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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 (.4036*sine), 177 weeks (.3626*sine), and 150 weeks (.077*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 2/13/2017 for AFTEX (American Fds, The Tax-Exempt Bo), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
06.01508   0 
1.53837 -3.74916 (1*2π)/19491,949 weeks
2.25454 -1.87066 (2*2π)/1949975 weeks
3.15979 -1.36784 (3*2π)/1949650 weeks
4-.00013 -1.08836 (4*2π)/1949487 weeks
5-.02945 -.76679 (5*2π)/1949390 weeks
6.05645 -.58874 (6*2π)/1949325 weeks
7.01017 -.50503 (7*2π)/1949278 weeks
8.07128 -.53315 (8*2π)/1949244 weeks
9-.02205 -.4463 (9*2π)/1949217 weeks
10.02737 -.40358 (10*2π)/1949195 weeks
11.02409 -.36256 (11*2π)/1949177 weeks
12.00249 -.30597 (12*2π)/1949162 weeks
13-.07704 -.30822 (13*2π)/1949150 weeks
14-.04367 -.20375 (14*2π)/1949139 weeks
15-.01757 -.20843 (15*2π)/1949130 weeks
16.06821 -.21299 (16*2π)/1949122 weeks
17.01846 -.25002 (17*2π)/1949115 weeks
18-.01828 -.25603 (18*2π)/1949108 weeks
19-.00989 -.22253 (19*2π)/1949103 weeks
20-.03853 -.20183 (20*2π)/194997 weeks
21.01099 -.19599 (21*2π)/194993 weeks
22-.0247 -.18296 (22*2π)/194989 weeks
23-.03518 -.17554 (23*2π)/194985 weeks
24-.03796 -.13705 (24*2π)/194981 weeks
25-.01772 -.13131 (25*2π)/194978 weeks
26.00122 -.1389 (26*2π)/194975 weeks
27-.01655 -.12493 (27*2π)/194972 weeks
28-.01697 -.11806 (28*2π)/194970 weeks
29.00633 -.12251 (29*2π)/194967 weeks
30-.00543 -.14314 (30*2π)/194965 weeks
31-.02158 -.13184 (31*2π)/194963 weeks
32-.03732 -.1171 (32*2π)/194961 weeks
33-.0239 -.08872 (33*2π)/194959 weeks
34-.00285 -.09939 (34*2π)/194957 weeks
35.00163 -.10344 (35*2π)/194956 weeks
36-.00983 -.09681 (36*2π)/194954 weeks
37-.01014 -.09348 (37*2π)/194953 weeks
38-.01665 -.0868 (38*2π)/194951 weeks
39-.00145 -.0929 (39*2π)/194950 weeks
40.00351 -.09907 (40*2π)/194949 weeks
41.00059 -.10184 (41*2π)/194948 weeks
42-.0197 -.09015 (42*2π)/194946 weeks
43-.01348 -.08314 (43*2π)/194945 weeks
44-.01848 -.08161 (44*2π)/194944 weeks
45-.01623 -.07305 (45*2π)/194943 weeks
46.00713 -.06465 (46*2π)/194942 weeks
47-.0063 -.07353 (47*2π)/194941 weeks
48.00153 -.06929 (48*2π)/194941 weeks
49-.01087 -.08259 (49*2π)/194940 weeks
50-.02146 -.06987 (50*2π)/194939 weeks
51-.00181 -.04461 (51*2π)/194938 weeks
52.00673 -.07892 (52*2π)/194937 weeks
53.00326 -.06367 (53*2π)/194937 weeks
54-.00975 -.06329 (54*2π)/194936 weeks
55-.01357 -.06731 (55*2π)/194935 weeks
56-.01313 -.04421 (56*2π)/194935 weeks
57.00317 -.06168 (57*2π)/194934 weeks
58.00471 -.06507 (58*2π)/194934 weeks
59-.0055 -.05494 (59*2π)/194933 weeks
60.00133 -.05722 (60*2π)/194932 weeks
61.00009 -.06635 (61*2π)/194932 weeks
62-.01127 -.06418 (62*2π)/194931 weeks
63-.00899 -.05468 (63*2π)/194931 weeks
64-.01355 -.04506 (64*2π)/194930 weeks
65.00663 -.04783 (65*2π)/194930 weeks
66-.00208 -.05631 (66*2π)/194930 weeks
67-.00802 -.0505 (67*2π)/194929 weeks
68-.00743 -.04539 (68*2π)/194929 weeks
