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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 (1.7714*sine), 233 weeks (1.6487*sine), and 167 weeks (1.5917*cosine).

AXP (American Express Company Common) has an average price of 20.96 (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 6/1/1972 to 2/13/2017 for AXP (American Express Company Common), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
020.96032   0 
110.86196 -22.69864 (1*2π)/23332,333 weeks
22.02302 -8.71921 (2*2π)/23331,167 weeks
35.32025 -9.16527 (3*2π)/2333778 weeks
4.91913 -8.00537 (4*2π)/2333583 weeks
5.53719 -8.30416 (5*2π)/2333467 weeks
6-3.86082 -6.38396 (6*2π)/2333389 weeks
7-2.80516 -1.15664 (7*2π)/2333333 weeks
8.29733 -1.98967 (8*2π)/2333292 weeks
9-.88526 -2.60941 (9*2π)/2333259 weeks
10-.81945 -1.6487 (10*2π)/2333233 weeks
11-1.24763 -1.57356 (11*2π)/2333212 weeks
12-1.42063 .00606 (12*2π)/2333194 weeks
131.04626 .95715 (13*2π)/2333179 weeks
141.59165 -1.2611 (14*2π)/2333167 weeks
15.41865 -1.77137 (15*2π)/2333156 weeks
16.25735 -1.19621 (16*2π)/2333146 weeks
17-.12821 -.98543 (17*2π)/2333137 weeks
18.5151 -.34707 (18*2π)/2333130 weeks
191.07467 -1.24606 (19*2π)/2333123 weeks
20.29591 -1.60129 (20*2π)/2333117 weeks
21.25082 -1.41329 (21*2π)/2333111 weeks
22-.5318 -1.15086 (22*2π)/2333106 weeks
23-.15651 -.51038 (23*2π)/2333101 weeks
24.46256 -.46629 (24*2π)/233397 weeks
25.53467 -.96277 (25*2π)/233393 weeks
26.15726 -.96185 (26*2π)/233390 weeks
27.26258 -.84069 (27*2π)/233386 weeks
28.13077 -1.06835 (28*2π)/233383 weeks
29-.0758 -.56963 (29*2π)/233380 weeks
30.53155 -.48392 (30*2π)/233378 weeks
31.41218 -1.11323 (31*2π)/233375 weeks
32.0677 -.95603 (32*2π)/233373 weeks
33.20703 -.9507 (33*2π)/233371 weeks
34-.36353 -.94092 (34*2π)/233369 weeks
35-.18282 -.2495 (35*2π)/233367 weeks
36.60714 -.50037 (36*2π)/233365 weeks
37.17133 -.91226 (37*2π)/233363 weeks
38.19495 -.88723 (38*2π)/233361 weeks
39-.13187 -.95531 (39*2π)/233360 weeks
40-.14907 -.56806 (40*2π)/233358 weeks
41.02697 -.73265 (41*2π)/233357 weeks
42-.05723 -.67996 (42*2π)/233356 weeks
43-.12176 -.65039 (43*2π)/233354 weeks
44-.26386 -.64616 (44*2π)/233353 weeks
45-.11424 -.28056 (45*2π)/233352 weeks
46.00983 -.34522 (46*2π)/233351 weeks
47.2024 -.42591 (47*2π)/233350 weeks
48.15796 -.71583 (48*2π)/233349 weeks
49-.15374 -.79341 (49*2π)/233348 weeks
50-.36397 -.47713 (50*2π)/233347 weeks
51-.21089 -.17737 (51*2π)/233346 weeks
52.14263 -.32661 (52*2π)/233345 weeks
53-.17413 -.44357 (53*2π)/233344 weeks
54-.07641 -.19552 (54*2π)/233343 weeks
55.0451 -.31454 (55*2π)/233342 weeks
56-.06461 -.13968 (56*2π)/233342 weeks
57.39652 -.16691 (57*2π)/233341 weeks
58.13199 -.63401 (58*2π)/233340 weeks
59.0201 -.23702 (59*2π)/233340 weeks
60.27728 -.45362 (60*2π)/233339 weeks
61-.05434 -.42243 (61*2π)/233338 weeks
62.32203 -.21233 (62*2π)/233338 weeks
63.19835 -.68541 (63*2π)/233337 weeks
64-.07488 -.47744 (64*2π)/233336 weeks
65.13409 -.33783 (65*2π)/233336 weeks
