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# Fourier Analysis of AMR (AMR Corporation Common Stock)

AMR (AMR Corporation Common Stock) appears to have interesting cyclic behaviour every 18 weeks (.1028*sine), 28 weeks (.0899*sine), and 23 weeks (.0829*sine).

AMR (AMR Corporation Common Stock) has an average price of 1.38 (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 4/29/2011 to 10/17/2016 for AMR (AMR Corporation Common Stock), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
01.38207   0
1.12813 .98375 (1*2π)/277277 weeks
2-.35969 .29337 (2*2π)/277139 weeks
3.04587 -.01015 (3*2π)/27792 weeks
4.08038 .262 (4*2π)/27769 weeks
5-.1096 .15493 (5*2π)/27755 weeks
6-.05219 .08282 (6*2π)/27746 weeks
7.01602 .06035 (7*2π)/27740 weeks
8.02901 -.0009 (8*2π)/27735 weeks
9.10995 .08436 (9*2π)/27731 weeks
10-.04107 .08987 (10*2π)/27728 weeks
11.00945 -.00534 (11*2π)/27725 weeks
12.04173 .08288 (12*2π)/27723 weeks
13-.01311 -.00201 (13*2π)/27721 weeks
14.04898 .06452 (14*2π)/27720 weeks
15-.03325 .10278 (15*2π)/27718 weeks
16-.04599 .01406 (16*2π)/27717 weeks
17.03374 .0224 (17*2π)/27716 weeks
18-.01512 .04343 (18*2π)/27715 weeks
19-.01264 .01306 (19*2π)/27715 weeks
20.0292 .03037 (20*2π)/27714 weeks
21.0146 .01126 (21*2π)/27713 weeks
22.00708 .00865 (22*2π)/27713 weeks
23.00659 .02732 (23*2π)/27712 weeks
24.00558 .02442 (24*2π)/27712 weeks
25.02005 .0121 (25*2π)/27711 weeks
26.01401 .02653 (26*2π)/27711 weeks
27-.00853 .04074 (27*2π)/27710 weeks
28.01525 .02631 (28*2π)/27710 weeks
29.00634 .04025 (29*2π)/27710 weeks
30-.00152 .00989 (30*2π)/2779 weeks
31-.00183 .02026 (31*2π)/2779 weeks
32.00474 .0272 (32*2π)/2779 weeks
33.00822 .0019 (33*2π)/2778 weeks
34.00753 .01191 (34*2π)/2778 weeks
35-.01869 .01682 (35*2π)/2778 weeks
36.00665 -.00333 (36*2π)/2778 weeks
37.0105 .01646 (37*2π)/2777 weeks
38.01504 .00072 (38*2π)/2777 weeks
39.01182 .02307 (39*2π)/2777 weeks
40.00478 .017 (40*2π)/2777 weeks
41.01672 .02619 (41*2π)/2777 weeks
42-.00054 .00532 (42*2π)/2777 weeks
43-.00838 .00196 (43*2π)/2776 weeks
44.01152 .00417 (44*2π)/2776 weeks
45.00434 .0079 (45*2π)/2776 weeks
46-.00126 -.00037 (46*2π)/2776 weeks
47-.00094 -.00378 (47*2π)/2776 weeks
48.01368 -.00159 (48*2π)/2776 weeks
49.01237 .02216 (49*2π)/2776 weeks
50.01619 .00852 (50*2π)/2776 weeks
51.00391 .00683 (51*2π)/2775 weeks
52.01658 .00993 (52*2π)/2775 weeks
53.02918 .01538 (53*2π)/2775 weeks
54.00848 .01629 (54*2π)/2775 weeks
55.0048 .01143 (55*2π)/2775 weeks
56.00715 .00827 (56*2π)/2775 weeks
57.00058 .00945 (57*2π)/2775 weeks
58.00466 .01094 (58*2π)/2775 weeks
59-.00502 .00002 (59*2π)/2775 weeks
60.0081 .00481 (60*2π)/2775 weeks
61.00429 .01723 (61*2π)/2775 weeks
