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Fourier Analysis of AFTEX (American Fds, The Tax-Exempt Bo)


AFTEX (American Fds, The Tax-Exempt Bo) appears to have interesting cyclic behaviour every 194 weeks (.4009*sine), 176 weeks (.3613*sine), and 149 weeks (.0608*cosine).

AFTEX (American Fds, The Tax-Exempt Bo) has an average price of 6.02 (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 10/10/1979 to 11/28/2016 for AFTEX (American Fds, The Tax-Exempt Bo), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
06.02471   0 
1.53623 -3.7471 (1*2π)/19381,938 weeks
2.25523 -1.86272 (2*2π)/1938969 weeks
3.17064 -1.35945 (3*2π)/1938646 weeks
4.01562 -1.09286 (4*2π)/1938485 weeks
5-.0267 -.77629 (5*2π)/1938388 weeks
6.05356 -.58619 (6*2π)/1938323 weeks
7.0075 -.50157 (7*2π)/1938277 weeks
8.08463 -.52047 (8*2π)/1938242 weeks
9-.01129 -.45087 (9*2π)/1938215 weeks
10.03683 -.40095 (10*2π)/1938194 weeks
11.0372 -.36129 (11*2π)/1938176 weeks
12.01475 -.30793 (12*2π)/1938162 weeks
13-.06083 -.33165 (13*2π)/1938149 weeks
14-.05826 -.22233 (14*2π)/1938138 weeks
15-.03604 -.2127 (15*2π)/1938129 weeks
16.05631 -.18472 (16*2π)/1938121 weeks
17.03383 -.22941 (17*2π)/1938114 weeks
18.00697 -.25237 (18*2π)/1938108 weeks
19.00914 -.2228 (19*2π)/1938102 weeks
20-.0248 -.21486 (20*2π)/193897 weeks
21.02418 -.19172 (21*2π)/193892 weeks
22-.00545 -.19241 (22*2π)/193888 weeks
23-.01614 -.1942 (23*2π)/193884 weeks
24-.03679 -.16237 (24*2π)/193881 weeks
25-.02437 -.14544 (25*2π)/193878 weeks
26.00079 -.14101 (26*2π)/193875 weeks
27-.01701 -.13492 (27*2π)/193872 weeks
28-.02325 -.1272 (28*2π)/193869 weeks
29.00103 -.11435 (29*2π)/193867 weeks
30.01016 -.13631 (30*2π)/193865 weeks
31-.00206 -.13967 (31*2π)/193863 weeks
32-.02326 -.14257 (32*2π)/193861 weeks
33-.03423 -.11323 (33*2π)/193859 weeks
34-.01329 -.10562 (34*2π)/193857 weeks
35-.00125 -.10311 (35*2π)/193855 weeks
36-.01007 -.10312 (36*2π)/193854 weeks
37-.01117 -.10006 (37*2π)/193852 weeks
38-.02318 -.09845 (38*2π)/193851 weeks
39-.00982 -.09208 (39*2π)/193850 weeks
40.00275 -.09078 (40*2π)/193848 weeks
41.01208 -.09326 (41*2π)/193847 weeks
42-.00606 -.10073 (42*2π)/193846 weeks
43-.00686 -.09359 (43*2π)/193845 weeks
44-.01108 -.09807 (44*2π)/193844 weeks
45-.01835 -.09579 (45*2π)/193843 weeks
46-.0092 -.06892 (46*2π)/193842 weeks
47-.01007 -.07923 (47*2π)/193841 weeks
48-.00668 -.06679 (48*2π)/193840 weeks
49.0011 -.08332 (49*2π)/193840 weeks
50-.01232 -.09376 (50*2π)/193839 weeks
51-.02959 -.06233 (51*2π)/193838 weeks
52.00268 -.07002 (52*2π)/193837 weeks
