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Fourier Analysis of AXP (American Express Company Common)


AXP (American Express Company Common) appears to have interesting cyclic behaviour every 194 weeks (2.0343*cosine), 211 weeks (1.9815*sine), and 166 weeks (1.2684*cosine).

AXP (American Express Company Common) has an average price of 20.79 (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 11/28/2016 for AXP (American Express Company Common), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
020.7866   0 
110.78374 -22.52878 (1*2π)/23222,322 weeks
21.876 -8.59646 (2*2π)/23221,161 weeks
35.40863 -8.83972 (3*2π)/2322774 weeks
41.16038 -7.89011 (4*2π)/2322581 weeks
5.98842 -8.30428 (5*2π)/2322464 weeks
6-3.50818 -6.95707 (6*2π)/2322387 weeks
7-3.11087 -1.68409 (7*2π)/2322332 weeks
8.08094 -2.05334 (8*2π)/2322290 weeks
9-.91919 -2.83848 (9*2π)/2322258 weeks
10-.97532 -1.92784 (10*2π)/2322232 weeks
11-1.43425 -1.98152 (11*2π)/2322211 weeks
12-2.03433 -.48154 (12*2π)/2322194 weeks
13.12647 1.13119 (13*2π)/2322179 weeks
141.26844 -.7508 (14*2π)/2322166 weeks
15.37657 -1.56946 (15*2π)/2322155 weeks
16.11593 -1.11443 (16*2π)/2322145 weeks
17-.35325 -1.02631 (17*2π)/2322137 weeks
18.04101 -.16011 (18*2π)/2322129 weeks
19.92042 -.75502 (19*2π)/2322122 weeks
20.4024 -1.35349 (20*2π)/2322116 weeks
21.37707 -1.26538 (21*2π)/2322111 weeks
22-.47114 -1.3525 (22*2π)/2322106 weeks
23-.45829 -.65454 (23*2π)/2322101 weeks
24.06992 -.28757 (24*2π)/232297 weeks
25.39921 -.64603 (25*2π)/232293 weeks
26.10602 -.80315 (26*2π)/232289 weeks
27.16716 -.64866 (27*2π)/232286 weeks
28.18196 -.94257 (28*2π)/232283 weeks
29-.2611 -.61656 (29*2π)/232280 weeks
30.20511 -.16483 (30*2π)/232277 weeks
31.48175 -.70895 (31*2π)/232275 weeks
32.17363 -.77616 (32*2π)/232273 weeks
33.35494 -.72124 (33*2π)/232270 weeks
34-.12724 -1.08845 (34*2π)/232268 weeks
35-.47854 -.4535 (35*2π)/232266 weeks
36.29334 -.10077 (36*2π)/232265 weeks
37.24769 -.59157 (37*2π)/232263 weeks
38.33966 -.57855 (38*2π)/232261 weeks
39.17229 -.87607 (39*2π)/232260 weeks
40-.0947 -.6162 (40*2π)/232258 weeks
41.12768 -.63313 (41*2π)/232257 weeks
42.07884 -.64204 (42*2π)/232255 weeks
43.035 -.66898 (43*2π)/232254 weeks
44-.07778 -.83631 (44*2π)/232253 weeks
45-.24628 -.49462 (45*2π)/232252 weeks
46-.19261 -.40668 (46*2π)/232250 weeks
47-.00613 -.24796 (47*2π)/232249 weeks
48.25002 -.4092 (48*2π)/232248 weeks
49.21787 -.73467 (49*2π)/232247 weeks
50-.12745 -.79622 (50*2π)/232246 weeks
51-.35725 -.53632 (51*2π)/232246 weeks
52-.03817 -.30942 (52*2π)/232245 weeks
53-.1247 -.61552 (53*2π)/232244 weeks
54-.28427 -.43176 (54*2π)/232243 weeks
55-.13719 -.41496 (55*2π)/232242 weeks
56-.41228 -.41004 (56*2π)/232241 weeks
57-.17839 .04357 (57*2π)/232241 weeks
58.11287 -.38176 (58*2π)/232240 weeks
59-.25205 -.27866 (59*2π)/232239 weeks
60.06325 -.15575 (60*2π)/232239 weeks
61-.13079 -.43901 (61*2π)/232238 weeks
62-.15737 .03772 (62*2π)/232237 weeks
63.22513 -.21202 (63*2π)/232237 weeks
64-.00349 -.40192 (64*2π)/232236 weeks
65-.05273 -.1681 (65*2π)/232236 weeks