66.10622 -.50061 (66*2π)/233335 weeks
67-.01971 -.53059 (67*2π)/233335 weeks
68-.07576 -.29386 (68*2π)/233334 weeks
69.22133 -.35645 (69*2π)/233334 weeks
70.05037 -.5166 (70*2π)/233333 weeks
71-.02041 -.42185 (71*2π)/233333 weeks
72.1058 -.38787 (72*2π)/233332 weeks
73.08239 -.50554 (73*2π)/233332 weeks
74-.01948 -.51313 (74*2π)/233332 weeks
75-.08028 -.45367 (75*2π)/233331 weeks
76-.10486 -.48359 (76*2π)/233331 weeks
77-.14944 -.29424 (77*2π)/233330 weeks
78-.0545 -.30933 (78*2π)/233330 weeks
79-.0408 -.33592 (79*2π)/233330 weeks
80-.07147 -.26104 (80*2π)/233329 weeks
81.0322 -.2947 (81*2π)/233329 weeks
82.08042 -.35725 (82*2π)/233328 weeks
83-.00938 -.38568 (83*2π)/233328 weeks
84-.07512 -.42558 (84*2π)/233328 weeks
85-.04729 -.27606 (85*2π)/233327 weeks
86.09328 -.37797 (86*2π)/233327 weeks
87-.08889 -.47839 (87*2π)/233327 weeks
88-.05111 -.44392 (88*2π)/233327 weeks
89-.24138 -.48018 (89*2π)/233326 weeks
90-.37327 -.23692 (90*2π)/233326 weeks
91-.02565 -.09954 (91*2π)/233326 weeks
92-.11069 -.34767 (92*2π)/233325 weeks
93-.23152 -.2422 (93*2π)/233325 weeks
94-.13016 -.18885 (94*2π)/233325 weeks
95-.20692 -.06613 (95*2π)/233325 weeks
96.01685 -.04573 (96*2π)/233324 weeks
97.02847 -.18938 (97*2π)/233324 weeks
98-.03987 -.1677 (98*2π)/233324 weeks
99-.04819 -.08878 (99*2π)/233324 weeks
100.19915 -.0372 (100*2π)/233323 weeks
101.14697 -.30373 (101*2π)/233323 weeks
102.07454 -.27839 (102*2π)/233323 weeks
103.08175 -.33273 (103*2π)/233323 weeks
104-.06219 -.29895 (104*2π)/233322 weeks
105.03455 -.21692 (105*2π)/233322 weeks
106.02536 -.32662 (106*2π)/233322 weeks
107-.04749 -.28182 (107*2π)/233322 weeks
108-.07028 -.22801 (108*2π)/233322 weeks
109.03527 -.16895 (109*2π)/233321 weeks
110.09921 -.24982 (110*2π)/233321 weeks
111.03308 -.40836 (111*2π)/233321 weeks
112-.08667 -.35033 (112*2π)/233321 weeks
113-.15165 -.30702 (113*2π)/233321 weeks
114-.12497 -.17772 (114*2π)/233320 weeks
115-.0762 -.15542 (115*2π)/233320 weeks
116-.01435 -.18887 (116*2π)/233320 weeks
117.03814 -.18233 (117*2π)/233320 weeks
118-.00891 -.31888 (118*2π)/233320 weeks
119-.1212 -.17837 (119*2π)/233320 weeks
120.12215 -.1642 (120*2π)/233319 weeks
121-.00014 -.37799 (121*2π)/233319 weeks
122-.0902 -.24239 (122*2π)/233319 weeks
123.00348 -.31834 (123*2π)/233319 weeks
124-.12956 -.26911 (124*2π)/233319 weeks
125-.07283 -.23982 (125*2π)/233319 weeks
126-.10872 -.28248 (126*2π)/233319 weeks
127-.08445 -.22267 (127*2π)/233318 weeks
128-.15603 -.341 (128*2π)/233318 weeks
129-.26782 -.0923 (129*2π)/233318 weeks
130-.02123 -.0996 (130*2π)/233318 weeks
131-.13321 -.16711 (131*2π)/233318 weeks
132-.03184 -.07722 (132*2π)/233318 weeks
133-.0259 -.26122 (133*2π)/233318 weeks
134-.22097 -.16459 (134*2π)/233317 weeks
135-.10871 -.02219 (135*2π)/233317 weeks
136-.02894 -.05827 (136*2π)/233317 weeks
137.06714 -.06971 (137*2π)/233317 weeks
138.06792 -.25624 (138*2π)/233317 weeks
139-.14118 -.31772 (139*2π)/233317 weeks
140-.23377 -.11321 (140*2π)/233317 weeks
