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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 195 weeks (.4042*sine), 178 weeks (.362*sine), and 150 weeks (.0814*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 3/20/2017 for AFTEX (American Fds, The Tax-Exempt Bo), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
06.01777   0
1.53989 -3.75449 (1*2π)/19541,954 weeks
2.25432 -1.87638 (2*2π)/1954977 weeks
3.15483 -1.37286 (3*2π)/1954651 weeks
4-.00708 -1.08703 (4*2π)/1954489 weeks
5-.03032 -.76328 (5*2π)/1954391 weeks
6.05771 -.59067 (6*2π)/1954326 weeks
7.01096 -.50719 (7*2π)/1954279 weeks
8.06455 -.53842 (8*2π)/1954244 weeks
9-.02665 -.44369 (9*2π)/1954217 weeks
10.02308 -.40422 (10*2π)/1954195 weeks
11.01842 -.36205 (11*2π)/1954178 weeks
12-.00228 -.30369 (12*2π)/1954163 weeks
13-.08141 -.29657 (13*2π)/1954150 weeks
14-.03481 -.19765 (14*2π)/1954140 weeks
15-.00948 -.20962 (15*2π)/1954130 weeks
16.0694 -.22697 (16*2π)/1954122 weeks
17.00834 -.25625 (17*2π)/1954115 weeks
18-.02987 -.25331 (18*2π)/1954109 weeks
19-.01735 -.21876 (19*2π)/1954103 weeks
20-.04205 -.19358 (20*2π)/195498 weeks
21.00584 -.1952 (21*2π)/195493 weeks
22-.03014 -.17488 (22*2π)/195489 weeks
23-.03825 -.16425 (23*2π)/195485 weeks
24-.0323 -.12664 (24*2π)/195481 weeks
25-.01139 -.12761 (25*2π)/195478 weeks
26.00271 -.13893 (26*2π)/195475 weeks
27-.01373 -.12132 (27*2π)/195472 weeks
28-.01246 -.11629 (28*2π)/195470 weeks
29.00669 -.12696 (29*2π)/195467 weeks
30-.01277 -.14178 (30*2π)/195465 weeks
31-.02577 -.1235 (31*2π)/195463 weeks
32-.03466 -.10437 (32*2π)/195461 weeks
33-.01239 -.0832 (33*2π)/195459 weeks
34.0032 -.10147 (34*2π)/195457 weeks
35.00309 -.1054 (35*2π)/195456 weeks
36-.00762 -.09508 (36*2π)/195454 weeks
37-.00731 -.09216 (37*2π)/195453 weeks
38-.01119 -.08529 (38*2π)/195451 weeks
39.00082 -.09664 (39*2π)/195450 weeks
40.00096 -.10234 (40*2π)/195449 weeks
41-.00507 -.10076 (41*2π)/195448 weeks
42-.01977 -.08169 (42*2π)/195447 weeks
43-.01032 -.07796 (43*2π)/195445 weeks
44-.01385 -.07511 (44*2π)/195444 weeks
45-.00705 -.06889 (45*2π)/195443 weeks
46.01488 -.07092 (46*2π)/195442 weeks
47-.00389 -.07453 (47*2π)/195442 weeks
48.00348 -.07334 (48*2π)/195441 weeks
49-.01361 -.07894 (49*2π)/195440 weeks
50-.0145 -.06195 (50*2π)/195439 weeks
51.01284 -.05144 (51*2π)/195438 weeks
52.00296 -.08601 (52*2π)/195438 weeks
53.0037 -.06663 (53*2π)/195437 weeks
54-.00879 -.06153 (54*2π)/195436 weeks
55-.01149 -.06316 (55*2π)/195436 weeks
56.00004 -.04579 (56*2π)/195435 weeks
57.00498 -.07091 (57*2π)/195434 weeks
58.0023 -.07084 (58*2π)/195434 weeks
59-.003 -.05683 (59*2π)/195433 weeks
60.00084 -.0634 (60*2π)/195433 weeks
61-.00612 -.06859 (61*2π)/195432 weeks
62-.0134 -.0588 (62*2π)/195432 weeks
63-.00507 -.05169 (63*2π)/195431 weeks
64-.00375 -.0444 (64*2π)/195431 weeks
65.00951 -.05864 (65*2π)/195430 weeks
66-.00529 -.0592 (66*2π)/195430 weeks
67-.00635 -.05054 (67*2π)/195429 weeks
