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# Fourier Analysis of FAGIX (Fidelity Capital and Income Fun)

FAGIX (Fidelity Capital and Income Fun) appears to have interesting cyclic behaviour every 149 weeks (.2677*sine), 161 weeks (.2671*sine), and 193 weeks (.2059*sine).

FAGIX (Fidelity Capital and Income Fun) has an average price of 3.06 (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.

## Fourier Analysis

Using data from 1/2/1980 to 1/9/2017 for FAGIX (Fidelity Capital and Income Fun), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
03.05557   0
11.18573 -2.51089 (1*2π)/19321,932 weeks
2.45696 -1.58425 (2*2π)/1932966 weeks
3.0606 -1.05009 (3*2π)/1932644 weeks
4.04876 -.92154 (4*2π)/1932483 weeks
5-.14585 -.63162 (5*2π)/1932386 weeks
6.0573 -.32047 (6*2π)/1932322 weeks
7.04772 -.50159 (7*2π)/1932276 weeks
8-.01934 -.4207 (8*2π)/1932242 weeks
9-.07101 -.34753 (9*2π)/1932215 weeks
10-.11322 -.20587 (10*2π)/1932193 weeks
11.08653 -.13723 (11*2π)/1932176 weeks
12.1011 -.26706 (12*2π)/1932161 weeks
13-.01176 -.26773 (13*2π)/1932149 weeks
14-.04895 -.2014 (14*2π)/1932138 weeks
15-.01966 -.13764 (15*2π)/1932129 weeks
16.05512 -.13679 (16*2π)/1932121 weeks
17.04744 -.18083 (17*2π)/1932114 weeks
18-.01119 -.19538 (18*2π)/1932107 weeks
19.01428 -.12129 (19*2π)/1932102 weeks
20.03005 -.15632 (20*2π)/193297 weeks
21.03503 -.15075 (21*2π)/193292 weeks
22.01279 -.17513 (22*2π)/193288 weeks
23-.0398 -.15018 (23*2π)/193284 weeks
24-.01536 -.0826 (24*2π)/193281 weeks
25.04552 -.08586 (25*2π)/193277 weeks
26.04693 -.15103 (26*2π)/193274 weeks
27.01173 -.15215 (27*2π)/193272 weeks
28-.03348 -.14809 (28*2π)/193269 weeks
29-.02372 -.07686 (29*2π)/193267 weeks
30.02493 -.09683 (30*2π)/193264 weeks
31.01958 -.12345 (31*2π)/193262 weeks
32-.01712 -.13641 (32*2π)/193260 weeks
33-.03247 -.10124 (33*2π)/193259 weeks
34-.01914 -.0913 (34*2π)/193257 weeks
35-.00885 -.09242 (35*2π)/193255 weeks
36-.02625 -.08989 (36*2π)/193254 weeks
37-.02366 -.05193 (37*2π)/193252 weeks
38.00548 -.07526 (38*2π)/193251 weeks
39.00347 -.06377 (39*2π)/193250 weeks
40.01112 -.092 (40*2π)/193248 weeks
41-.03151 -.09029 (41*2π)/193247 weeks
42-.01752 -.05587 (42*2π)/193246 weeks
43-.00358 -.05307 (43*2π)/193245 weeks
44.00196 -.06796 (44*2π)/193244 weeks
45.00012 -.06857 (45*2π)/193243 weeks
46-.00562 -.06803 (46*2π)/193242 weeks
47-.0082 -.05366 (47*2π)/193241 weeks
48.00956 -.06444 (48*2π)/193240 weeks
49-.00641 -.07134 (49*2π)/193239 weeks
50-.01454 -.06858 (50*2π)/193239 weeks
51-.01849 -.04337 (51*2π)/193238 weeks
52.00872 -.05498 (52*2π)/193237 weeks
53-.00225 -.06087 (53*2π)/193236 weeks
54-.00638 -.05813 (54*2π)/193236 weeks
55-.01113 -.05375 (55*2π)/193235 weeks
56-.01187 -.04594 (56*2π)/193235 weeks
57-.00448 -.04043 (57*2π)/193234 weeks
58-.00007 -.04692 (58*2π)/193233 weeks
59-.00136 -.0416 (59*2π)/193233 weeks
60.00745 -.04312 (60*2π)/193232 weeks
