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Fourier Analysis of AXP (American Express Company Common)


AXP (American Express Company Common) appears to have interesting cyclic behaviour every 156 weeks (1.956*sine), 167 weeks (1.761*sine), and 180 weeks (1.737*cosine).

AXP (American Express Company Common) has an average price of 21.1 (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 6/1/1972 to 4/17/2017 for AXP (American Express Company Common), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
021.09619   0 
110.93278 -22.82421 (1*2π)/23422,342 weeks
22.15198 -8.81821 (2*2π)/23421,171 weeks
35.24644 -9.41826 (3*2π)/2342781 weeks
4.73231 -8.07437 (4*2π)/2342586 weeks
5.19726 -8.25916 (5*2π)/2342468 weeks
6-4.06056 -5.88759 (6*2π)/2342390 weeks
7-2.47165 -.77155 (7*2π)/2342335 weeks
8.50777 -1.97739 (8*2π)/2342293 weeks
9-.80031 -2.44408 (9*2π)/2342260 weeks
10-.6206 -1.46592 (10*2π)/2342234 weeks
11-.99847 -1.31152 (11*2π)/2342213 weeks
12-.8279 .23363 (12*2π)/2342195 weeks
131.737 .59694 (13*2π)/2342180 weeks
141.72275 -1.76104 (14*2π)/2342167 weeks
15.39507 -1.95601 (15*2π)/2342156 weeks
16.34993 -1.30973 (16*2π)/2342146 weeks
17.04995 -1.03944 (17*2π)/2342138 weeks
18.81128 -.6395 (18*2π)/2342130 weeks
191.03271 -1.67538 (19*2π)/2342123 weeks
20.12506 -1.7532 (20*2π)/2342117 weeks
21.12269 -1.48081 (21*2π)/2342112 weeks
22-.50224 -.9951 (22*2π)/2342106 weeks
23.11852 -.54 (23*2π)/2342102 weeks
24.67032 -.76574 (24*2π)/234298 weeks
25.49184 -1.25953 (25*2π)/234294 weeks
26.10907 -1.09981 (26*2π)/234290 weeks
27.24072 -1.01487 (27*2π)/234287 weeks
28.03404 -1.14911 (28*2π)/234284 weeks
29.0503 -.62687 (29*2π)/234281 weeks
30.58879 -.84567 (30*2π)/234278 weeks
31.14978 -1.34542 (31*2π)/234276 weeks
32-.10335 -.99648 (32*2π)/234273 weeks
33.01961 -1.00865 (33*2π)/234271 weeks
34-.43691 -.73518 (34*2π)/234269 weeks
35.0977 -.28147 (35*2π)/234267 weeks
36.58121 -.92277 (36*2π)/234265 weeks
37-.09 -1.04062 (37*2π)/234263 weeks
38-.05445 -.95259 (38*2π)/234262 weeks
39-.34263 -.80681 (39*2π)/234260 weeks
40-.12679 -.48088 (40*2π)/234259 weeks
41-.06335 -.73038 (41*2π)/234257 weeks
42-.12399 -.60966 (42*2π)/234256 weeks
43-.15439 -.54374 (43*2π)/234254 weeks
44-.21527 -.46467 (44*2π)/234253 weeks
45.11918 -.28619 (45*2π)/234252 weeks
46.13583 -.48075 (46*2π)/234251 weeks
47.17415 -.653 (47*2π)/234250 weeks
48-.0833 -.78701 (48*2π)/234249 weeks
49-.32526 -.56974 (49*2π)/234248 weeks
50-.20018 -.20374 (50*2π)/234247 weeks
51.12572 -.17537 (51*2π)/234246 weeks
52.2319 -.53509 (52*2π)/234245 weeks
53-.09721 -.40122 (53*2π)/234244 weeks
54.16572 -.31216 (54*2π)/234243 weeks
55.15243 -.50412 (55*2π)/234243 weeks
56.16604 -.34798 (56*2π)/234242 weeks
57.38305 -.69441 (57*2π)/234241 weeks
58-.16123 -.7646 (58*2π)/234240 weeks
59.07081 -.38859 (59*2π)/234240 weeks
60.06622 -.72457 (60*2π)/234239 weeks