69-.00399 -.05083 (69*2π)/194928 weeks
70.00569 -.05201 (70*2π)/194928 weeks
71-.00132 -.05723 (71*2π)/194927 weeks
72-.00974 -.05619 (72*2π)/194927 weeks
73-.00864 -.04862 (73*2π)/194927 weeks
74-.01156 -.036 (74*2π)/194926 weeks
75.00242 -.05245 (75*2π)/194926 weeks
76-.00027 -.0471 (76*2π)/194926 weeks
77-.00267 -.04198 (77*2π)/194925 weeks
78-.00399 -.04199 (78*2π)/194925 weeks
79-.00867 -.04164 (79*2π)/194925 weeks
80-.00082 -.05126 (80*2π)/194924 weeks
81-.00244 -.04694 (81*2π)/194924 weeks
82-.00588 -.04954 (82*2π)/194924 weeks
83-.0115 -.04962 (83*2π)/194923 weeks
84-.00743 -.05064 (84*2π)/194923 weeks
85-.01384 -.04598 (85*2π)/194923 weeks
86-.00486 -.03294 (86*2π)/194923 weeks
87.00138 -.03333 (87*2π)/194922 weeks
88-.00107 -.03923 (88*2π)/194922 weeks
89-.00501 -.04076 (89*2π)/194922 weeks
90-.00323 -.04634 (90*2π)/194922 weeks
91-.00559 -.04265 (91*2π)/194921 weeks
92-.0045 -.03484 (92*2π)/194921 weeks
93-.00546 -.04158 (93*2π)/194921 weeks
94-.0138 -.03535 (94*2π)/194921 weeks
95-.00408 -.03242 (95*2π)/194921 weeks
96-.00477 -.0414 (96*2π)/194920 weeks
97-.00314 -.03465 (97*2π)/194920 weeks
98-.00359 -.04159 (98*2π)/194920 weeks
99-.00832 -.04205 (99*2π)/194920 weeks
100-.00311 -.03548 (100*2π)/194919 weeks
101.00017 -.03424 (101*2π)/194919 weeks
102-.00183 -.04335 (102*2π)/194919 weeks
103-.00933 -.03829 (103*2π)/194919 weeks
104-.00534 -.03845 (104*2π)/194919 weeks
105-.00537 -.03119 (105*2π)/194919 weeks
106-.00005 -.03169 (106*2π)/194918 weeks
107-.00092 -.04256 (107*2π)/194918 weeks
108-.01052 -.03097 (108*2π)/194918 weeks
109-.00533 -.03348 (109*2π)/194918 weeks
110.00106 -.03134 (110*2π)/194918 weeks
111.00255 -.03515 (111*2π)/194918 weeks
112-.0018 -.04343 (112*2π)/194917 weeks
113-.01532 -.0349 (113*2π)/194917 weeks
114-.00729 -.02935 (114*2π)/194917 weeks
115-.00099 -.0319 (115*2π)/194917 weeks
116-.00681 -.03179 (116*2π)/194917 weeks
117-.00559 -.02892 (117*2π)/194917 weeks
118-.01046 -.03039 (118*2π)/194917 weeks
119-.00781 -.02947 (119*2π)/194916 weeks
120-.00163 -.0333 (120*2π)/194916 weeks
121-.00701 -.02946 (121*2π)/194916 weeks
122-.00417 -.03171 (122*2π)/194916 weeks
123-.008 -.02582 (123*2π)/194916 weeks
124-.00014 -.03269 (124*2π)/194916 weeks
125-.00181 -.03435 (125*2π)/194916 weeks
126-.006 -.02926 (126*2π)/194915 weeks
127-.00736 -.03069 (127*2π)/194915 weeks
128-.00528 -.03295 (128*2π)/194915 weeks
129-.01011 -.0262 (129*2π)/194915 weeks
130-.00719 -.02462 (130*2π)/194915 weeks
131-.00177 -.0275 (131*2π)/194915 weeks
132-.00653 -.02997 (132*2π)/194915 weeks
133-.00795 -.02986 (133*2π)/194915 weeks
134-.00892 -.02414 (134*2π)/194915 weeks
135-.00615 -.02597 (135*2π)/194914 weeks
136-.00257 -.02601 (136*2π)/194914 weeks
137-.00582 -.03305 (137*2π)/194914 weeks
138-.0097 -.02353 (138*2π)/194914 weeks
139-.00161 -.02594 (139*2π)/194914 weeks
140-.0024 -.02958 (140*2π)/194914 weeks
141-.00763 -.02758 (141*2π)/194914 weeks
142-.00633 -.02742 (142*2π)/194914 weeks
