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Fourier Analysis of AIG (American International Group, I)


AIG (American International Group, I) appears to have interesting cyclic behaviour every 176 weeks (37.9343*sine), 164 weeks (35.1657*cosine), and 143 weeks (19.0692*cosine).

AIG (American International Group, I) has an average price of 299.57 (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 11/28/2016 for AIG (American International Group, I), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0299.5735   0 
1-233.7575 -383.089 (1*2π)/22912,291 weeks
2-165.8144 209.249 (2*2π)/22911,146 weeks
3125.6199 49.21009 (3*2π)/2291764 weeks
417.02871 -23.66761 (4*2π)/2291573 weeks
546.95029 -27.63277 (5*2π)/2291458 weeks
6-40.79776 -70.85347 (6*2π)/2291382 weeks
7-59.51717 46.1382 (7*2π)/2291327 weeks
835.65248 38.97766 (8*2π)/2291286 weeks
925.92791 -20.33868 (9*2π)/2291255 weeks
102.03508 -14.89145 (10*2π)/2291229 weeks
11-5.49419 -17.76262 (11*2π)/2291208 weeks
12-32.8191 -4.04292 (12*2π)/2291191 weeks
131.14209 37.93432 (13*2π)/2291176 weeks
1435.16574 1.43525 (14*2π)/2291164 weeks
151.48083 -32.53038 (15*2π)/2291153 weeks
16-19.06924 -.61463 (16*2π)/2291143 weeks
17-2.59153 7.2165 (17*2π)/2291135 weeks
18-.46473 5.23564 (18*2π)/2291127 weeks
196.60455 2.71903 (19*2π)/2291121 weeks
204.19657 -3.34998 (20*2π)/2291115 weeks
211.50311 -9.64784 (21*2π)/2291109 weeks
22-9.49769 -1.56586 (22*2π)/2291104 weeks
23-7.04681 6.70399 (23*2π)/2291100 weeks
2410.59673 9.92066 (24*2π)/229195 weeks
257.87973 -12.28561 (25*2π)/229192 weeks
26-10.59327 -5.62142 (26*2π)/229188 weeks
27-.19776 8.10245 (27*2π)/229185 weeks
281.37304 -4.45989 (28*2π)/229182 weeks
29-2.83163 3.50713 (29*2π)/229179 weeks
305.70567 -.09922 (30*2π)/229176 weeks
31-1.08382 -3.09015 (31*2π)/229174 weeks
321.27192 .73297 (32*2π)/229172 weeks
33-.0307 -7.57523 (33*2π)/229169 weeks
34-9.0842 4.14225 (34*2π)/229167 weeks
356.78601 8.29283 (35*2π)/229165 weeks
365.71003 -8.99877 (36*2π)/229164 weeks
37-4.61864 -.06683 (37*2π)/229162 weeks
381.12579 -2.56752 (38*2π)/229160 weeks
39-5.17963 .88252 (39*2π)/229159 weeks
404.21452 6.44818 (40*2π)/229157 weeks
414.99358 -5.85374 (41*2π)/229156 weeks
42-4.0553 -3.31301 (42*2π)/229155 weeks
43-2.0466 1.88195 (43*2π)/229153 weeks
441.6218 .85258 (44*2π)/229152 weeks
45-.1937 -1.73322 (45*2π)/229151 weeks
46-.43341 1.19349 (46*2π)/229150 weeks
472.16123 -.58565 (47*2π)/229149 weeks
48-1.24479 -2.1034 (48*2π)/229148 weeks
49.65298 .70281 (49*2π)/229147 weeks
50-2.55365 -3.82069 (50*2π)/229146 weeks
51-2.86644 6.65947 (51*2π)/229145 weeks
528.50347 -.07241 (52*2π)/229144 weeks
53-1.87518 -8.86519 (53*2π)/229143 weeks
54-4.71318 4.40824 (54*2π)/229142 weeks
551.36477 -.92601 (55*2π)/229142 weeks
56-.13396 3.6515 (56*2π)/229141 weeks
575.19351 -3.9542 (57*2π)/229140 weeks
58-5.07884 -1.91838 (58*2π)/229140 weeks
591.73993 3.35919 (59*2π)/229139 weeks
60.54052 -4.26983 (60*2π)/229138 weeks
61-4.15217 3.60576 (61*2π)/229138 weeks
625.45161 1.02582 (62*2π)/229137 weeks
63.40678 -5.08843 (63*2π)/229136 weeks
64-4.24289 .32698 (64*2π)/229136 weeks
65.406 2.41721 (65*2π)/229135 weeks
662.17001 -.07043 (66*2π)/229135 weeks
67-.85275 -2.60367 (67*2π)/229134 weeks
