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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 (.4024*sine), 177 weeks (.3623*sine), and 150 weeks (.0708*cosine).

AFTEX (American Fds, The Tax-Exempt Bo) has an average price of 6.01 (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 1/9/2017 for AFTEX (American Fds, The Tax-Exempt Bo), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
06.01427   0 
1.53693 -3.74501 (1*2π)/19441,944 weeks
2.25468 -1.86548 (2*2π)/1944972 weeks
3.16462 -1.36301 (3*2π)/1944648 weeks
4.00691 -1.08969 (4*2π)/1944486 weeks
5-.02837 -.77049 (5*2π)/1944389 weeks
6.0551 -.58704 (6*2π)/1944324 weeks
7.00908 -.50302 (7*2π)/1944278 weeks
8.07756 -.52733 (8*2π)/1944243 weeks
9-.01726 -.44839 (9*2π)/1944216 weeks
10.03166 -.40242 (10*2π)/1944194 weeks
11.02994 -.36226 (11*2π)/1944177 weeks
12.00779 -.3073 (12*2π)/1944162 weeks
13-.07076 -.31923 (13*2π)/1944150 weeks
14-.05124 -.21132 (14*2π)/1944139 weeks
15-.02602 -.20908 (15*2π)/1944130 weeks
16.06429 -.19942 (16*2π)/1944122 weeks
17.02678 -.24155 (17*2π)/1944114 weeks
18-.00649 -.25589 (18*2π)/1944108 weeks
19-.00144 -.22402 (19*2π)/1944102 weeks
20-.03312 -.20871 (20*2π)/194497 weeks
21.01688 -.1951 (21*2π)/194493 weeks
22-.01688 -.18887 (22*2π)/194488 weeks
23-.0284 -.18548 (23*2π)/194485 weeks
24-.03982 -.14863 (24*2π)/194481 weeks
25-.02222 -.13699 (25*2π)/194478 weeks
26.00041 -.13962 (26*2π)/194475 weeks
27-.01785 -.12933 (27*2π)/194472 weeks
28-.02068 -.12144 (28*2π)/194469 weeks
29.00462 -.11833 (29*2π)/194467 weeks
30.00218 -.14167 (30*2π)/194465 weeks
31-.01394 -.13769 (31*2π)/194463 weeks
32-.03419 -.13009 (32*2π)/194461 weeks
33-.03173 -.09857 (33*2π)/194459 weeks
34-.0087 -.10061 (34*2π)/194457 weeks
35-.00004 -.10269 (35*2π)/194456 weeks
36-.01091 -.09951 (36*2π)/194454 weeks
37-.01175 -.09618 (37*2π)/194453 weeks
38-.02107 -.09098 (38*2π)/194451 weeks
39-.00517 -.09107 (39*2π)/194450 weeks
40.00427 -.09509 (40*2π)/194449 weeks
41.00665 -.09976 (41*2π)/194447 weeks
42-.0152 -.09716 (42*2π)/194446 weeks
43-.01263 -.0891 (43*2π)/194445 weeks
44-.01826 -.09006 (44*2π)/194444 weeks
45-.02126 -.08245 (45*2π)/194443 weeks
46-.00175 -.06387 (46*2π)/194442 weeks
47-.00905 -.07493 (47*2π)/194441 weeks
48-.00204 -.06693 (48*2π)/194441 weeks
49-.00606 -.08471 (49*2π)/194440 weeks
50-.02208 -.08155 (50*2π)/194439 weeks
51-.01767 -.04771 (51*2π)/194438 weeks
52.00594 -.07295 (52*2π)/194437 weeks
53.00135 -.06134 (53*2π)/194437 weeks
54-.00962 -.06535 (54*2π)/194436 weeks
55-.01188 -.07309 (55*2π)/194435 weeks
56-.02482 -.0518 (56*2π)/194435 weeks
57-.00408 -.05755 (57*2π)/194434 weeks
58.00291 -.06009 (58*2π)/194434 weeks
59-.00965 -.05554 (59*2π)/194433 weeks
60-.00307 -.05256 (60*2π)/194432 weeks
61.00299 -.06061 (61*2π)/194432 weeks
62-.00604 -.06679 (62*2π)/194431 weeks
63-.0087 -.05969 (63*2π)/194431 weeks
64-.02043 -.05355 (64*2π)/194430 weeks
65-.00249 -.04303 (65*2π)/194430 weeks
66-.00229 -.05301 (66*2π)/194429 weeks