68-.003 -.04876 (68*2π)/195429 weeks
69-.0033 -.05642 (69*2π)/195428 weeks
70.00197 -.06079 (70*2π)/195428 weeks
71-.00864 -.05846 (71*2π)/195428 weeks
72-.01295 -.05125 (72*2π)/195427 weeks
73-.00596 -.04572 (73*2π)/195427 weeks
74-.00189 -.03804 (74*2π)/195426 weeks
75-.00111 -.05997 (75*2π)/195426 weeks
76-.00173 -.05022 (76*2π)/195426 weeks
77-.00222 -.04504 (77*2π)/195425 weeks
78-.00468 -.04551 (78*2π)/195425 weeks
79-.00838 -.0445 (79*2π)/195425 weeks
80-.00759 -.05593 (80*2π)/195424 weeks
81-.00719 -.04878 (81*2π)/195424 weeks
82-.0118 -.04793 (82*2π)/195424 weeks
83-.01423 -.04427 (83*2π)/195424 weeks
84-.00971 -.04652 (84*2π)/195423 weeks
85-.00931 -.03842 (85*2π)/195423 weeks
86.00528 -.03684 (86*2π)/195423 weeks
87.0044 -.04289 (87*2π)/195422 weeks
88-.00438 -.045 (88*2π)/195422 weeks
89-.00826 -.0431 (89*2π)/195422 weeks
90-.00939 -.04681 (90*2π)/195422 weeks
91-.00746 -.04048 (91*2π)/195421 weeks
92-.00271 -.03654 (92*2π)/195421 weeks
93-.00901 -.0407 (93*2π)/195421 weeks
94-.00886 -.03185 (94*2π)/195421 weeks
95-.00093 -.03945 (95*2π)/195421 weeks
96-.00885 -.04409 (96*2π)/195420 weeks
97-.00349 -.0395 (97*2π)/195420 weeks
98-.00974 -.04332 (98*2π)/195420 weeks
99-.01082 -.03903 (99*2π)/195420 weeks
100-.00217 -.03868 (100*2π)/195420 weeks
101-.00269 -.04023 (101*2π)/195419 weeks
102-.01139 -.04238 (102*2π)/195419 weeks
103-.01013 -.03284 (103*2π)/195419 weeks
104-.00611 -.03689 (104*2π)/195419 weeks
105-.00187 -.03289 (105*2π)/195419 weeks
106-.00228 -.03821 (106*2π)/195418 weeks
107-.01124 -.04079 (107*2π)/195418 weeks
108-.00658 -.0265 (108*2π)/195418 weeks
109-.00521 -.03567 (109*2π)/195418 weeks
110-.00187 -.03815 (110*2π)/195418 weeks
111-.00726 -.03886 (111*2π)/195418 weeks
112-.01496 -.0359 (112*2π)/195417 weeks
113-.01174 -.02136 (113*2π)/195417 weeks
114-.00201 -.02927 (114*2π)/195417 weeks
115-.0035 -.03448 (115*2π)/195417 weeks
116-.00759 -.02829 (116*2π)/195417 weeks
117-.00502 -.02848 (117*2π)/195417 weeks
118-.00906 -.02705 (118*2π)/195417 weeks
119-.00602 -.03061 (119*2π)/195416 weeks
120-.00625 -.03562 (120*2π)/195416 weeks
121-.00647 -.02777 (121*2π)/195416 weeks
122-.00669 -.03164 (122*2π)/195416 weeks
123-.00483 -.02662 (123*2π)/195416 weeks
124-.00756 -.03644 (124*2π)/195416 weeks
125-.00913 -.03125 (125*2π)/195416 weeks
126-.00677 -.02477 (126*2π)/195416 weeks
127-.00865 -.02616 (127*2π)/195415 weeks
128-.00796 -.02806 (128*2π)/195415 weeks
129-.00427 -.02151 (129*2π)/195415 weeks
130-.00336 -.02643 (130*2π)/195415 weeks
131-.0055 -.03091 (131*2π)/195415 weeks
132-.00965 -.02581 (132*2π)/195415 weeks
133-.00789 -.02481 (133*2π)/195415 weeks
134-.00364 -.02325 (134*2π)/195415 weeks
135-.00564 -.02796 (135*2π)/195414 weeks
136-.0057 -.02933 (136*2π)/195414 weeks
137-.01162 -.02701 (137*2π)/195414 weeks
138-.00332 -.02132 (138*2π)/195414 weeks
139-.00483 -.03038 (139*2π)/195414 weeks
140-.00882 -.02709 (140*2π)/195414 weeks
141-.00769 -.02126 (141*2π)/195414 weeks