68-.45483 1.64284 (68*2π)/229134 weeks
691.80108 -.52678 (69*2π)/229133 weeks
70-1.13054 -2.21091 (70*2π)/229133 weeks
71-1.07466 1.40343 (71*2π)/229132 weeks
72.93607 -.06046 (72*2π)/229132 weeks
73-.63294 .5599 (73*2π)/229131 weeks
741.94955 .64651 (74*2π)/229131 weeks
75.69698 -3.33259 (75*2π)/229131 weeks
76-3.44824 -.06974 (76*2π)/229130 weeks
77.01018 2.64141 (77*2π)/229130 weeks
782.39178 .12619 (78*2π)/229129 weeks
79.56568 -1.63752 (79*2π)/229129 weeks
80-2.23585 -2.41542 (80*2π)/229129 weeks
81-1.30113 3.40502 (81*2π)/229128 weeks
823.29605 .7366 (82*2π)/229128 weeks
83-1.00865 -4.28382 (83*2π)/229128 weeks
84-2.55592 2.66949 (84*2π)/229127 weeks
854.0217 .8439 (85*2π)/229127 weeks
86-1.17704 -4.57512 (86*2π)/229127 weeks
87-3.19222 3.19737 (87*2π)/229126 weeks
884.23302 1.11263 (88*2π)/229126 weeks
89-1.31106 -3.73347 (89*2π)/229126 weeks
90-.0359 2.19789 (90*2π)/229125 weeks
91.43956 -2.09699 (91*2π)/229125 weeks
92-2.62859 1.78566 (92*2π)/229125 weeks
934.49968 .30931 (93*2π)/229125 weeks
94-1.72717 -4.13353 (94*2π)/229124 weeks
95-2.92663 3.12275 (95*2π)/229124 weeks
963.89121 .65851 (96*2π)/229124 weeks
97-.55944 -3.05227 (97*2π)/229124 weeks
98-1.9437 -.13081 (98*2π)/229123 weeks
99-.35969 1.63193 (99*2π)/229123 weeks
1002.20868 .76689 (100*2π)/229123 weeks
101.03057 -3.11657 (101*2π)/229123 weeks
102-2.579 .27424 (102*2π)/229122 weeks
103.85071 1.89429 (103*2π)/229122 weeks
1041.02399 -1.68682 (104*2π)/229122 weeks
105-1.62751 .12022 (105*2π)/229122 weeks
1061.13091 .35771 (106*2π)/229122 weeks
107-.00847 -.73318 (107*2π)/229121 weeks
108-.0055 -1.33189 (108*2π)/229121 weeks
109-1.79573 .19888 (109*2π)/229121 weeks
110-.18887 1.76742 (110*2π)/229121 weeks
1112.4028 .3405 (111*2π)/229121 weeks
112.07575 -2.79926 (112*2π)/229120 weeks
113-2.07185 -.21015 (113*2π)/229120 weeks
114-.22856 1.50258 (114*2π)/229120 weeks
115.42703 .07013 (115*2π)/229120 weeks
1161.21649 .4545 (116*2π)/229120 weeks
117.38052 -2.79436 (117*2π)/229120 weeks
118-3.55787 1.15274 (118*2π)/229119 weeks
1193.15552 2.17943 (119*2π)/229119 weeks
120-.04836 -4.08844 (120*2π)/229119 weeks
121-3.42859 2.86733 (121*2π)/229119 weeks
1223.73386 .77745 (122*2π)/229119 weeks
123-.83115 -2.68286 (123*2π)/229119 weeks
124-.05257 1.06738 (124*2π)/229118 weeks
125-1.04401 -1.45803 (125*2π)/229118 weeks
126-.09369 2.94748 (126*2π)/229118 weeks
1271.76952 -2.23933 (127*2π)/229118 weeks
128-1.62658 1.26284 (128*2π)/229118 weeks
1292.77355 -.86724 (129*2π)/229118 weeks
130-2.79354 -2.58054 (130*2π)/229118 weeks
131-.93816 3.17542 (131*2π)/229117 weeks
1322.01137 -.06134 (132*2π)/229117 weeks
133.29988 -.25696 (133*2π)/229117 weeks
1341.00214 -1.08483 (134*2π)/229117 weeks
135-1.77321 -1.88882 (135*2π)/229117 weeks
136-1.76869 1.97283 (136*2π)/229117 weeks
1371.98952 1.45312 (137*2π)/229117 weeks
1381.23739 -1.42606 (138*2π)/229117 weeks
139-.43713 -1.3386 (139*2π)/229116 weeks
140-.53504 -.58868 (140*2π)/229116 weeks
141-1.49738 .42464 (141*2π)/229116 weeks
142.35517 1.71236 (142*2π)/229116 weeks
1432.30855 -.33414 (143*2π)/229116 weeks
144-.20452 -2.0526 (144*2π)/229116 weeks
145-1.61109 -.54094 (145*2π)/229116 weeks
146-.62181 .95575 (146*2π)/229116 weeks
147-.07078 1.49158 (147*2π)/229116 weeks