67-.00957 -.05229 (67*2π)/194429 weeks
68-.01361 -.0471 (68*2π)/194429 weeks
69-.00956 -.04927 (69*2π)/194428 weeks
70.00098 -.04369 (70*2π)/194428 weeks
71.00162 -.05073 (71*2π)/194427 weeks
72-.00421 -.0569 (72*2π)/194427 weeks
73-.00716 -.05261 (73*2π)/194427 weeks
74-.02043 -.04267 (74*2π)/194426 weeks
75-.00071 -.04707 (75*2π)/194426 weeks
76-.00214 -.04454 (76*2π)/194426 weeks
77-.00613 -.04067 (77*2π)/194425 weeks
78-.00733 -.0397 (78*2π)/194425 weeks
79-.01343 -.04096 (79*2π)/194425 weeks
80-.00144 -.04407 (80*2π)/194424 weeks
81-.00268 -.04119 (81*2π)/194424 weeks
82-.00235 -.04461 (82*2π)/194424 weeks
83-.00645 -.04961 (83*2π)/194423 weeks
84-.0015 -.05015 (84*2π)/194423 weeks
85-.00848 -.0545 (85*2π)/194423 weeks
86-.01203 -.04013 (86*2π)/194423 weeks
87-.00836 -.03217 (87*2π)/194422 weeks
88-.00566 -.03472 (88*2π)/194422 weeks
89-.00751 -.03748 (89*2π)/194422 weeks
90-.00122 -.04126 (90*2π)/194422 weeks
91-.00294 -.04194 (91*2π)/194421 weeks
92-.00752 -.03463 (92*2π)/194421 weeks
93-.00262 -.0389 (93*2π)/194421 weeks
94-.01357 -.04219 (94*2π)/194421 weeks
95-.01195 -.03285 (95*2π)/194420 weeks
96-.00587 -.03887 (96*2π)/194420 weeks
97-.00902 -.03241 (97*2π)/194420 weeks
98-.00395 -.03596 (98*2π)/194420 weeks
99-.0055 -.04206 (99*2π)/194420 weeks
100-.00686 -.03547 (100*2π)/194419 weeks
101-.00627 -.02918 (101*2π)/194419 weeks
102.00139 -.03484 (102*2π)/194419 weeks
103-.00569 -.03878 (103*2π)/194419 weeks
104-.00279 -.03834 (104*2π)/194419 weeks
105-.00879 -.03415 (105*2π)/194419 weeks
106-.00721 -.02761 (106*2π)/194418 weeks
107.00403 -.03367 (107*2π)/194418 weeks
108-.00965 -.03523 (108*2π)/194418 weeks
109-.00778 -.03468 (109*2π)/194418 weeks
110-.00627 -.02724 (110*2π)/194418 weeks
111-.00178 -.02398 (111*2π)/194418 weeks
112.00749 -.03028 (112*2π)/194417 weeks
113-.00482 -.03965 (113*2π)/194417 weeks
114-.0078 -.03339 (114*2π)/194417 weeks
115-.00208 -.02785 (115*2π)/194417 weeks
116-.00394 -.03122 (116*2π)/194417 weeks
117-.00547 -.02786 (117*2π)/194417 weeks
118-.00818 -.03274 (118*2π)/194416 weeks
119-.00978 -.03188 (119*2π)/194416 weeks
120-.00216 -.02843 (120*2π)/194416 weeks
121-.0071 -.03007 (121*2π)/194416 weeks
122-.00315 -.02926 (122*2π)/194416 weeks
123-.01194 -.02953 (123*2π)/194416 weeks
124-.00372 -.02576 (124*2π)/194416 weeks
125.00077 -.02639 (125*2π)/194416 weeks
126-.00391 -.02648 (126*2π)/194415 weeks
127-.00436 -.02853 (127*2π)/194415 weeks
128.00097 -.02856 (128*2π)/194415 weeks
129-.00602 -.03055 (129*2π)/194415 weeks
130-.00913 -.0285 (130*2π)/194415 weeks
131-.00505 -.02302 (131*2π)/194415 weeks
132-.00372 -.02633 (132*2π)/194415 weeks
133-.00238 -.02881 (133*2π)/194415 weeks
134-.00837 -.02843 (134*2π)/194415 weeks
135-.00787 -.02754 (135*2π)/194414 weeks
136-.00734 -.02231 (136*2π)/194414 weeks
137.00048 -.02722 (137*2π)/194414 weeks
138-.00909 -.0293 (138*2π)/194414 weeks
139-.00637 -.02287 (139*2π)/194414 weeks
140-.0015 -.02193 (140*2π)/194414 weeks
141-.00349 -.02534 (141*2π)/194414 weeks