142-.00619 -.02337 (142*2π)/195414 weeks
143-.00421 -.02034 (143*2π)/195414 weeks
144-.00578 -.02722 (144*2π)/195414 weeks
145-.00925 -.0243 (145*2π)/195413 weeks
146-.00538 -.02229 (146*2π)/195413 weeks
147-.00325 -.02368 (147*2π)/195413 weeks
148-.00476 -.02567 (148*2π)/195413 weeks
149-.00752 -.0222 (149*2π)/195413 weeks
150-.01122 -.021 (150*2π)/195413 weeks
151-.0093 -.01541 (151*2π)/195413 weeks
152-.00109 -.01737 (152*2π)/195413 weeks
153-.00204 -.02318 (153*2π)/195413 weeks
154-.00525 -.02006 (154*2π)/195413 weeks
155-.00248 -.02601 (155*2π)/195413 weeks
156-.00326 -.02445 (156*2π)/195413 weeks
157-.00581 -.02632 (157*2π)/195412 weeks
158-.0059 -.02329 (158*2π)/195412 weeks
159-.00772 -.01978 (159*2π)/195412 weeks
160-.00421 -.02033 (160*2π)/195412 weeks
161-.00373 -.02339 (161*2π)/195412 weeks
162-.00433 -.0221 (162*2π)/195412 weeks
163-.007 -.02009 (163*2π)/195412 weeks
164-.01053 -.02302 (164*2π)/195412 weeks
165-.00405 -.01748 (165*2π)/195412 weeks
166-.00284 -.02342 (166*2π)/195412 weeks
167-.00822 -.02345 (167*2π)/195412 weeks
168-.00795 -.02128 (168*2π)/195412 weeks
169-.00744 -.01893 (169*2π)/195412 weeks
170-.00089 -.02053 (170*2π)/195411 weeks
171-.00349 -.0259 (171*2π)/195411 weeks
172-.00786 -.02043 (172*2π)/195411 weeks
173-.0064 -.01713 (173*2π)/195411 weeks
174-.00221 -.02085 (174*2π)/195411 weeks
175-.00041 -.02215 (175*2π)/195411 weeks
176-.00568 -.02828 (176*2π)/195411 weeks
177-.01213 -.01798 (177*2π)/195411 weeks
178-.00781 -.01627 (178*2π)/195411 weeks
179-.00374 -.01881 (179*2π)/195411 weeks
180-.0038 -.0199 (180*2π)/195411 weeks
181-.00701 -.0212 (181*2π)/195411 weeks
182-.00892 -.01611 (182*2π)/195411 weeks
183-.00361 -.01647 (183*2π)/195411 weeks
184-.00288 -.02008 (184*2π)/195411 weeks
185-.00175 -.02054 (185*2π)/195411 weeks
186-.007 -.02033 (186*2π)/195411 weeks
187-.00754 -.01874 (187*2π)/195410 weeks
188-.00455 -.01684 (188*2π)/195410 weeks
189-.00624 -.02031 (189*2π)/195410 weeks
190-.00375 -.01836 (190*2π)/195410 weeks
191-.00549 -.0159 (191*2π)/195410 weeks
192-.00294 -.0177 (192*2π)/195410 weeks
193-.00606 -.02255 (193*2π)/195410 weeks
194-.00682 -.02048 (194*2π)/195410 weeks
195-.00872 -.01864 (195*2π)/195410 weeks
196-.00489 -.01497 (196*2π)/195410 weeks
197-.00255 -.02034 (197*2π)/195410 weeks
198-.00644 -.02128 (198*2π)/195410 weeks
199-.00465 -.01815 (199*2π)/195410 weeks
200-.00512 -.01602 (200*2π)/195410 weeks
201-.00244 -.01876 (201*2π)/195410 weeks
202-.00638 -.02072 (202*2π)/195410 weeks
203-.00849 -.0142 (203*2π)/195410 weeks
204-.00474 -.01809 (204*2π)/195410 weeks
205-.00106 -.01846 (205*2π)/195410 weeks
206-.00648 -.02156 (206*2π)/19549 weeks
207-.00642 -.01863 (207*2π)/19549 weeks
208-.00682 -.0176 (208*2π)/19549 weeks
209-.00531 -.01614 (209*2π)/19549 weeks
210-.00272 -.01845 (210*2π)/19549 weeks
211-.00496 -.02075 (211*2π)/19549 weeks
212-.00872 -.01717 (212*2π)/19549 weeks
213-.00842 -.01418 (213*2π)/19549 weeks