53-.00154 -.06027 (53*2π)/193837 weeks
54-.00781 -.06694 (54*2π)/193836 weeks
55-.0037 -.07732 (55*2π)/193835 weeks
56-.02855 -.06836 (56*2π)/193835 weeks
57-.01201 -.06175 (57*2π)/193834 weeks
58-.00116 -.05835 (58*2π)/193833 weeks
59-.01275 -.06069 (59*2π)/193833 weeks
60-.01083 -.05336 (60*2π)/193832 weeks
61.00046 -.05375 (61*2π)/193832 weeks
62.00062 -.06446 (62*2π)/193831 weeks
63-.00257 -.06236 (63*2π)/193831 weeks
64-.01732 -.06738 (64*2π)/193830 weeks
65-.01208 -.04768 (65*2π)/193830 weeks
66-.00434 -.05168 (66*2π)/193829 weeks
67-.00821 -.05561 (67*2π)/193829 weeks
68-.01599 -.05504 (68*2π)/193829 weeks
69-.01397 -.05587 (69*2π)/193828 weeks
70-.00979 -.04342 (70*2π)/193828 weeks
71-.00311 -.04426 (71*2π)/193827 weeks
72.00007 -.05245 (72*2π)/193827 weeks
73-.00084 -.0528 (73*2π)/193827 weeks
74-.0203 -.05664 (74*2π)/193826 weeks
75-.00525 -.04807 (75*2π)/193826 weeks
76-.0045 -.04545 (76*2π)/193826 weeks
77-.009 -.04389 (77*2π)/193825 weeks
78-.01111 -.04232 (78*2π)/193825 weeks
79-.01765 -.04804 (79*2π)/193825 weeks
80-.00797 -.04272 (80*2π)/193824 weeks
81-.00976 -.03948 (81*2π)/193824 weeks
82-.00701 -.03904 (82*2π)/193824 weeks
83-.00557 -.04546 (83*2π)/193823 weeks
84.0007 -.04233 (84*2π)/193823 weeks
85.0047 -.05241 (85*2π)/193823 weeks
86-.00585 -.04976 (86*2π)/193823 weeks
87-.01232 -.04173 (87*2π)/193822 weeks
88-.01134 -.03879 (88*2π)/193822 weeks
89-.01237 -.04111 (89*2π)/193822 weeks
90-.00506 -.03828 (90*2π)/193822 weeks
91-.00175 -.03923 (91*2π)/193821 weeks
92-.01007 -.03775 (92*2π)/193821 weeks
93-.00381 -.03376 (93*2π)/193821 weeks
94-.00533 -.04528 (94*2π)/193821 weeks
95-.01374 -.04159 (95*2π)/193820 weeks
96-.00598 -.0406 (96*2π)/193820 weeks
97-.0133 -.03944 (97*2π)/193820 weeks
98-.00971 -.03603 (98*2π)/193820 weeks
99-.003 -.04084 (99*2π)/193820 weeks
100-.00626 -.04042 (100*2π)/193819 weeks
101-.0139 -.0369 (101*2π)/193819 weeks
102-.00673 -.03038 (102*2π)/193819 weeks
103-.00536 -.03695 (103*2π)/193819 weeks
104-.00098 -.03505 (104*2π)/193819 weeks
105-.00515 -.03924 (105*2π)/193818 weeks
106-.01343 -.03683 (106*2π)/193818 weeks
107-.00316 -.02624 (107*2π)/193818 weeks
108-.00594 -.03663 (108*2π)/193818 weeks
109-.00405 -.03903 (109*2π)/193818 weeks
110-.00973 -.03703 (110*2π)/193818 weeks
111-.01528 -.03163 (111*2π)/193817 weeks
112-.00772 -.01961 (112*2π)/193817 weeks
113-.00067 -.03079 (113*2π)/193817 weeks
114-.00394 -.03501 (114*2π)/193817 weeks
115-.00699 -.02792 (115*2π)/193817 weeks
116-.00456 -.02876 (116*2π)/193817 weeks