61-.13053 -.45097 (61*2π)/234238 weeks
62.22622 -.59472 (62*2π)/234238 weeks
63-.25057 -.75235 (63*2π)/234237 weeks
64-.19467 -.36756 (64*2π)/234237 weeks
65.03798 -.4725 (65*2π)/234236 weeks
66-.14685 -.53508 (66*2π)/234235 weeks
67-.19896 -.42212 (67*2π)/234235 weeks
68-.03325 -.28508 (68*2π)/234234 weeks
69.0376 -.56313 (69*2π)/234234 weeks
70-.21998 -.46407 (70*2π)/234233 weeks
71-.14057 -.35157 (71*2π)/234233 weeks
72-.06182 -.43502 (72*2π)/234233 weeks
73-.1932 -.43723 (73*2π)/234232 weeks
74-.22173 -.31929 (74*2π)/234232 weeks
75-.17189 -.24471 (75*2π)/234231 weeks
76-.16324 -.25211 (76*2π)/234231 weeks
77-.02334 -.15209 (77*2π)/234230 weeks
78-.01701 -.28822 (78*2π)/234230 weeks
79-.04797 -.30118 (79*2π)/234230 weeks
80-.01875 -.25597 (80*2π)/234229 weeks
81-.02798 -.37089 (81*2π)/234229 weeks
82-.08753 -.38324 (82*2π)/234229 weeks
83-.15321 -.28022 (83*2π)/234228 weeks
84-.16431 -.24811 (84*2π)/234228 weeks
85-.02346 -.22733 (85*2π)/234228 weeks
86-.10184 -.35938 (86*2π)/234227 weeks
87-.23628 -.18927 (87*2π)/234227 weeks
88-.11905 -.18304 (88*2π)/234227 weeks
89-.15693 -.03668 (89*2π)/234226 weeks
90.07204 .03816 (90*2π)/234226 weeks
91.22523 -.28487 (91*2π)/234226 weeks
92-.08781 -.24125 (92*2π)/234225 weeks
93.03944 -.11438 (93*2π)/234225 weeks
94.12695 -.23562 (94*2π)/234225 weeks
95.15508 -.1838 (95*2π)/234225 weeks
96.15818 -.41111 (96*2π)/234224 weeks
97-.01931 -.39258 (97*2π)/234224 weeks
98.00473 -.29951 (98*2π)/234224 weeks
99.05317 -.32244 (99*2π)/234224 weeks
100.05857 -.49759 (100*2π)/234223 weeks
101-.23743 -.40721 (101*2π)/234223 weeks
102-.15351 -.27701 (102*2π)/234223 weeks
103-.1617 -.27235 (103*2π)/234223 weeks
104-.12035 -.1493 (104*2π)/234223 weeks
105-.03346 -.25481 (105*2π)/234222 weeks
106-.14504 -.23626 (106*2π)/234222 weeks
107-.07323 -.1577 (107*2π)/234222 weeks
108-.03165 -.18201 (108*2π)/234222 weeks
109-.01371 -.27597 (109*2π)/234221 weeks
110-.132 -.27565 (110*2π)/234221 weeks
111-.21844 -.16762 (111*2π)/234221 weeks
112-.07982 -.0573 (112*2π)/234221 weeks
113-.01187 -.07769 (113*2π)/234221 weeks
114.08231 -.15507 (114*2π)/234221 weeks
115.02687 -.22529 (115*2π)/234220 weeks
116-.03462 -.26498 (116*2π)/234220 weeks
117-.04872 -.25091 (117*2π)/234220 weeks
118-.14037 -.17829 (118*2π)/234220 weeks
119.01218 -.11785 (119*2π)/234220 weeks
120-.03884 -.31927 (120*2π)/234220 weeks
121-.20323 -.11407 (121*2π)/234219 weeks
122-.00242 -.07162 (122*2π)/234219 weeks
123-.06831 -.17334 (123*2π)/234219 weeks
124.00535 -.04922 (124*2π)/234219 weeks
125.02011 -.15067 (125*2π)/234219 weeks
126-.01035 -.11828 (126*2π)/234219 weeks
127.05435 -.14511 (127*2π)/234218 weeks
128-.0048 -.09945 (128*2π)/234218 weeks
129.21402 -.11729 (129*2π)/234218 weeks
130.06421 -.35139 (130*2π)/234218 weeks
131-.00682 -.17676 (131*2π)/234218 weeks
132.0473 -.27582 (132*2π)/234218 weeks