214-.00572 -.01476 (214*2π)/19549 weeks
215-.00475 -.01748 (215*2π)/19549 weeks
216-.00538 -.02 (216*2π)/19549 weeks
217-.00893 -.0201 (217*2π)/19549 weeks
218-.01017 -.01506 (218*2π)/19549 weeks
219-.00662 -.01527 (219*2π)/19549 weeks
220-.00822 -.01667 (220*2π)/19549 weeks
221-.00877 -.01659 (221*2π)/19549 weeks
222-.00853 -.01323 (222*2π)/19549 weeks
223-.00387 -.00879 (223*2π)/19549 weeks
224-.00213 -.01645 (224*2π)/19549 weeks
225-.00551 -.019 (225*2π)/19549 weeks
226-.01021 -.01632 (226*2π)/19549 weeks
227-.00491 -.01466 (227*2π)/19549 weeks
228-.00544 -.01455 (228*2π)/19549 weeks
229-.00451 -.01899 (229*2π)/19549 weeks
230-.01007 -.01614 (230*2π)/19548 weeks
231-.0094 -.01334 (231*2π)/19548 weeks
232-.00267 -.01275 (232*2π)/19548 weeks
233-.00358 -.01504 (233*2π)/19548 weeks
234-.00712 -.01661 (234*2π)/19548 weeks
235-.00579 -.01462 (235*2π)/19548 weeks
236-.00744 -.01461 (236*2π)/19548 weeks
237-.00663 -.01468 (237*2π)/19548 weeks
238-.00695 -.01539 (238*2π)/19548 weeks
239-.00913 -.01424 (239*2π)/19548 weeks
240-.00632 -.01283 (240*2π)/19548 weeks
241-.00575 -.01183 (241*2π)/19548 weeks
242-.00653 -.01556 (242*2π)/19548 weeks
243-.00613 -.01212 (243*2π)/19548 weeks
244-.00649 -.01354 (244*2π)/19548 weeks
245-.00387 -.01366 (245*2π)/19548 weeks
246-.00341 -.01596 (246*2π)/19548 weeks
247-.00775 -.01529 (247*2π)/19548 weeks
248-.00827 -.01327 (248*2π)/19548 weeks
249-.00661 -.01171 (249*2π)/19548 weeks
250-.00392 -.0132 (250*2π)/19548 weeks
251-.00626 -.01577 (251*2π)/19548 weeks
252-.007 -.0113 (252*2π)/19548 weeks
253-.00754 -.0128 (253*2π)/19548 weeks
254-.0048 -.01217 (254*2π)/19548 weeks
255-.00587 -.01127 (255*2π)/19548 weeks
256-.00583 -.01482 (256*2π)/19548 weeks
257-.0057 -.01063 (257*2π)/19548 weeks
258-.00471 -.01239 (258*2π)/19548 weeks
259-.00457 -.01551 (259*2π)/19548 weeks
260-.00623 -.01425 (260*2π)/19548 weeks
261-.00546 -.01576 (261*2π)/19547 weeks
262-.00797 -.01093 (262*2π)/19547 weeks
263-.00333 -.01326 (263*2π)/19547 weeks
264-.00533 -.0137 (264*2π)/19547 weeks
265-.00637 -.01165 (265*2π)/19547 weeks
266-.00516 -.01302 (266*2π)/19547 weeks
267-.00539 -.01242 (267*2π)/19547 weeks
268-.00548 -.0121 (268*2π)/19547 weeks
269-.00621 -.0126 (269*2π)/19547 weeks
270-.00788 -.01145 (270*2π)/19547 weeks
271-.00496 -.01234 (271*2π)/19547 weeks
272-.00543 -.01182 (272*2π)/19547 weeks
273-.00473 -.01169 (273*2π)/19547 weeks
274-.00432 -.01178 (274*2π)/19547 weeks
275-.00632 -.01213 (275*2π)/19547 weeks
276-.00575 -.01097 (276*2π)/19547 weeks
277-.00551 -.0123 (277*2π)/19547 weeks
278-.0033 -.01179 (278*2π)/19547 weeks
279-.00723 -.01412 (279*2π)/19547 weeks
280-.00721 -.01213 (280*2π)/19547 weeks
281-.00623 -.01271 (281*2π)/19547 weeks
282-.00686 -.01218 (282*2π)/19547 weeks
283-.00622 -.01068 (283*2π)/19547 weeks
284-.0061 -.01101 (284*2π)/19547 weeks
285-.00521 -.00958 (285*2π)/19547 weeks
286-.00353 -.01183 (286*2π)/19547 weeks
287-.00514 -.01331 (287*2π)/19547 weeks
