*2π)/230714 weeks
165.06914 -.93335 (165*2π)/230714 weeks
166-.96239 -.25411 (166*2π)/230714 weeks
167-.96386 .73441 (167*2π)/230714 weeks
1681.37197 .68198 (168*2π)/230714 weeks
169.48779 -.84656 (169*2π)/230714 weeks
170-.47128 -.88337 (170*2π)/230714 weeks
171-1.07991 .4792 (171*2π)/230713 weeks
1721.40324 .79658 (172*2π)/230713 weeks
173-.24963 -1.57222 (173*2π)/230713 weeks
174-.93584 .8715 (174*2π)/230713 weeks
1751.28539 .13305 (175*2π)/230713 weeks
176-.52117 -1.01425 (176*2π)/230713 weeks
177-.51558 .32521 (177*2π)/230713 weeks
178.4063 .06363 (178*2π)/230713 weeks
179-.28196 .21046 (179*2π)/230713 weeks
180.83608 -.20226 (180*2π)/230713 weeks
181-.5901 -.93067 (181*2π)/230713 weeks
182-.63778 .49737 (182*2π)/230713 weeks
183.15306 .28262 (183*2π)/230713 weeks
184.59245 -.03489 (184*2π)/230713 weeks
185-.54136 -.97907 (185*2π)/230712 weeks
186-.43552 1.18655 (186*2π)/230712 weeks
1871.46593 -.43785 (187*2π)/230712 weeks
188-1.12413 -1.30421 (188*2π)/230712 weeks
189-.86357 1.3641 (189*2π)/230712 weeks
1901.45539 .51504 (190*2π)/230712 weeks
191.59455 -1.23208 (191*2π)/230712 weeks
192-1.57182 -.65232 (192*2π)/230712 weeks
193-.00539 1.49826 (193*2π)/230712 weeks
1941.14959 -.46515 (194*2π)/230712 weeks
195-.39177 -.99743 (195*2π)/230712 weeks
196-1.00241 .47856 (196*2π)/230712 weeks
1971.0723 .765 (197*2π)/230712 weeks
198.36293 -1.90917 (198*2π)/230712 weeks
199-2.07357 .27932 (199*2π)/230712 weeks
200.75087 1.92986 (200*2π)/230712 weeks
2011.9266 -1.26169 (201*2π)/230711 weeks
202-1.94426 -1.58419 (202*2π)/230711 weeks
203-.57501 1.89785 (203*2π)/230711 weeks
204.91854 -.53125 (204*2π)/230711 weeks
205-.35292 .43071 (205*2π)/230711 weeks
2061.46343 -.33932 (206*2π)/230711 weeks
207-1.64405 -1.55584 (207*2π)/230711 weeks
208-.34706 2.28137 (208*2π)/230711 weeks
2092.11652 -1.24147 (209*2π)/230711 weeks
210-2.39861 -.86779 (210*2π)/230711 weeks
211.94342 2.24938 (211*2π)/230711 weeks
2121.36228 -1.96517 (212*2π)/230711 weeks
213-1.93496 -.41977 (213*2π)/230711 weeks
214.114 1.43644 (214*2π)/230711 weeks
2151.13887 -.37222 (215*2π)/230711 weeks
216-.36853 -.76547 (216*2π)/230711 weeks
217-.32834 .30062