1482.64791 .03369 (148*2π)/229115 weeks
149-.25373 -2.76711 (149*2π)/229115 weeks
150-1.98265 .55639 (150*2π)/229115 weeks
151.36152 .23956 (151*2π)/229115 weeks
152-1.13879 .94799 (152*2π)/229115 weeks
1532.70278 1.27332 (153*2π)/229115 weeks
154.48791 -3.21546 (154*2π)/229115 weeks
155-1.98894 -.22775 (155*2π)/229115 weeks
156-.72155 .63436 (156*2π)/229115 weeks
157.17923 1.79116 (157*2π)/229115 weeks
1582.27902 -.503 (158*2π)/229115 weeks
159-.26652 -1.95304 (159*2π)/229114 weeks
160-1.20431 -.12213 (160*2π)/229114 weeks
161-.58614 .41353 (161*2π)/229114 weeks
162.31398 .9813 (162*2π)/229114 weeks
163.75816 -.36191 (163*2π)/229114 weeks
164.68576 -.7664 (164*2π)/229114 weeks
165-.5296 -.8639 (165*2π)/229114 weeks
166-1.44046 -.13802 (166*2π)/229114 weeks
167.48682 1.32011 (167*2π)/229114 weeks
168.86667 -.16195 (168*2π)/229114 weeks
169.33279 -1.01315 (169*2π)/229114 weeks
170-1.25474 -.55594 (170*2π)/229113 weeks
171.4141 1.55719 (171*2π)/229113 weeks
172.91099 -1.26867 (172*2π)/229113 weeks
173-1.32783 -.16414 (173*2π)/229113 weeks
174.68552 1.05221 (174*2π)/229113 weeks
175.41777 -.95362 (175*2π)/229113 weeks
176-.58047 -.3175 (176*2π)/229113 weeks
177.17526 .21325 (177*2π)/229113 weeks
178-.53283 -.06925 (178*2π)/229113 weeks
179.59415 .68085 (179*2π)/229113 weeks
180.53445 -.93299 (180*2π)/229113 weeks
181-.68193 -.41225 (181*2π)/229113 weeks
182-.37793 .08637 (182*2π)/229113 weeks
183.20056 .62506 (183*2π)/229113 weeks
184.6408 -1.0521 (184*2π)/229112 weeks
185-1.41989 -.01695 (185*2π)/229112 weeks
186.84485 1.27651 (186*2π)/229112 weeks
187.9406 -1.49214 (187*2π)/229112 weeks
188-1.56952 -.71115 (188*2π)/229112 weeks
189-.4321 1.364 (189*2π)/229112 weeks
1901.25849 .62885 (190*2π)/229112 weeks
191.37328 -1.71356 (191*2π)/229112 weeks
192-1.52173 .0797 (192*2π)/229112 weeks
193.31277 1.01327 (193*2π)/229112 weeks
194.95686 -.3571 (194*2π)/229112 weeks
195-.6308 -1.1384 (195*2π)/229112 weeks
196-.99451 1.15841 (196*2π)/229112 weeks
1971.96502 .40372 (197*2π)/229112 weeks
198-.05919 -2.21461 (198*2π)/229112 weeks
199-2.19103 .30019 (199*2π)/229112 weeks
200.856 2.21151 (200*2π)/229111 weeks
2011.74582 -1.65367 (201*2π)/229111 weeks
202-1.63629 -.78227 (202*2π)/229111 weeks
203.37504 .36202 (203*2π)/229111 weeks
204-.81613 -.61708 (204*2π)/229111 weeks
205-.03816 1.84619 (205*2π)/229111 weeks
2061.90673 -1.41205 (206*2π)/229111 weeks
207-2.28421 -1.02162 (207*2π)/229111 weeks
208.6365 2.33878 (208*2π)/229111 weeks
2091.36965 -2.24801 (209*2π)/229111 weeks
210-2.51373 .01291 (210*2π)/229111 weeks
2111.06342 1.86548 (211*2π)/229111 weeks
2121.13626 -1.39344 (212*2π)/229111 weeks
213-1.18609 -.8108 (213*2π)/229111 weeks
214-.41445 .85963 (214*2π)/229111 weeks
215.57926 .03502 (215*2π)/229111 weeks
216-.24903 -.4703 (216*2π)/229111 weeks
217.06574 .34891 (217*2π)/229111 weeks
218.06536 -.23984 (218*2π)/229111 weeks
219-.09524 -.26251 (219*2π)/229110 weeks
220-.18071 .23302 (220*2π)/229110 weeks
221.28503 .06405 (221*2π)/229110 weeks
222-.19717 -.75572 (222*2π)/229110 weeks
223-.5552 1.23395 (223*2π)/229110 weeks
2241.80473 -.34677 (224*2π)/229110 weeks
225-1.27069 -1.73167 (225*2π)/229110 weeks
226-.6745 1.65257 (226*2π)/229110 weeks
227.9452