288-.00613 -.01225 (288*2π)/19547 weeks
289-.00688 -.00955 (289*2π)/19547 weeks
290-.00573 -.00963 (290*2π)/19547 weeks
291-.00409 -.01161 (291*2π)/19547 weeks
292-.00489 -.01121 (292*2π)/19547 weeks
293-.00539 -.01347 (293*2π)/19547 weeks
294-.00472 -.01096 (294*2π)/19547 weeks
295-.006 -.0128 (295*2π)/19547 weeks
296-.00559 -.01312 (296*2π)/19547 weeks
297-.00536 -.012 (297*2π)/19547 weeks
298-.00602 -.01186 (298*2π)/19547 weeks
299-.00622 -.01115 (299*2π)/19547 weeks
300-.00531 -.0091 (300*2π)/19547 weeks
301-.00492 -.01154 (301*2π)/19546 weeks
302-.00474 -.0107 (302*2π)/19546 weeks
303-.0063 -.01041 (303*2π)/19546 weeks
304-.0043 -.01063 (304*2π)/19546 weeks
305-.00414 -.01077 (305*2π)/19546 weeks
306-.00503 -.0134 (306*2π)/19546 weeks
307-.00552 -.01095 (307*2π)/19546 weeks
308-.00882 -.01156 (308*2π)/19546 weeks
309-.00511 -.01093 (309*2π)/19546 weeks
310-.00471 -.01195 (310*2π)/19546 weeks
311-.00417 -.01298 (311*2π)/19546 weeks
312-.00603 -.00942 (312*2π)/19546 weeks
313-.00661 -.01171 (313*2π)/19546 weeks
314-.00557 -.01114 (314*2π)/19546 weeks
315-.00838 -.01188 (315*2π)/19546 weeks
316-.00791 -.01027 (316*2π)/19546 weeks
317-.00701 -.0083 (317*2π)/19546 weeks
318-.0043 -.0112 (318*2π)/19546 weeks
319-.00555 -.01154 (319*2π)/19546 weeks
320-.00596 -.01143 (320*2π)/19546 weeks
321-.00648 -.0119 (321*2π)/19546 weeks
322-.00588 -.01057 (322*2π)/19546 weeks
323-.00716 -.00992 (323*2π)/19546 weeks
324-.00597 -.01106 (324*2π)/19546 weeks
325-.00549 -.00987 (325*2π)/19546 weeks
326-.00589 -.01119 (326*2π)/19546 weeks
327-.00698 -.00914 (327*2π)/19546 weeks
328-.0065 -.00838 (328*2π)/19546 weeks
329-.00498 -.00898 (329*2π)/19546 weeks
330-.00358 -.01001 (330*2π)/19546 weeks
331-.00782 -.01165 (331*2π)/19546 weeks
332-.00607 -.00922 (332*2π)/19546 weeks
333-.00528 -.01011 (333*2π)/19546 weeks
334-.00618 -.01074 (334*2π)/19546 weeks
335-.00604 -.00932 (335*2π)/19546 weeks
336-.00648 -.00975 (336*2π)/19546 weeks
337-.00641 -.00784 (337*2π)/19546 weeks
338-.00501 -.00774 (338*2π)/19546 weeks
339-.00403 -.00909 (339*2π)/19546 weeks
340-.00509 -.0092 (340*2π)/19546 weeks
341-.0046 -.01027 (341*2π)/19546 weeks
342-.0065 -.01044 (342*2π)/19546 weeks
343-.00588 -.00875 (343*2π)/19546 weeks
344-.00483 -.00943 (344*2π)/19546 weeks
345-.0061 -.01002 (345*2π)/19546 weeks
346-.00679 -.00952 (346*2π)/19546 weeks
347-.00605 -.01039 (347*2π)/19546 weeks
348-.00655 -.00806 (348*2π)/19546 weeks
349-.0058 -.00848 (349*2π)/19546 weeks
350-.00598 -.00967 (350*2π)/19546 weeks
351-.00615 -.00847 (351*2π)/19546 weeks
352-.00438 -.00903 (352*2π)/19546 weeks
353-.00485 -.00979 (353*2π)/19546 weeks
354-.00577 -.01031 (354*2π)/19546 weeks
355-.00703 -.00933 (355*2π)/19546 weeks
356-.00493 -.00929 (356*2π)/19545 weeks
357-.00548 -.01027 (357*2π)/19545 weeks
358-.00787 -.00844 (358*2π)/19545 weeks
359-.00644 -.00688 (359*2π)/19545 weeks
360-.00462 -.0093 (360*2π)/19545 weeks
361-.00478 -.00905