133-.09517 -.20006 (133*2π)/234218 weeks
134.08377 -.1018 (134*2π)/234217 weeks
135.10276 -.30961 (135*2π)/234217 weeks
136-.04066 -.31745 (136*2π)/234217 weeks
137-.08636 -.2941 (137*2π)/234217 weeks
138-.17865 -.16587 (138*2π)/234217 weeks
139-.03577 -.02988 (139*2π)/234217 weeks
140.15786 -.1622 (140*2π)/234217 weeks
141.0824 -.34892 (141*2π)/234217 weeks
142-.1242 -.36037 (142*2π)/234216 weeks
143-.13619 -.20371 (143*2π)/234216 weeks
144-.09631 -.18145 (144*2π)/234216 weeks
145-.08624 -.1182 (145*2π)/234216 weeks
146.08479 -.16716 (146*2π)/234216 weeks
147-.02256 -.34903 (147*2π)/234216 weeks
148-.19188 -.23655 (148*2π)/234216 weeks
149-.10907 -.15932 (149*2π)/234216 weeks
150-.13905 -.13225 (150*2π)/234216 weeks
151-.04562 -.08973 (151*2π)/234216 weeks
152-.0277 -.15738 (152*2π)/234215 weeks
153-.03701 -.18375 (153*2π)/234215 weeks
154-.10749 -.18471 (154*2π)/234215 weeks
155-.08603 -.0999 (155*2π)/234215 weeks
156-.01579 -.1276 (156*2π)/234215 weeks
157-.04669 -.14218 (157*2π)/234215 weeks
158.00645 -.1715 (158*2π)/234215 weeks
159-.06951 -.20171 (159*2π)/234215 weeks
160-.06677 -.14014 (160*2π)/234215 weeks
161-.07231 -.17954 (161*2π)/234215 weeks
162-.07507 -.12679 (162*2π)/234214 weeks
163-.0634 -.17421 (163*2π)/234214 weeks
164-.13345 -.12329 (164*2π)/234214 weeks
165-.06299 -.06197 (165*2π)/234214 weeks
166-.03355 -.12054 (166*2π)/234214 weeks
167-.06576 -.12733 (167*2π)/234214 weeks
168-.08918 -.06375 (168*2π)/234214 weeks
169-.01092 -.04773 (169*2π)/234214 weeks
170.02204 -.11776 (170*2π)/234214 weeks
171-.0013 -.0743 (171*2π)/234214 weeks
172.06137 -.1832 (172*2π)/234214 weeks
173-.04668 -.16491 (173*2π)/234214 weeks
174.02471 -.13582 (174*2π)/234213 weeks
175-.03746 -.2466 (175*2π)/234213 weeks
176-.10913 -.14775 (176*2π)/234213 weeks
177-.01089 -.1305 (177*2π)/234213 weeks
178-.10473 -.22034 (178*2π)/234213 weeks
179-.12376 -.08982 (179*2π)/234213 weeks
180-.02168 -.08406 (180*2π)/234213 weeks
181-.05066 -.19485 (181*2π)/234213 weeks
182-.1537 -.1548 (182*2π)/234213 weeks
183-.16305 -.04877 (183*2π)/234213 weeks
184-.09133 .01778 (184*2π)/234213 weeks
185-.00824 .00478 (185*2π)/234213 weeks
186.05898 -.033 (186*2π)/234213 weeks
187.02092 -.13771 (187*2π)/234213 weeks
188-.01987 -.07904 (188*2π)/234212 weeks
189.05236 -.10952 (189*2π)/234212 weeks
190-.03572 -.15167 (190*2π)/234212 weeks
191-.02098 -.08305 (191*2π)/234212 weeks
192.02383 -.12875 (192*2π)/234212 weeks
193-.03712 -.16358 (193*2π)/234212 weeks
194-.0556 -.11851 (194*2π)/234212 weeks
195-.05131 -.0837 (195*2π)/234212 weeks
196.00334 -.08226 (196*2π)/234212 weeks
197.00327 -.12293 (197*2π)/234212 weeks
198-.03129 -.13934 (198*2π)/234212 weeks
199-.02887 -.109 (199*2π)/234212 weeks
200-.06041 -.1131 (200*2π)/234212 weeks
201-.07252 -.0531 (201*2π)/234212 weeks
202.02694 -.01357 (202*2π)/234212 weeks
203.06203 -.10348 (203*2π)/234212 weeks