143-.00982 -.02272 (143*2π)/194914 weeks
144-.00396 -.02495 (144*2π)/194914 weeks
145-.00625 -.02884 (145*2π)/194913 weeks
146-.00756 -.02613 (146*2π)/194913 weeks
147-.00586 -.02318 (147*2π)/194913 weeks
148-.0022 -.0236 (148*2π)/194913 weeks
149-.00391 -.02415 (149*2π)/194913 weeks
150-.00553 -.0292 (150*2π)/194913 weeks
151-.0129 -.02958 (151*2π)/194913 weeks
152-.01298 -.0219 (152*2π)/194913 weeks
153-.00778 -.02132 (153*2π)/194913 weeks
154-.01251 -.02248 (154*2π)/194913 weeks
155-.00668 -.02145 (155*2π)/194913 weeks
156-.00647 -.02006 (156*2π)/194912 weeks
157-.00343 -.02265 (157*2π)/194912 weeks
158-.00357 -.02251 (158*2π)/194912 weeks
159-.00783 -.02445 (159*2π)/194912 weeks
160-.00871 -.02173 (160*2π)/194912 weeks
161-.0055 -.02085 (161*2π)/194912 weeks
162-.00491 -.01951 (162*2π)/194912 weeks
163-.00767 -.01981 (163*2π)/194912 weeks
164-.0056 -.02677 (164*2π)/194912 weeks
165-.01099 -.02132 (165*2π)/194912 weeks
166-.00627 -.01805 (166*2π)/194912 weeks
167-.0051 -.02224 (167*2π)/194912 weeks
168-.0058 -.02361 (168*2π)/194912 weeks
169-.00944 -.02555 (169*2π)/194912 weeks
170-.00931 -.01879 (170*2π)/194911 weeks
171-.00211 -.01875 (171*2π)/194911 weeks
172-.00457 -.02249 (172*2π)/194911 weeks
173-.00989 -.02312 (173*2π)/194911 weeks
174-.00844 -.0201 (174*2π)/194911 weeks
175-.00784 -.0144 (175*2π)/194911 weeks
176.00252 -.01625 (176*2π)/194911 weeks
177-.00386 -.02343 (177*2π)/194911 weeks
178-.00796 -.02347 (178*2π)/194911 weeks
179-.00726 -.02011 (179*2π)/194911 weeks
180-.00632 -.01768 (180*2π)/194911 weeks
181-.00296 -.01964 (181*2π)/194911 weeks
182-.00746 -.02387 (182*2π)/194911 weeks
183-.00987 -.02068 (183*2π)/194911 weeks
184-.00774 -.01929 (184*2π)/194911 weeks
185-.00612 -.01502 (185*2π)/194911 weeks
186-.00511 -.0181 (186*2π)/194910 weeks
187-.0055 -.02069 (187*2π)/194910 weeks
188-.00854 -.01819 (188*2π)/194910 weeks
189-.00554 -.02026 (189*2π)/194910 weeks
190-.0054 -.01777 (190*2π)/194910 weeks
191-.00892 -.01919 (191*2π)/194910 weeks
192-.01061 -.01553 (192*2π)/194910 weeks
193-.00571 -.01667 (193*2π)/194910 weeks
194-.00465 -.01705 (194*2π)/194910 weeks
195-.00432 -.02105 (195*2π)/194910 weeks
196-.01008 -.02001 (196*2π)/194910 weeks
197-.0075 -.01581 (197*2π)/194910 weeks
198-.00405 -.01848 (198*2π)/194910 weeks
199-.00466 -.01746 (199*2π)/194910 weeks
200-.00802 -.01856 (200*2π)/194910 weeks
201-.00753 -.0142 (201*2π)/194910 weeks
202-.00263 -.01511 (202*2π)/194910 weeks
203-.00854 -.01977 (203*2π)/194910 weeks
204-.00764 -.01935 (204*2π)/194910 weeks
205-.00896 -.0132 (205*2π)/194910 weeks
206-.00452 -.01519 (206*2π)/19499 weeks
207-.0047 -.01566 (207*2π)/19499 weeks
208-.00472 -.01717 (208*2π)/19499 weeks
209-.0073 -.0177 (209*2π)/19499 weeks
210-.00746 -.01383 (210*2π)/19499 weeks
211-.00335 -.01168 (211*2π)/19499 weeks
212-.00287 -.01454 (212*2π)/19499 weeks
213-.00561 -.01727 (213*2π)/19499 weeks
214-.00821 -.01664 (214*2π)/19499 weeks
215-.00851 -.01473 (215*2π)/19499 weeks
216-.00627 -.01196 (216*2π)/19499 weeks