66.07481 -.20447 (66*2π)/232235 weeks
67.11834 -.35555 (67*2π)/232235 weeks
68-.15033 -.36405 (68*2π)/232234 weeks
69-.01847 -.08615 (69*2π)/232234 weeks
70.08674 -.23287 (70*2π)/232233 weeks
71-.00447 -.29576 (71*2π)/232233 weeks
72-.0079 -.15442 (72*2π)/232232 weeks
73.10801 -.15477 (73*2π)/232232 weeks
74.14235 -.22554 (74*2π)/232231 weeks
75.10028 -.26573 (75*2π)/232231 weeks
76.17738 -.34074 (76*2π)/232231 weeks
77-.00181 -.36314 (77*2π)/232230 weeks
78-.00745 -.30595 (78*2π)/232230 weeks
79.02784 -.29818 (79*2π)/232229 weeks
80-.07836 -.32131 (80*2π)/232229 weeks
81-.07328 -.24125 (81*2π)/232229 weeks
82-.0036 -.14835 (82*2π)/232228 weeks
83.01646 -.17569 (83*2π)/232228 weeks
84.0861 -.27425 (84*2π)/232228 weeks
85-.06729 -.25157 (85*2π)/232227 weeks
86.01643 -.06285 (86*2π)/232227 weeks
87.10836 -.1927 (87*2π)/232227 weeks
88.16445 -.10464 (88*2π)/232226 weeks
89.30064 -.27035 (89*2π)/232226 weeks
90.11414 -.53934 (90*2π)/232226 weeks
91-.06888 -.23812 (91*2π)/232226 weeks
92.1331 -.26134 (92*2π)/232225 weeks
93.09515 -.40691 (93*2π)/232225 weeks
94.10995 -.35949 (94*2π)/232225 weeks
95-.03664 -.51045 (95*2π)/232224 weeks
96-.14444 -.35202 (96*2π)/232224 weeks
97-.04899 -.292 (97*2π)/232224 weeks
98-.03114 -.34447 (98*2π)/232224 weeks
99-.11785 -.46206 (99*2π)/232223 weeks
100-.30593 -.22319 (100*2π)/232223 weeks
101-.13414 -.16308 (101*2π)/232223 weeks
102-.13313 -.17233 (102*2π)/232223 weeks
103-.0489 -.09414 (103*2π)/232223 weeks
104-.01706 -.23353 (104*2π)/232222 weeks
105-.11773 -.17479 (105*2π)/232222 weeks
106-.0215 -.12964 (106*2π)/232222 weeks
107.00126 -.17413 (107*2π)/232222 weeks
108-.01348 -.26489 (108*2π)/232222 weeks
109-.12924 -.22946 (109*2π)/232221 weeks
110-.18236 -.11002 (110*2π)/232221 weeks
111-.02468 -.03423 (111*2π)/232221 weeks
112.03089 -.07254 (112*2π)/232221 weeks
113.1077 -.15926 (113*2π)/232221 weeks
114.04083 -.2211 (114*2π)/232220 weeks
115-.02247 -.255 (115*2π)/232220 weeks
116-.03471 -.23999 (116*2π)/232220 weeks
117-.12911 -.16992 (117*2π)/232220 weeks
118.02068 -.10203 (118*2π)/232220 weeks
119-.01392 -.31162 (119*2π)/232220 weeks
120-.20443 -.1285 (120*2π)/232219 weeks
121-.01727 -.05811 (121*2π)/232219 weeks
122-.07116 -.16992 (122*2π)/232219 weeks
123-.02617 -.03101 (123*2π)/232219 weeks
124.00707 -.12094 (124*2π)/232219 weeks
125-.03521 -.09522 (125*2π)/232219 weeks
126.03157 -.10149 (126*2π)/232218 weeks
127-.05131 -.06751 (127*2π)/232218 weeks
128.16701 .01269 (128*2π)/232218 weeks
129.13329 -.25607 (129*2π)/232218 weeks
130.00629 -.12953 (130*2π)/232218 weeks
131.09982 -.19826 (131*2π)/232218 weeks
132-.06905 -.20413 (132*2π)/232218 weeks
133.02621 -.01372 (133*2π)/232217 weeks
134.16639 -.15602 (134*2π)/232217 weeks
135.08087 -.24539 (135*2π)/232217 weeks
136.04595 -.28175 (136*2π)/232217 weeks
137-.12301 -.26137 (137*2π)/232217 weeks
138-.14686 -.06017 (138*2π)/232217 weeks
139.07403 .01633 (139*2π)/232217 weeks
140.19383 -.13143 (140*2π)/232217 weeks
141.09582 -.30866 (141*2π)/232216 weeks
142-.01801 -.24701 (142*2π)/232216 weeks
143-.02428 -.21948 (143*2π)/232216 weeks