204.01425 -.11707 (204*2π)/234211 weeks
205.04563 -.10066 (205*2π)/234211 weeks
206.05308 -.17356 (206*2π)/234211 weeks
207-.04291 -.16161 (207*2π)/234211 weeks
208.01691 -.12709 (208*2π)/234211 weeks
209-.00056 -.20783 (209*2π)/234211 weeks
210-.07572 -.15014 (210*2π)/234211 weeks
211-.02721 -.13701 (211*2π)/234211 weeks
212-.0808 -.16828 (212*2π)/234211 weeks
213-.07434 -.06146 (213*2π)/234211 weeks
214.01001 -.12953 (214*2π)/234211 weeks
215-.07333 -.13681 (215*2π)/234211 weeks
216-.03099 -.06833 (216*2π)/234211 weeks
217.01389 -.13516 (217*2π)/234211 weeks
218-.02703 -.18061 (218*2π)/234211 weeks
219-.08097 -.13921 (219*2π)/234211 weeks
220-.03903 -.13079 (220*2π)/234211 weeks
221-.1083 -.18008 (221*2π)/234211 weeks
222-.14782 -.04676 (222*2π)/234211 weeks
223-.04061 -.03832 (223*2π)/234211 weeks
224-.02343 -.07537 (224*2π)/234210 weeks
225-.03359 -.09021 (225*2π)/234210 weeks
226-.06268 -.11939 (226*2π)/234210 weeks
227-.12117 -.08323 (227*2π)/234210 weeks
228-.09016 .04457 (228*2π)/234210 weeks
229.06543 .01626 (229*2π)/234210 weeks
230.04494 -.11789 (230*2π)/234210 weeks
231-.01736 -.07458 (231*2π)/234210 weeks
232.01044 -.09774 (232*2π)/234210 weeks
233-.02796 -.08159 (233*2π)/234210 weeks
234.03375 -.05855 (234*2π)/234210 weeks
235.01342 -.14599 (235*2π)/234210 weeks
236-.03344 -.10481 (236*2π)/234210 weeks
237-.03517 -.0852 (237*2π)/234210 weeks
238-.0011 -.03055 (238*2π)/234210 weeks
239.08352 -.10224 (239*2π)/234210 weeks
240.02059 -.16703 (240*2π)/234210 weeks
241-.00957 -.12891 (241*2π)/234210 weeks
242-.01968 -.1674 (242*2π)/234210 weeks
243-.04322 -.11799 (243*2π)/234210 weeks
244-.01174 -.12098 (244*2π)/234210 weeks
245-.02802 -.17296 (245*2π)/234210 weeks
246-.09034 -.13212 (246*2π)/234210 weeks
247-.05971 -.0967 (247*2π)/23429 weeks
248-.06398 -.1268 (248*2π)/23429 weeks
249-.08224 -.07203 (249*2π)/23429 weeks
250-.03326 -.08496 (250*2π)/23429 weeks
251-.06618 -.07884 (251*2π)/23429 weeks
252-.02021 -.07731 (252*2π)/23429 weeks
253-.05316 -.11014 (253*2π)/23429 weeks
254-.06844 -.0414 (254*2π)/23429 weeks
255.04969 -.06696 (255*2π)/23429 weeks
256-.04612 -.16103 (256*2π)/23429 weeks
257-.0638 -.05488 (257*2π)/23429 weeks
258.01294 -.11901 (258*2π)/23429 weeks
259-.09287 -.11324 (259*2π)/23429 weeks
260-.03728 -.0486 (260*2π)/23429 weeks
261-.02223 -.09638 (261*2π)/23429 weeks
262-.03853 -.08282 (262*2π)/23429 weeks
263-.02301 -.10498 (263*2π)/23429 weeks
264-.04193 -.09301 (264*2π)/23429 weeks
265-.05766 -.12402 (265*2π)/23429 weeks
266-.11203 -.07119 (266*2π)/23429 weeks
267-.05835 -.0407 (267*2π)/23429 weeks
268-.07521 -.02929 (268*2π)/23429 weeks
269-.01051 .01328 (269*2π)/23429 weeks
270.0358 -.02643 (270*2π)/23429 weeks
271.02696 -.07366 (271*2π)/23429 weeks
272.05904 -.06694 (272*2π)/23429 weeks
273.0381 -.16065 (273*2π)/23429 weeks
274-.05224 -.15402 (274*2π)/23429 weeks
275-.03448