117-.00856 -.02705 (117*2π)/193817 weeks
118-.00581 -.03108 (118*2π)/193816 weeks
119-.00637 -.03594 (119*2π)/193816 weeks
120-.00623 -.02793 (120*2π)/193816 weeks
121-.00652 -.03193 (121*2π)/193816 weeks
122-.00467 -.02679 (122*2π)/193816 weeks
123-.00697 -.03692 (123*2π)/193816 weeks
124-.00878 -.03215 (124*2π)/193816 weeks
125-.007 -.02546 (125*2π)/193816 weeks
126-.00885 -.02697 (126*2π)/193815 weeks
127-.00809 -.02903 (127*2π)/193815 weeks
128-.0056 -.02166 (128*2π)/193815 weeks
129-.00356 -.02576 (129*2π)/193815 weeks
130-.00416 -.03098 (130*2π)/193815 weeks
131-.00953 -.02748 (131*2π)/193815 weeks
132-.00871 -.02609 (132*2π)/193815 weeks
133-.00508 -.02272 (133*2π)/193815 weeks
134-.00513 -.02743 (134*2π)/193814 weeks
135-.00402 -.02923 (135*2π)/193814 weeks
136-.01077 -.03029 (136*2π)/193814 weeks
137-.00597 -.02115 (137*2π)/193814 weeks
138-.00258 -.02954 (138*2π)/193814 weeks
139-.00685 -.02979 (139*2π)/193814 weeks
140-.00919 -.02429 (140*2π)/193814 weeks
141-.00737 -.0251 (141*2π)/193814 weeks
142-.00729 -.02037 (142*2π)/193814 weeks
143-.00435 -.02659 (143*2π)/193814 weeks
144-.00873 -.02742 (144*2π)/193813 weeks
145-.0075 -.02388 (145*2π)/193813 weeks
146-.00454 -.02288 (146*2π)/193813 weeks
147-.00284 -.02529 (147*2π)/193813 weeks
148-.00595 -.02473 (148*2π)/193813 weeks
149-.01006 -.0276 (149*2π)/193813 weeks
150-.01529 -.02343 (150*2π)/193813 weeks
151-.01028 -.01729 (151*2π)/193813 weeks
152-.0057 -.02015 (152*2π)/193813 weeks
153-.01047 -.01975 (153*2π)/193813 weeks
154-.00434 -.0214 (154*2π)/193813 weeks
155-.00427 -.02047 (155*2π)/193813 weeks
156-.00298 -.02399 (156*2π)/193812 weeks
157-.00386 -.02334 (157*2π)/193812 weeks
158-.00856 -.02345 (158*2π)/193812 weeks
159-.00796 -.02056 (159*2π)/193812 weeks
160-.00462 -.02088 (160*2π)/193812 weeks
161-.00422 -.01992 (161*2π)/193812 weeks
162-.00722 -.01994 (162*2π)/193812 weeks
163-.00685 -.02686 (163*2π)/193812 weeks
164-.01055 -.01987 (164*2π)/193812 weeks
165-.00505 -.01818 (165*2π)/193812 weeks
166-.00505 -.02275 (166*2π)/193812 weeks
167-.00616 -.02376 (167*2π)/193812 weeks
168-.0099 -.0248 (168*2π)/193812 weeks
169-.0085 -.0181 (169*2π)/193811 weeks
170-.00149 -.01922 (170*2π)/193811 weeks
171-.00469 -.02268 (171*2π)/193811 weeks
172-.00999 -.02274 (172*2π)/193811 weeks
173-.00816 -.0198 (173*2π)/193811 weeks
174-.0073 -.01423 (174*2π)/193811 weeks
175.00291 -.01646 (175*2π)/193811 weeks
176-.0037 -.02352 (176*2π)/193811 weeks
177-.00775 -.02357 (177*2π)/193811 weeks
178-.00711 -.02023 (178*2π)/193811 weeks