217-.00189 -.01289 (217*2π)/19499 weeks
218-.00388 -.01692 (218*2π)/19499 weeks
219-.00556 -.01483 (219*2π)/19499 weeks
220-.00435 -.01523 (220*2π)/19499 weeks
221-.00168 -.01612 (221*2π)/19499 weeks
222-.00127 -.01931 (222*2π)/19499 weeks
223-.01026 -.01913 (223*2π)/19499 weeks
224-.00962 -.01415 (224*2π)/19499 weeks
225-.00584 -.01172 (225*2π)/19499 weeks
226-.0039 -.01767 (226*2π)/19499 weeks
227-.00575 -.01556 (227*2π)/19499 weeks
228-.00852 -.01597 (228*2π)/19499 weeks
229-.00506 -.01074 (229*2π)/19499 weeks
230-.00281 -.01436 (230*2π)/19498 weeks
231-.00296 -.01952 (231*2π)/19498 weeks
232-.00678 -.01597 (232*2π)/19498 weeks
233-.0077 -.01301 (233*2π)/19498 weeks
234-.00471 -.01425 (234*2π)/19498 weeks
235-.00575 -.01306 (235*2π)/19498 weeks
236-.00552 -.01431 (236*2π)/19498 weeks
237-.00592 -.0139 (237*2π)/19498 weeks
238-.0049 -.01255 (238*2π)/19498 weeks
239-.00323 -.01548 (239*2π)/19498 weeks
240-.00399 -.0151 (240*2π)/19498 weeks
241-.00735 -.01528 (241*2π)/19498 weeks
242-.0037 -.01438 (242*2π)/19498 weeks
243-.00604 -.01511 (243*2π)/19498 weeks
244-.00539 -.01679 (244*2π)/19498 weeks
245-.00725 -.01576 (245*2π)/19498 weeks
246-.00692 -.01128 (246*2π)/19498 weeks
247-.0046 -.01207 (247*2π)/19498 weeks
248-.00358 -.01413 (248*2π)/19498 weeks
249-.00514 -.01618 (249*2π)/19498 weeks
250-.00745 -.01368 (250*2π)/19498 weeks
251-.00341 -.01181 (251*2π)/19498 weeks
252-.00566 -.01338 (252*2π)/19498 weeks
253-.00405 -.01525 (253*2π)/19498 weeks
254-.00495 -.01359 (254*2π)/19498 weeks
255-.00743 -.01509 (255*2π)/19498 weeks
256-.0037 -.01327 (256*2π)/19498 weeks
257-.00626 -.01529 (257*2π)/19498 weeks
258-.00826 -.01563 (258*2π)/19498 weeks
259-.00686 -.01305 (259*2π)/19498 weeks
260-.00683 -.01415 (260*2π)/19497 weeks
261-.0039 -.01058 (261*2π)/19497 weeks
262-.0047 -.01609 (262*2π)/19497 weeks
263-.00614 -.01306 (263*2π)/19497 weeks
264-.00487 -.01175 (264*2π)/19497 weeks
265-.00564 -.01377 (265*2π)/19497 weeks
266-.00528 -.01278 (266*2π)/19497 weeks
267-.00536 -.0125 (267*2π)/19497 weeks
268-.00614 -.01218 (268*2π)/19497 weeks
269-.00573 -.01111 (269*2π)/19497 weeks
270-.00486 -.01429 (270*2π)/19497 weeks
271-.00503 -.01298 (271*2π)/19497 weeks
272-.00487 -.01336 (272*2π)/19497 weeks
273-.00524 -.01322 (273*2π)/19497 weeks
274-.00659 -.01181 (274*2π)/19497 weeks
275-.00527 -.01216 (275*2π)/19497 weeks
276-.00635 -.01327 (276*2π)/19497 weeks
277-.0052 -.01385 (277*2π)/19497 weeks
278-.00909 -.01166 (278*2π)/19497 weeks
279-.00634 -.01105 (279*2π)/19497 weeks
280-.00612 -.01239 (280*2π)/19497 weeks
281-.00585 -.01146 (281*2π)/19497 weeks
282-.00444 -.01139 (282*2π)/19497 weeks
283-.00497 -.01201 (283*2π)/19497 weeks
284-.00391 -.01213 (284*2π)/19497 weeks
285-.00536 -.01444 (285*2π)/19497 weeks
286-.00724 -.01306 (286*2π)/19497 weeks
287-.00629 -.01129 (287*2π)/19497 weeks
288-.00481 -.00979 (288*2π)/19497 weeks
289-.00471 -.01178 (289*2π)/19497 weeks
290-.0055 -.01399 (290*2π)/19497 weeks