142-.00164 -.02477 (142*2π)/194414 weeks
143-.00825 -.02725 (143*2π)/194414 weeks
144-.0065 -.02245 (144*2π)/194414 weeks
145-.00245 -.02482 (145*2π)/194413 weeks
146-.00339 -.02648 (146*2π)/194413 weeks
147-.00603 -.02516 (147*2π)/194413 weeks
148-.00519 -.02037 (148*2π)/194413 weeks
149-.00616 -.01853 (149*2π)/194413 weeks
150-.00077 -.01841 (150*2π)/194413 weeks
151.00165 -.02635 (151*2π)/194413 weeks
152-.00448 -.0283 (152*2π)/194413 weeks
153-.00497 -.0235 (153*2π)/194413 weeks
154-.0063 -.02949 (154*2π)/194413 weeks
155-.00593 -.02609 (155*2π)/194413 weeks
156-.00852 -.02535 (156*2π)/194412 weeks
157-.00607 -.02239 (157*2π)/194412 weeks
158-.00554 -.01946 (158*2π)/194412 weeks
159-.00342 -.02283 (159*2π)/194412 weeks
160-.00526 -.02502 (160*2π)/194412 weeks
161-.00534 -.02272 (161*2π)/194412 weeks
162-.00686 -.01994 (162*2π)/194412 weeks
163-.0102 -.02134 (163*2π)/194412 weeks
164-.00172 -.02019 (164*2π)/194412 weeks
165-.00485 -.02572 (165*2π)/194412 weeks
166-.00932 -.02238 (166*2π)/194412 weeks
167-.0072 -.02069 (167*2π)/194412 weeks
168-.00543 -.01952 (168*2π)/194412 weeks
169-.00091 -.02392 (169*2π)/194412 weeks
170-.00615 -.02658 (170*2π)/194411 weeks
171-.00753 -.01929 (171*2π)/194411 weeks
172-.00464 -.01782 (172*2π)/194411 weeks
173-.00243 -.02318 (173*2π)/194411 weeks
174-.00212 -.02443 (174*2π)/194411 weeks
175-.00922 -.02727 (175*2π)/194411 weeks
176-.01121 -.01522 (176*2π)/194411 weeks
177-.00599 -.01606 (177*2π)/194411 weeks
178-.00314 -.01996 (178*2π)/194411 weeks
179-.00401 -.02075 (179*2π)/194411 weeks
180-.00745 -.0209 (180*2π)/194411 weeks
181-.00774 -.01565 (181*2π)/194411 weeks
182-.00263 -.01762 (182*2π)/194411 weeks
183-.00298 -.02126 (183*2π)/194411 weeks
184-.00225 -.02156 (184*2π)/194411 weeks
185-.00746 -.02031 (185*2π)/194411 weeks
186-.00747 -.01866 (186*2π)/194410 weeks
187-.00424 -.01729 (187*2π)/194410 weeks
188-.00636 -.02056 (188*2π)/194410 weeks
189-.00366 -.01872 (189*2π)/194410 weeks
190-.00529 -.01617 (190*2π)/194410 weeks
191-.00291 -.01819 (191*2π)/194410 weeks
192-.00627 -.02284 (192*2π)/194410 weeks
193-.00688 -.02065 (193*2π)/194410 weeks
194-.00872 -.01879 (194*2π)/194410 weeks
195-.0049 -.01509 (195*2π)/194410 weeks
196-.00243 -.02039 (196*2π)/194410 weeks
197-.00625 -.0215 (197*2π)/194410 weeks
198-.00458 -.01831 (198*2π)/194410 weeks
199-.00521 -.01608 (199*2π)/194410 weeks
200-.00218 -.01849 (200*2π)/194410 weeks
201-.00576 -.02099 (201*2π)/194410 weeks
202-.00884 -.01468 (202*2π)/194410 weeks
203-.0048 -.01786 (203*2π)/194410 weeks
204-.00073 -.01756 (204*2π)/194410 weeks
205-.00528 -.02165 (205*2π)/19449 weeks
206-.00578 -.01903 (206*2π)/19449 weeks
207-.00649 -.01811 (207*2π)/19449 weeks
208-.00546 -.01617 (208*2π)/19449 weeks
209-.0021 -.01757 (209*2π)/19449 weeks
210-.00308 -.02061 (210*2π)/19449 weeks
211-.00758 -.01854 (211*2π)/19449 weeks
212-.00867 -.01546 (212*2π)/19449 weeks
213-.00623 -.0147 (213*2π)/19449 weeks
214-.00422 -.01661 (214*2π)/19449 weeks