179-.0063 -.0177 (179*2π)/193811 weeks
180-.00271 -.01936 (180*2π)/193811 weeks
181-.00673 -.02406 (181*2π)/193811 weeks
182-.00953 -.02136 (182*2π)/193811 weeks
183-.00769 -.01989 (183*2π)/193811 weeks
184-.0067 -.01524 (184*2π)/193811 weeks
185-.00519 -.01786 (185*2π)/193810 weeks
186-.00492 -.0206 (186*2π)/193810 weeks
187-.00846 -.0188 (187*2π)/193810 weeks
188-.00512 -.02035 (188*2π)/193810 weeks
189-.00516 -.01788 (189*2π)/193810 weeks
190-.00817 -.02022 (190*2π)/193810 weeks
191-.01138 -.01724 (191*2π)/193810 weeks
192-.00674 -.01678 (192*2π)/193810 weeks
193-.00539 -.01643 (193*2π)/193810 weeks
194-.00316 -.02013 (194*2π)/193810 weeks
195-.00885 -.02177 (195*2π)/193810 weeks
196-.00858 -.01715 (196*2π)/193810 weeks
197-.00429 -.01818 (197*2π)/193810 weeks
198-.00449 -.01731 (198*2π)/193810 weeks
199-.007 -.02 (199*2π)/193810 weeks
200-.00899 -.01602 (200*2π)/193810 weeks
201-.00404 -.01364 (201*2π)/193810 weeks
202-.00684 -.02034 (202*2π)/193810 weeks
203-.006 -.02101 (203*2π)/193810 weeks
204-.01071 -.01657 (204*2π)/193810 weeks
205-.00653 -.0156 (205*2π)/19389 weeks
206-.00609 -.01559 (206*2π)/19389 weeks
207-.00477 -.01668 (207*2π)/19389 weeks
208-.00613 -.01928 (208*2π)/19389 weeks
209-.00893 -.01709 (209*2π)/19389 weeks
210-.00751 -.01216 (210*2π)/19389 weeks
211-.00518 -.01255 (211*2π)/19389 weeks
212-.00488 -.01604 (212*2π)/19389 weeks
213-.00697 -.0181 (213*2π)/19389 weeks
214-.00897 -.01809 (214*2π)/19389 weeks
215-.01037 -.01489 (215*2π)/19389 weeks
216-.00707 -.01128 (216*2π)/19389 weeks
217-.00502 -.01473 (217*2π)/19389 weeks
218-.00748 -.01471 (218*2π)/19389 weeks
219-.00716 -.01421 (219*2π)/19389 weeks
220-.00463 -.01206 (220*2π)/19389 weeks
221.00028 -.01224 (221*2π)/19389 weeks
222-.00402 -.01967 (222*2π)/19389 weeks
223-.0082 -.01853 (223*2π)/19389 weeks
224-.00986 -.01379 (224*2π)/19389 weeks
225-.004 -.01518 (225*2π)/19389 weeks
226-.00522 -.01506 (226*2π)/19389 weeks
227-.00642 -.01896 (227*2π)/19389 weeks
228-.01003 -.01368 (228*2π)/19389 weeks
229-.00755 -.01199 (229*2π)/19388 weeks
230-.00139 -.0141 (230*2π)/19388 weeks
231-.0039 -.01588 (231*2π)/19388 weeks
232-.00772 -.01612 (232*2π)/19388 weeks
233-.00575 -.01442 (233*2π)/19388 weeks
234-.00739 -.01415 (234*2π)/19388 weeks
235-.00655 -.01446 (235*2π)/19388 weeks
236-.00702 -.01508 (236*2π)/19388 weeks
237-.0089 -.01362 (237*2π)/19388 weeks
238-.00586 -.01268 (238*2π)/19388 weeks
239-.00536 -.01186 (239*2π)/19388 weeks
240-.00648 -.01558 (240*2π)/19388 weeks
241-.00594 -.0121 (241*2π)/19388 weeks