62.00736 .00014 (62*2π)/2774 weeks
63.00944 .0119 (63*2π)/2774 weeks
64.01254 .00352 (64*2π)/2774 weeks
65.01901 .00601 (65*2π)/2774 weeks
66.01292 .01549 (66*2π)/2774 weeks
67.00519 .00873 (67*2π)/2774 weeks
68.00885 .00766 (68*2π)/2774 weeks
69-.00346 .00474 (69*2π)/2774 weeks
70.00953 .00229 (70*2π)/2774 weeks
71.00873 .0112 (71*2π)/2774 weeks
72.00169 .01337 (72*2π)/2774 weeks
73-.00413 .01097 (73*2π)/2774 weeks
74.0019 -.00013 (74*2π)/2774 weeks
75.008 .00444 (75*2π)/2774 weeks
76.01225 .00712 (76*2π)/2774 weeks
77.00948 .00211 (77*2π)/2774 weeks
78.00622 .00644 (78*2π)/2774 weeks
79.00944 .00722 (79*2π)/2774 weeks
80.00432 .00582 (80*2π)/2773 weeks
81-.00192 .00132 (81*2π)/2773 weeks
82.00967 .00093 (82*2π)/2773 weeks
83.00723 .00501 (83*2π)/2773 weeks
84.00605 .0137 (84*2π)/2773 weeks
85.00489 .00829 (85*2π)/2773 weeks
86-.00235 -.00043 (86*2π)/2773 weeks
87.00691 -.00157 (87*2π)/2773 weeks
88.02358 .00762 (88*2π)/2773 weeks
89.003 .00718 (89*2π)/2773 weeks
90.00327 .00149 (90*2π)/2773 weeks
91.00772 -.00055 (91*2π)/2773 weeks
92.00844 .00601 (92*2π)/2773 weeks
93.00921 .01063 (93*2π)/2773 weeks
94-.00328 .00433 (94*2π)/2773 weeks
95.00048 .00062 (95*2π)/2773 weeks
96.01086 .01427 (96*2π)/2773 weeks
97.00349 .00232 (97*2π)/2773 weeks
98-.00387 .00125 (98*2π)/2773 weeks
99.00411 -.00359 (99*2π)/2773 weeks
100.01062 -.00056 (100*2π)/2773 weeks
101.00471 -.00288 (101*2π)/2773 weeks
102.00624 -.01217 (102*2π)/2773 weeks
103.01065 -.0005 (103*2π)/2773 weeks
104.0076 .00459 (104*2π)/2773 weeks
105.00369 -.0004 (105*2π)/2773 weeks
106.00804 -.00857 (106*2π)/2773 weeks
107.01041 .00456 (107*2π)/2773 weeks
108.01672 .00517 (108*2π)/2773 weeks
109.01244 .00973 (109*2π)/2773 weeks
110.00131 .00159 (110*2π)/2773 weeks
111.01044 .00094 (111*2π)/2772 weeks
112.00781 .0062 (112*2π)/2772 weeks
113.00232 -.00269 (113*2π)/2772 weeks
114.01041 -.0065 (114*2π)/2772 weeks
115.01042 .00237 (115*2π)/2772 weeks
116.00429 .00629 (116*2π)/2772 weeks
117.00958 -.00183 (117*2π)/2772 weeks
118.01428 .00715 (118*2π)/2772 weeks
119.00027 .00839 (119*2π)/2772 weeks
120.00995 .00097 (120*2π)/2772 weeks
121.01124 .00498 (121*2π)/2772 weeks
122.00642 .00305 (122*2π)/2772 weeks
123.01035 .00027 (123*2π)/2772 weeks
124.00578 .0102 (124*2π)/2772 weeks
125-.00258 .00114 (125*2π)/2772 weeks
126.00983 -.00453 (126*2π)/2772 weeks
127.00119 .00418 (127*2π)/2772 weeks
128.00344 .0007 (128*2π)/2772 weeks
129.0069 -.00209 (129*2π)/2772 weeks
130.01065 .00366 (130*2π)/2772 weeks
131.00501 .00162 (131*2π)/2772 weeks
132.00945 .00171 (132*2π)/2772 weeks
133.00855 .0043 (133*2π)/2772 weeks
134.0049 -.00337 (134*2π)/2772 weeks
135.00936 .00033 (135*2π)/2772 weeks