215-.00334 -.01933 (215*2π)/19449 weeks
216-.00621 -.02142 (216*2π)/19449 weeks
217-.00964 -.01761 (217*2π)/19449 weeks
218-.00658 -.01618 (218*2π)/19449 weeks
219-.00735 -.01805 (219*2π)/19449 weeks
220-.00796 -.01886 (220*2π)/19449 weeks
221-.00968 -.01629 (221*2π)/19449 weeks
222-.00815 -.00902 (222*2π)/19449 weeks
223-.00273 -.0136 (223*2π)/19449 weeks
224-.0032 -.01773 (224*2π)/19449 weeks
225-.00888 -.01868 (225*2π)/19449 weeks
226-.00562 -.01488 (226*2π)/19449 weeks
227-.00605 -.01417 (227*2π)/19449 weeks
228-.00197 -.01743 (228*2π)/19449 weeks
229-.00762 -.01895 (229*2π)/19448 weeks
230-.01009 -.0172 (230*2π)/19448 weeks
231-.00536 -.01231 (231*2π)/19448 weeks
232-.00384 -.0133 (232*2π)/19448 weeks
233-.00525 -.01686 (233*2π)/19448 weeks
234-.00514 -.01485 (234*2π)/19448 weeks
235-.0065 -.01571 (235*2π)/19448 weeks
236-.00595 -.01531 (236*2π)/19448 weeks
237-.0053 -.01614 (237*2π)/19448 weeks
238-.00785 -.01749 (238*2π)/19448 weeks
239-.00717 -.01505 (239*2π)/19448 weeks
240-.00779 -.01297 (240*2π)/19448 weeks
241-.00566 -.01625 (241*2π)/19448 weeks
242-.00763 -.01375 (242*2π)/19448 weeks
243-.0077 -.01487 (243*2π)/19448 weeks
244-.00602 -.01276 (244*2π)/19448 weeks
245-.00268 -.01296 (245*2π)/19448 weeks
246-.00475 -.01597 (246*2π)/19448 weeks
247-.0069 -.01631 (247*2π)/19448 weeks
248-.0082 -.01446 (248*2π)/19448 weeks
249-.00569 -.01225 (249*2π)/19448 weeks
250-.00369 -.01557 (250*2π)/19448 weeks
251-.00731 -.01385 (251*2π)/19448 weeks
252-.0075 -.0156 (252*2π)/19448 weeks
253-.00644 -.01323 (253*2π)/19448 weeks
254-.00832 -.01259 (254*2π)/19448 weeks
255-.0051 -.01488 (255*2π)/19448 weeks
256-.00851 -.01278 (256*2π)/19448 weeks
257-.00798 -.01187 (257*2π)/19448 weeks
258-.00468 -.01276 (258*2π)/19448 weeks
259-.00579 -.0137 (259*2π)/19448 weeks
260-.00264 -.01433 (260*2π)/19447 weeks
261-.00828 -.01528 (261*2π)/19447 weeks
262-.00516 -.01204 (262*2π)/19447 weeks
263-.00435 -.01311 (263*2π)/19447 weeks
264-.00673 -.01339 (264*2π)/19447 weeks
265-.00535 -.01295 (265*2π)/19447 weeks
266-.00552 -.0127 (266*2π)/19447 weeks
267-.00579 -.01219 (267*2π)/19447 weeks
268-.00522 -.01264 (268*2π)/19447 weeks
269-.00734 -.01476 (269*2π)/19447 weeks
270-.00594 -.0131 (270*2π)/19447 weeks
271-.00631 -.01319 (271*2π)/19447 weeks
272-.00633 -.01239 (272*2π)/19447 weeks
273-.00602 -.01097 (273*2π)/19447 weeks
274-.00593 -.01266 (274*2π)/19447 weeks
275-.00739 -.01226 (275*2π)/19447 weeks
276-.00667 -.01281 (276*2π)/19447 weeks
277-.00683 -.00899 (277*2π)/19447 weeks
278-.00474 -.01211 (278*2π)/19447 weeks
279-.006 -.01291 (279*2π)/19447 weeks
280-.00509 -.01245 (280*2π)/19447 weeks
281-.00478 -.01338 (281*2π)/19447 weeks
282-.00603 -.01309 (282*2π)/19447 weeks
283-.00583 -.01356 (283*2π)/19447 weeks
284-.00827 -.01314 (284*2π)/19447 weeks
285-.00732 -.01075 (285*2π)/19447 weeks
286-.00513 -.011 (286*2π)/19447 weeks
287-.00412 -.01161 (287*2π)/19447 weeks
288-.00648 -.01301 (288*2π)/19447 weeks
289-.00822 -.01319 (289*2π)/19447 weeks