242-.0064 -.01355 (242*2π)/19388 weeks
243-.00378 -.01362 (243*2π)/19388 weeks
244-.00314 -.01589 (244*2π)/19388 weeks
245-.0075 -.01554 (245*2π)/19388 weeks
246-.00831 -.01367 (246*2π)/19388 weeks
247-.00699 -.01189 (247*2π)/19388 weeks
248-.00402 -.01286 (248*2π)/19388 weeks
249-.00573 -.01599 (249*2π)/19388 weeks
250-.00736 -.01179 (250*2π)/19388 weeks
251-.00787 -.01334 (251*2π)/19388 weeks
252-.00537 -.01207 (252*2π)/19388 weeks
253-.00664 -.01117 (253*2π)/19388 weeks
254-.00559 -.01476 (254*2π)/19388 weeks
255-.00688 -.01072 (255*2π)/19388 weeks
256-.00553 -.01147 (256*2π)/19388 weeks
257-.00392 -.01437 (257*2π)/19388 weeks
258-.00573 -.01412 (258*2π)/19388 weeks
259-.00407 -.01572 (259*2π)/19387 weeks
260-.00885 -.01266 (260*2π)/19387 weeks
261-.00389 -.01221 (261*2π)/19387 weeks
262-.0047 -.01355 (262*2π)/19387 weeks
263-.00681 -.01235 (263*2π)/19387 weeks
264-.00521 -.01281 (264*2π)/19387 weeks
265-.00546 -.01244 (265*2π)/19387 weeks
266-.0056 -.01202 (266*2π)/19387 weeks
267-.00569 -.01282 (267*2π)/19387 weeks
268-.00828 -.01331 (268*2π)/19387 weeks
269-.00582 -.01237 (269*2π)/19387 weeks
270-.00629 -.01222 (270*2π)/19387 weeks
271-.00588 -.0115 (271*2π)/19387 weeks
272-.00517 -.01072 (272*2π)/19387 weeks
273-.00614 -.01234 (273*2π)/19387 weeks
274-.00706 -.01124 (274*2π)/19387 weeks
275-.00634 -.01198 (275*2π)/19387 weeks
276-.00488 -.00896 (276*2π)/19387 weeks
277-.00479 -.01312 (277*2π)/19387 weeks
278-.00634 -.01292 (278*2π)/19387 weeks
279-.0053 -.01277 (279*2π)/19387 weeks
280-.00565 -.01351 (280*2π)/19387 weeks
281-.00671 -.01252 (281*2π)/19387 weeks
282-.00668 -.01285 (282*2π)/19387 weeks
283-.00845 -.01136 (283*2π)/19387 weeks
284-.00628 -.00983 (284*2π)/19387 weeks
285-.00456 -.01121 (285*2π)/19387 weeks
286-.00441 -.01209 (286*2π)/19387 weeks
287-.00734 -.01237 (287*2π)/19387 weeks
288-.00862 -.01177 (288*2π)/19387 weeks
289-.00677 -.01051 (289*2π)/19387 weeks
290-.00762 -.01022 (290*2π)/19387 weeks
291-.00514 -.01153 (291*2π)/19387 weeks
292-.00699 -.00985 (292*2π)/19387 weeks
293-.00608 -.01118 (293*2π)/19387 weeks
294-.00483 -.01137 (294*2π)/19387 weeks
295-.00504 -.0108 (295*2π)/19387 weeks
296-.00476 -.0113 (296*2π)/19387 weeks
297-.00467 -.01207 (297*2π)/19387 weeks
298-.00748 -.01128 (298*2π)/19387 weeks
299-.0058 -.011 (299*2π)/19386 weeks
300-.00606 -.01001 (300*2π)/19386 weeks
301-.00676 -.01194 (301*2π)/19386 weeks
302-.00704 -.01063 (302*2π)/19386 weeks
303-.00821 -.00945 (303*2π)/19386 weeks
304-.00507 -.00915 (304*2π)/19386 weeks
305-.00652 -.00809 (305*2π)/19386 weeks