144-.10061 -.16964 (144*2π)/232216 weeks
145.03847 -.02761 (145*2π)/232216 weeks
146.16771 -.19199 (146*2π)/232216 weeks
147.01379 -.29616 (147*2π)/232216 weeks
148-.00326 -.2231 (148*2π)/232216 weeks
149-.06402 -.2485 (149*2π)/232216 weeks
150-.07654 -.14776 (150*2π)/232215 weeks
151-.02368 -.14176 (151*2π)/232215 weeks
152.01645 -.14422 (152*2π)/232215 weeks
153.00508 -.22214 (153*2π)/232215 weeks
154-.07305 -.19216 (154*2π)/232215 weeks
155-.03886 -.13301 (155*2π)/232215 weeks
156-.05194 -.15288 (156*2π)/232215 weeks
157.00186 -.09384 (157*2π)/232215 weeks
158.03048 -.16232 (158*2π)/232215 weeks
159-.01607 -.14443 (159*2π)/232215 weeks
160.02535 -.16823 (160*2π)/232215 weeks
161-.02128 -.15671 (161*2π)/232214 weeks
162.04375 -.15032 (162*2π)/232214 weeks
163.00547 -.23307 (163*2π)/232214 weeks
164-.06418 -.1842 (164*2π)/232214 weeks
165-.02339 -.15214 (165*2π)/232214 weeks
166.00816 -.17654 (166*2π)/232214 weeks
167-.0529 -.22884 (167*2π)/232214 weeks
168-.10882 -.18144 (168*2π)/232214 weeks
169-.05569 -.14046 (169*2π)/232214 weeks
170-.13898 -.15045 (170*2π)/232214 weeks
171-.04834 -.05299 (171*2π)/232214 weeks
172-.04007 -.13681 (172*2π)/232214 weeks
173-.09722 -.05253 (173*2π)/232213 weeks
174.03659 -.05169 (174*2π)/232213 weeks
175.00318 -.15089 (175*2π)/232213 weeks
176-.0528 -.05143 (176*2π)/232213 weeks
177.08208 -.09221 (177*2π)/232213 weeks
178.0197 -.18012 (178*2π)/232213 weeks
179-.0654 -.10896 (179*2π)/232213 weeks
180.02929 -.03996 (180*2π)/232213 weeks
181.1117 -.10126 (181*2π)/232213 weeks
182.10656 -.19637 (182*2π)/232213 weeks
183.03706 -.25176 (183*2π)/232213 weeks
184-.02304 -.25476 (184*2π)/232213 weeks
185-.10531 -.18887 (185*2π)/232213 weeks
186-.02834 -.13652 (186*2π)/232212 weeks
187-.04793 -.19976 (187*2π)/232212 weeks
188-.09155 -.1121 (188*2π)/232212 weeks
189-.01052 -.12617 (189*2π)/232212 weeks
190-.05433 -.17163 (190*2π)/232212 weeks
191-.08495 -.11042 (191*2π)/232212 weeks
192-.02589 -.09167 (192*2π)/232212 weeks
193-.00165 -.10666 (193*2π)/232212 weeks
194.00215 -.15651 (194*2π)/232212 weeks
195-.04454 -.15459 (195*2π)/232212 weeks
196-.05847 -.12186 (196*2π)/232212 weeks
197-.02091 -.10821 (197*2π)/232212 weeks
198-.03451 -.09424 (198*2π)/232212 weeks
199.01499 -.07876 (199*2π)/232212 weeks
200.07256 -.15473 (200*2π)/232212 weeks
201-.00981 -.21572 (201*2π)/232212 weeks
202-.04667 -.16451 (202*2π)/232211 weeks
203-.01612 -.17312 (203*2π)/232211 weeks
204-.07025 -.20577 (204*2π)/232211 weeks
205-.1094 -.11989 (205*2π)/232211 weeks
206-.03523 -.14429 (206*2π)/232211 weeks
207-.10341 -.17674 (207*2π)/232211 weeks
208-.10425 -.07967 (208*2π)/232211 weeks
209-.05245 -.1109 (209*2π)/232211 weeks
210-.10584 -.102 (210*2π)/232211 weeks
211-.03098 -.03523 (211*2π)/232211 weeks
212-.0118 -.14659 (212*2π)/232211 weeks
213-.08592 -.09886 (213*2π)/232211 weeks
214-.01086 -.0722 (214*2π)/232211 weeks
215-.01745 -.15539 (215*2π)/232211 weeks
216-.07728 -.16054 (216*2π)/232211 weeks
217-.09823 -.09544 (217*2π)/232211 weeks
218-.05432 -.10773 (218*2π)/232211 weeks
219-.13191