141-.11176 .03867 (141*2π)/233317 weeks
142.06098 -.05214 (142*2π)/233316 weeks
143.02607 -.13416 (143*2π)/233316 weeks
144.02907 -.15354 (144*2π)/233316 weeks
145-.05151 -.25591 (145*2π)/233316 weeks
146-.17241 -.08403 (146*2π)/233316 weeks
147.00659 .0263 (147*2π)/233316 weeks
148.07196 -.12254 (148*2π)/233316 weeks
149.04489 -.11288 (149*2π)/233316 weeks
150.05358 -.20014 (150*2π)/233316 weeks
151-.03871 -.189 (151*2π)/233315 weeks
152-.04208 -.15228 (152*2π)/233315 weeks
153-.02828 -.09987 (153*2π)/233315 weeks
154.04609 -.13951 (154*2π)/233315 weeks
155-.00396 -.20283 (155*2π)/233315 weeks
156-.03576 -.15526 (156*2π)/233315 weeks
157-.04275 -.18812 (157*2π)/233315 weeks
158-.06747 -.10665 (158*2π)/233315 weeks
159.00255 -.11063 (159*2π)/233315 weeks
160-.03659 -.12691 (160*2π)/233315 weeks
161.01255 -.11198 (161*2π)/233314 weeks
162-.02636 -.13652 (162*2π)/233314 weeks
163.01385 -.07416 (163*2π)/233314 weeks
164.06666 -.15079 (164*2π)/233314 weeks
165-.00597 -.182 (165*2π)/233314 weeks
166-.00928 -.13891 (166*2π)/233314 weeks
167.03666 -.12143 (167*2π)/233314 weeks
168.0436 -.20325 (168*2π)/233314 weeks
169-.02744 -.2286 (169*2π)/233314 weeks
170-.01366 -.17251 (170*2π)/233314 weeks
171-.0849 -.24434 (171*2π)/233314 weeks
172-.08911 -.11621 (172*2π)/233314 weeks
173-.03388 -.17006 (173*2π)/233313 weeks
174-.14124 -.13979 (174*2π)/233313 weeks
175-.04678 -.04758 (175*2π)/233313 weeks
176-.00453 -.13963 (176*2π)/233313 weeks
177-.112 -.08935 (177*2π)/233313 weeks
178.01818 -.03749 (178*2π)/233313 weeks
179.03364 -.14039 (179*2π)/233313 weeks
180-.07853 -.13816 (180*2π)/233313 weeks
181-.0497 -.02655 (181*2π)/233313 weeks
182.05431 -.0153 (182*2π)/233313 weeks
183.11704 -.08875 (183*2π)/233313 weeks
184.10219 -.17697 (184*2π)/233313 weeks
185.06225 -.22624 (185*2π)/233313 weeks
186-.04768 -.21768 (186*2π)/233313 weeks
187-.00884 -.14117 (187*2π)/233312 weeks
188-.00087 -.20893 (188*2π)/233312 weeks
189-.07967 -.14811 (189*2π)/233312 weeks
190-.00456 -.12712 (190*2π)/233312 weeks
191-.02603 -.18615 (191*2π)/233312 weeks
192-.08068 -.14321 (192*2π)/233312 weeks
193-.03718 -.1033 (193*2π)/233312 weeks
194-.00763 -.10341 (194*2π)/233312 weeks
195.01518 -.14967 (195*2π)/233312 weeks
196-.02769 -.16486 (196*2π)/233312 weeks
197-.05358 -.13937 (197*2π)/233312 weeks
198-.02254 -.1169 (198*2π)/233312 weeks
199-.04003 -.10347 (199*2π)/233312 weeks
200.00418 -.0735 (200*2π)/233312 weeks
201.08089 -.13485 (201*2π)/233312 weeks
202.01532 -.21369 (202*2π)/233312 weeks
203-.03102 -.17354 (203*2π)/233311 weeks
204-.0011 -.17861 (204*2π)/233311 weeks
205-.05165 -.22007 (205*2π)/233311 weeks
206-.10342 -.13928 (206*2π)/233311 weeks
207-.02963 -.15499 (207*2π)/233311 weeks
208-.09583 -.19245 (208*2π)/233311 weeks
209-.10426 -.09481 (209*2π)/233311 weeks
210-.05187 -.12155 (210*2π)/233311 weeks
211-.1052 -.11278 (211*2π)/233311 weeks
212-.03086 -.04467 (212*2π)/233311 weeks
213-.01233 -.15522 (213*2π)/233311 weeks