306-.00575 -.01261 (306*2π)/19386 weeks
307-.00681 -.01129 (307*2π)/19386 weeks
308-.00655 -.0106 (308*2π)/19386 weeks
309-.00403 -.00821 (309*2π)/19386 weeks
310-.00719 -.00917 (310*2π)/19386 weeks
311-.00583 -.00981 (311*2π)/19386 weeks
312-.00668 -.00783 (312*2π)/19386 weeks
313-.0046 -.00948 (313*2π)/19386 weeks
314-.0041 -.01061 (314*2π)/19386 weeks
315-.00691 -.013 (315*2π)/19386 weeks
316-.00691 -.0104 (316*2π)/19386 weeks
317-.00646 -.00997 (317*2π)/19386 weeks
318-.00648 -.00977 (318*2π)/19386 weeks
319-.00492 -.00975 (319*2π)/19386 weeks
320-.00541 -.00886 (320*2π)/19386 weeks
321-.00577 -.0107 (321*2π)/19386 weeks
322-.00471 -.01003 (322*2π)/19386 weeks
323-.00607 -.00993 (323*2π)/19386 weeks
324-.00461 -.00826 (324*2π)/19386 weeks
325-.00434 -.00927 (325*2π)/19386 weeks
326-.00474 -.01095 (326*2π)/19386 weeks
327-.00554 -.01153 (327*2π)/19386 weeks
328-.00854 -.00873 (328*2π)/19386 weeks
329-.00473 -.00928 (329*2π)/19386 weeks
330-.00555 -.01036 (330*2π)/19386 weeks
331-.00638 -.00966 (331*2π)/19386 weeks
332-.00508 -.00882 (332*2π)/19386 weeks
333-.00566 -.00897 (333*2π)/19386 weeks
334-.00427 -.00809 (334*2π)/19386 weeks
335-.00383 -.00949 (335*2π)/19386 weeks
336-.00464 -.01083 (336*2π)/19386 weeks
337-.00573 -.00988 (337*2π)/19386 weeks
338-.00601 -.01072 (338*2π)/19386 weeks
339-.00725 -.00938 (339*2π)/19386 weeks
340-.00549 -.00864 (340*2π)/19386 weeks
341-.00538 -.00988 (341*2π)/19386 weeks
342-.00684 -.00946 (342*2π)/19386 weeks
343-.00687 -.00876 (343*2π)/19386 weeks
344-.00643 -.00979 (344*2π)/19386 weeks
345-.00576 -.00754 (345*2π)/19386 weeks
346-.00546 -.00864 (346*2π)/19386 weeks
347-.00616 -.00957 (347*2π)/19386 weeks
348-.00573 -.00841 (348*2π)/19386 weeks
349-.00448 -.00968 (349*2π)/19386 weeks
350-.00547 -.01004 (350*2π)/19386 weeks
351-.00649 -.01001 (351*2π)/19386 weeks
352-.00715 -.00868 (352*2π)/19386 weeks
353-.00509 -.0093 (353*2π)/19385 weeks
354-.00605 -.00994 (354*2π)/19385 weeks
355-.00781 -.00756 (355*2π)/19385 weeks
356-.00595 -.00662 (356*2π)/19385 weeks
357-.0047 -.00943 (357*2π)/19385 weeks
358-.00496 -.00902 (358*2π)/19385 weeks
359-.00608 -.00952 (359*2π)/19385 weeks
360-.00565 -.00763 (360*2π)/19385 weeks
361-.00549 -.00655 (361*2π)/19385 weeks
362-.00429 -.01025 (362*2π)/19385 weeks
363-.00648 -.00929 (363*2π)/19385 weeks
364-.00504 -.00691 (364*2π)/19385 weeks
365-.00517 -.00863 (365*2π)/19385 weeks
366-.00605 -.00877 (366*2π)/19385 weeks
367-.00607 -.00951 (367*2π)/19385 weeks
368-.00687 -.00881 (368*2π)/19385 weeks
369-.00716 -.00504