291-.00605 -.01259 (291*2π)/19497 weeks
292-.00756 -.01347 (292*2π)/19497 weeks
293-.00528 -.0119 (293*2π)/19497 weeks
294-.0076 -.01243 (294*2π)/19497 weeks
295-.00685 -.01261 (295*2π)/19497 weeks
296-.00582 -.01165 (296*2π)/19497 weeks
297-.0062 -.01114 (297*2π)/19497 weeks
298-.00562 -.01068 (298*2π)/19497 weeks
299-.00405 -.01035 (299*2π)/19497 weeks
300-.00583 -.01248 (300*2π)/19496 weeks
301-.00522 -.01151 (301*2π)/19496 weeks
302-.00621 -.0106 (302*2π)/19496 weeks
303-.00495 -.01227 (303*2π)/19496 weeks
304-.00558 -.0122 (304*2π)/19496 weeks
305-.0078 -.01302 (305*2π)/19496 weeks
306-.00644 -.01041 (306*2π)/19496 weeks
307-.00883 -.00961 (307*2π)/19496 weeks
308-.00511 -.01184 (308*2π)/19496 weeks
309-.00595 -.01248 (309*2π)/19496 weeks
310-.00623 -.0127 (310*2π)/19496 weeks
311-.00588 -.00875 (311*2π)/19496 weeks
312-.00767 -.01083 (312*2π)/19496 weeks
313-.00643 -.01069 (313*2π)/19496 weeks
314-.00881 -.00963 (314*2π)/19496 weeks
315-.00676 -.00895 (315*2π)/19496 weeks
316-.00508 -.0087 (316*2π)/19496 weeks
317-.00505 -.01267 (317*2π)/19496 weeks
318-.00653 -.01154 (318*2π)/19496 weeks
319-.00669 -.01102 (319*2π)/19496 weeks
320-.0071 -.01095 (320*2π)/19496 weeks
321-.00582 -.01002 (321*2π)/19496 weeks
322-.0066 -.00913 (322*2π)/19496 weeks
323-.00601 -.01081 (323*2π)/19496 weeks
324-.00519 -.00988 (324*2π)/19496 weeks
325-.00631 -.01061 (325*2π)/19496 weeks
326-.00603 -.0083 (326*2π)/19496 weeks
327-.00521 -.00848 (327*2π)/19496 weeks
328-.00446 -.01003 (328*2π)/19496 weeks
329-.0044 -.0113 (329*2π)/19496 weeks
330-.00866 -.01038 (330*2π)/19496 weeks
331-.00544 -.00914 (331*2π)/19496 weeks
332-.00544 -.01038 (332*2π)/19496 weeks
333-.00649 -.01027 (333*2π)/19496 weeks
334-.00565 -.00901 (334*2π)/19496 weeks
335-.00616 -.00925 (335*2π)/19496 weeks
336-.00516 -.00778 (336*2π)/19496 weeks
337-.00407 -.0087 (337*2π)/19496 weeks
338-.00415 -.01032 (338*2π)/19496 weeks
339-.00537 -.00986 (339*2π)/19496 weeks
340-.00543 -.01087 (340*2π)/19496 weeks
341-.00709 -.01002 (341*2π)/19496 weeks
342-.00566 -.00881 (342*2π)/19496 weeks
343-.00516 -.00993 (343*2π)/19496 weeks
344-.00665 -.00988 (344*2π)/19496 weeks
345-.00691 -.00918 (345*2π)/19496 weeks
346-.00637 -.01014 (346*2π)/19496 weeks
347-.00602 -.00781 (347*2π)/19496 weeks
348-.00553 -.00875 (348*2π)/19496 weeks
349-.00611 -.00977 (349*2π)/19496 weeks
350-.00579 -.00859 (350*2π)/19496 weeks
351-.00444 -.00977 (351*2π)/19496 weeks
352-.00537 -.01022 (352*2π)/19496 weeks
353-.0064 -.01025 (353*2π)/19496 weeks
354-.00709 -.00892 (354*2π)/19496 weeks
355-.00505 -.00954 (355*2π)/19495 weeks
356-.00603 -.01013 (356*2π)/19495 weeks
357-.00765 -.00769 (357*2π)/19495 weeks
358-.00567 -.00692 (358*2π)/19495 weeks
359-.00465 -.00984 (359*2π)/19495 weeks
360-.00493 -.00938 (360*2π)/19495 weeks
361-.00609 -.00968 (361*2π)/19495 weeks
362-.00538 -.00788 (362*2π)/19495 weeks
363-.00506 -.00706 (363*2π)/19495 weeks
364-.00459 -.01087 (364*2π)/19495 weeks
365-.00653 -.00932