290-.00713 -.01145 (290*2π)/19447 weeks
291-.00821 -.01125 (291*2π)/19447 weeks
292-.00542 -.01172 (292*2π)/19447 weeks
293-.0076 -.0106 (293*2π)/19447 weeks
294-.00654 -.01149 (294*2π)/19447 weeks
295-.00518 -.01138 (295*2π)/19447 weeks
296-.00538 -.01084 (296*2π)/19447 weeks
297-.00485 -.01118 (297*2π)/19447 weeks
298-.0043 -.01196 (298*2π)/19447 weeks
299-.00721 -.012 (299*2π)/19447 weeks
300-.00579 -.01139 (300*2π)/19446 weeks
301-.00618 -.01037 (301*2π)/19446 weeks
302-.00643 -.01241 (302*2π)/19446 weeks
303-.00699 -.01135 (303*2π)/19446 weeks
304-.00856 -.0104 (304*2π)/19446 weeks
305-.00558 -.00941 (305*2π)/19446 weeks
306-.00709 -.00835 (306*2π)/19446 weeks
307-.00556 -.01265 (307*2π)/19446 weeks
308-.00677 -.01176 (308*2π)/19446 weeks
309-.00671 -.01114 (309*2π)/19446 weeks
310-.00445 -.00835 (310*2π)/19446 weeks
311-.00736 -.00957 (311*2π)/19446 weeks
312-.006 -.01006 (312*2π)/19446 weeks
313-.00707 -.00813 (313*2π)/19446 weeks
314-.00483 -.00945 (314*2π)/19446 weeks
315-.0041 -.01052 (315*2π)/19446 weeks
316-.00666 -.01323 (316*2π)/19446 weeks
317-.00691 -.01075 (317*2π)/19446 weeks
318-.00651 -.01026 (318*2π)/19446 weeks
319-.00655 -.01004 (319*2π)/19446 weeks
320-.00498 -.00995 (320*2π)/19446 weeks
321-.00546 -.00907 (321*2π)/19446 weeks
322-.00576 -.01091 (322*2π)/19446 weeks
323-.00471 -.01025 (323*2π)/19446 weeks
324-.00605 -.01016 (324*2π)/19446 weeks
325-.00458 -.00851 (325*2π)/19446 weeks
326-.00432 -.00956 (326*2π)/19446 weeks
327-.00478 -.01123 (327*2π)/19446 weeks
328-.00562 -.01174 (328*2π)/19446 weeks
329-.00842 -.00881 (329*2π)/19446 weeks
330-.00463 -.00961 (330*2π)/19446 weeks
331-.00556 -.01061 (331*2π)/19446 weeks
332-.0063 -.00983 (332*2π)/19446 weeks
333-.00492 -.00913 (333*2π)/19446 weeks
334-.0055 -.00925 (334*2π)/19446 weeks
335-.00405 -.0086 (335*2π)/19446 weeks
336-.00387 -.01011 (336*2π)/19446 weeks
337-.00493 -.01128 (337*2π)/19446 weeks
338-.00591 -.01014 (338*2π)/19446 weeks
339-.00628 -.01088 (339*2π)/19446 weeks
340-.0072 -.00932 (340*2π)/19446 weeks
341-.00531 -.00897 (341*2π)/19446 weeks
342-.00553 -.0102 (342*2π)/19446 weeks
343-.00687 -.00946 (343*2π)/19446 weeks
344-.00666 -.00882 (344*2π)/19446 weeks
345-.00634 -.00987 (345*2π)/19446 weeks
346-.00523 -.00788 (346*2π)/19446 weeks
347-.00528 -.00918 (347*2π)/19446 weeks
348-.00616 -.00986 (348*2π)/19446 weeks
349-.00541 -.00889 (349*2π)/19446 weeks
350-.00468 -.01044 (350*2π)/19446 weeks
351-.00587 -.01037 (351*2π)/19446 weeks
352-.00677 -.00993 (352*2π)/19446 weeks
353-.00683 -.00852 (353*2π)/19446 weeks
354-.00506 -.00976 (354*2π)/19445 weeks
355-.00628 -.00983 (355*2π)/19445 weeks
356-.00699 -.00711 (356*2π)/19445 weeks
357-.00482 -.0073 (357*2π)/19445 weeks
358-.00475 -.01039 (358*2π)/19445 weeks
359-.00504 -.00964 (359*2π)/19445 weeks
360-.00618 -.00955 (360*2π)/19445 weeks
361-.00502 -.00796 (361*2π)/19445 weeks
362-.00465 -.0075 (362*2π)/19445 weeks
363-.0051 -.01126 (363*2π)/19445 weeks
364-.0066 -.00909 (364*2π)/19445 weeks
365-.00435