136.0056 .00546 (136*2π)/2772 weeks
137-.0014 -.00122 (137*2π)/2772 weeks
138.00581 -.0038 (138*2π)/2772 weeks
139.00581 .0038 (139*2π)/2772 weeks
140-.0014 .00122 (140*2π)/2772 weeks
141.0056 -.00546 (141*2π)/2772 weeks
142.00936 -.00033 (142*2π)/2772 weeks
143.0049 .00337 (143*2π)/2772 weeks
144.00855 -.0043 (144*2π)/2772 weeks
145.00945 -.00171 (145*2π)/2772 weeks
146.00501 -.00162 (146*2π)/2772 weeks
147.01065 -.00366 (147*2π)/2772 weeks
148.0069 .00209 (148*2π)/2772 weeks
149.00344 -.0007 (149*2π)/2772 weeks
150.00119 -.00418 (150*2π)/2772 weeks
151.00983 .00453 (151*2π)/2772 weeks
152-.00258 -.00114 (152*2π)/2772 weeks
153.00578 -.0102 (153*2π)/2772 weeks
154.01035 -.00027 (154*2π)/2772 weeks
155.00642 -.00305 (155*2π)/2772 weeks
156.01124 -.00498 (156*2π)/2772 weeks
157.00995 -.00097 (157*2π)/2772 weeks
158.00027 -.00839 (158*2π)/2772 weeks
159.01428 -.00715 (159*2π)/2772 weeks
160.00958 .00183 (160*2π)/2772 weeks
161.00429 -.00629 (161*2π)/2772 weeks
162.01042 -.00237 (162*2π)/2772 weeks
163.01041 .0065 (163*2π)/2772 weeks
164.00232 .00269 (164*2π)/2772 weeks
165.00781 -.0062 (165*2π)/2772 weeks
166.01044 -.00094 (166*2π)/2772 weeks
167.00131 -.00159 (167*2π)/2772 weeks
168.01244 -.00973 (168*2π)/2772 weeks
169.01672 -.00517 (169*2π)/2772 weeks
170.01041 -.00456 (170*2π)/2772 weeks
171.00804 .00857 (171*2π)/2772 weeks
172.00369 .0004 (172*2π)/2772 weeks
173.0076 -.00459 (173*2π)/2772 weeks
174.01065 .0005 (174*2π)/2772 weeks
175.00624 .01217 (175*2π)/2772 weeks
176.00471 .00288 (176*2π)/2772 weeks
177.01062 .00056 (177*2π)/2772 weeks
178.00411 .00359 (178*2π)/2772 weeks
179-.00387 -.00125 (179*2π)/2772 weeks
180.00349 -.00232 (180*2π)/2772 weeks
181.01086 -.01427 (181*2π)/2772 weeks
182.00048 -.00062 (182*2π)/2772 weeks
183-.00328 -.00433 (183*2π)/2772 weeks
184.00921 -.01063 (184*2π)/2772 weeks
185.00844 -.00601 (185*2π)/2771 weeks
186.00772 .00055 (186*2π)/2771 weeks
187.00327 -.00149 (187*2π)/2771 weeks
188.003 -.00718 (188*2π)/2771 weeks
189.02358 -.00762 (189*2π)/2771 weeks
190.00691 .00157 (190*2π)/2771 weeks
191-.00235 .00043 (191*2π)/2771 weeks
192.00489 -.00829 (192*2π)/2771 weeks
193.00605 -.0137 (193*2π)/2771 weeks
194.00723 -.00501 (194*2π)/2771 weeks
195.00967 -.00093 (195*2π)/2771 weeks
196-.00192 -.00132 (196*2π)/2771 weeks
197.00432 -.00582 (197*2π)/2771 weeks
198.00944 -.00722 (198*2π)/2771 weeks
199.00622 -.00644 (199*2π)/2771 weeks
200.00948 -.00211 (200*2π)/2771 weeks
201.01225 -.00712 (201*2π)/2771 weeks
202.008 -.00444 (202*2π)/2771 weeks
203.0019 .00013 (203*2π)/2771 weeks
204-.00413 -.01097 (204*2π)/2771 weeks
205.00169 -.01337 (205*2π)/2771 weeks
206.00873 -.0112 (206*2π)/2771 weeks
207.00953 -.00229 (207*2π)/2771 weeks
208-.00346 -.00474 (208*2π)/2771 weeks
209.00885 -.00766 (209*2π)/2771 weeks
210.00519 -.00873 (210*2π)/2771 weeks
211.01292 -.01549 (211*2π)/2771 weeks
212.01901 -.00601 (212*2π)/2771 weeks
213.01254 -.00352 (213*2π)/2771 weeks
214.00944 -.0119 (214*2π)/2771 weeks
215.00736 -.00014 (215*2π)/2771 weeks
216.00429 -.01723 (216*2π)/2771 weeks
217.0081 -.00481 (217*2π)/2771 weeks
218-.00502 -.00002 (218*2π)/2771 weeks
219.00466 -.01094 (219*2π)/2771 weeks
220.00058 -.00945 (220*2π)/2771 weeks
221.00715 -.00827 (221*2π)/2771 weeks
222.0048 -.01143 (222*2π)/2771 weeks
223.00848 -.01629 (223*2π)/2771 weeks
224.02918 -.01538 (224*2π)/2771 weeks
225.01658 -.00993 (225*2π)/2771 weeks
226.00391 -.00683 (226*2π)/2771 weeks
227.01619 -.00852 (227*2π)/2771 weeks
228.01237 -.02216 (228*2π)/2771 weeks
229.01368 .00159 (229*2π)/2771 weeks
230-.00094 .00378 (230*2π)/2771 weeks
231-.00126 .00037 (231*2π)/2771 weeks
232.00434 -.0079 (232*2π)/2771 weeks
233.01152 -.00417 (233*2π)/2771 weeks
234-.00838 -.00196 (234*2π)/2771 weeks
235-.00054 -.00532 (235*2π)/2771 weeks
236.01672 -.02619 (236*2π)/2771 weeks
237.00478 -.017 (237*2π)/2771 weeks
238.01182 -.02307 (238*2π)/2771 weeks
239.01504 -.00072 (239*2π)/2771 weeks
240.0105 -.01646 (240*2π)/2771 weeks
241.00665 .00333 (241*2π)/2771 weeks
242-.01869 -.01682 (242*2π)/2771 weeks
243.00753 -.01191 (243*2π)/2771 weeks
244.00822 -.0019 (244*2π)/2771 weeks
245.00474 -.0272 (245*2π)/2771 weeks
246-.00183 -.02026 (246*2π)/2771 weeks
247-.00152 -.00989 (247*2π)/2771 weeks
248.00634 -.04025 (248*2π)/2771 weeks
249.01525 -.02631 (249*2π)/2771 weeks
250-.00853 -.04074 (250*2π)/2771 weeks
251.01401 -.02653 (251*2π)/2771 weeks
252.02005 -.0121 (252*2π)/2771 weeks
253.00558 -.02442 (253*2π)/2771 weeks
254.00659 -.02732 (254*2π)/2771 weeks
255.00708 -.00865 (255*2π)/2771 weeks
256.0146 -.01126 (256*2π)/2771 weeks
257.0292 -.03037 (257*2π)/2771 weeks
258-.01264 -.01306 (258*2π)/2771 weeks
259-.01512 -.04343 (259*2π)/2771 weeks
260.03374 -.0224 (260*2π)/2771 weeks
261-.04599 -.01406 (261*2π)/2771 weeks
262-.03325 -.10278 (262*2π)/2771 weeks
263.04898 -.06452 (263*2π)/2771 weeks
264-.01311 .00201 (264*2π)/2771 weeks
265.04173 -.08288 (265*2π)/2771 weeks
266.00945 .00534 (266*2π)/2771 weeks
267-.04107 -.08987 (267*2π)/2771 weeks
268.10995 -.08436 (268*2π)/2771 weeks
269.02901 .0009 (269*2π)/2771 weeks
270.01602 -.06035 (270*2π)/2771 weeks
271-.05219 -.08282 (271*2π)/2771 weeks
272-.1096 -.15493 (272*2π)/2771 weeks
273.08038 -.262 (273*2π)/2771 weeks
274.04587 .01015 (274*2π)/2771 weeks
275-.35969 -.29337 (275*2π)/2771 weeks

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