61.01109 -.05351 (61*2π)/193232 weeks
62-.00249 -.06261 (62*2π)/193231 weeks
63-.00797 -.05425 (63*2π)/193231 weeks
64-.01274 -.04185 (64*2π)/193230 weeks
65.00341 -.03981 (65*2π)/193230 weeks
66.00144 -.05667 (66*2π)/193229 weeks
67-.01113 -.04345 (67*2π)/193229 weeks
68.00183 -.04488 (68*2π)/193228 weeks
69-.00558 -.04541 (69*2π)/193228 weeks
70-.00075 -.04548 (70*2π)/193228 weeks
71-.00546 -.0456 (71*2π)/193227 weeks
72-.0076 -.048 (72*2π)/193227 weeks
73-.0095 -.04321 (73*2π)/193226 weeks
74-.00735 -.03758 (74*2π)/193226 weeks
75-.00899 -.04044 (75*2π)/193226 weeks
76-.00348 -.03648 (76*2π)/193225 weeks
77-.00426 -.0409 (77*2π)/193225 weeks
78-.00747 -.03829 (78*2π)/193225 weeks
79-.00843 -.03462 (79*2π)/193224 weeks
80-.00833 -.03365 (80*2π)/193224 weeks
81-.00508 -.03333 (81*2π)/193224 weeks
82-.0063 -.03377 (82*2π)/193224 weeks
83-.00773 -.02406 (83*2π)/193223 weeks
84.00383 -.03529 (84*2π)/193223 weeks
85-.0089 -.03624 (85*2π)/193223 weeks
86-.0045 -.02946 (86*2π)/193222 weeks
87-.00634 -.02964 (87*2π)/193222 weeks
88.00552 -.0263 (88*2π)/193222 weeks
89-.00329 -.03743 (89*2π)/193222 weeks
90-.00504 -.02806 (90*2π)/193221 weeks
91-.00457 -.02862 (91*2π)/193221 weeks
92.00406 -.02147 (92*2π)/193221 weeks
93.0109 -.0354 (93*2π)/193221 weeks
94-.00157 -.03901 (94*2π)/193221 weeks
95-.00602 -.03347 (95*2π)/193220 weeks
96-.00411 -.02852 (96*2π)/193220 weeks
97-.00033 -.02634 (97*2π)/193220 weeks
98.00408 -.03174 (98*2π)/193220 weeks
99-.00625 -.0314 (99*2π)/193220 weeks
100.00554 -.02493 (100*2π)/193219 weeks
101.00177 -.03753 (101*2π)/193219 weeks
102.00162 -.03275 (102*2π)/193219 weeks
103-.00336 -.04004 (103*2π)/193219 weeks
104-.0091 -.03415 (104*2π)/193219 weeks
105-.00834 -.02694 (105*2π)/193218 weeks
106.00171 -.028 (106*2π)/193218 weeks
107-.00302 -.03775 (107*2π)/193218 weeks
108-.00681 -.03416 (108*2π)/193218 weeks
109-.01233 -.02998 (109*2π)/193218 weeks
110-.00659 -.02272 (110*2π)/193218 weeks
111-.00028 -.02805 (111*2π)/193217 weeks
112-.00672 -.03518 (112*2π)/193217 weeks
113-.01159 -.0256 (113*2π)/193217 weeks
114-.00722 -.02222 (114*2π)/193217 weeks
115-.00103 -.0231 (115*2π)/193217 weeks
116-.0002 -.02992 (116*2π)/193217 weeks
117-.0131 -.03371 (117*2π)/193217 weeks
118-.01088 -.01681 (118*2π)/193216 weeks
119-.0008 -.02015 (119*2π)/193216 weeks
120-.00001 -.02155 (120*2π)/193216 weeks
121.00167 -.03406 (121*2π)/193216 weeks
122-.0138 -.03001 (122*2π)/193216 weeks
123-.00801 -.02091 (123*2π)/193216 weeks
124-.00778 -.01983 (124*2π)/193216 weeks
125-.0014 -.0217 (125*2π)/193215 weeks
126-.00556 -.02373 (126*2π)/193215 weeks
127-.00515 -.01919 (127*2π)/193215 weeks
128-.0012 -.02317 (128*2π)/193215 weeks
129-.004 -.02386 (129*2π)/193215 weeks
130-.00214 -.02157 (130*2π)/193215 weeks
131-.00212 -.02476 (131*2π)/193215 weeks
132-.00361 -.025 (132*2π)/193215 weeks
133-.00965 -.02507 (133*2π)/193215 weeks
134-.00515 -.01832 (134*2π)/193214 weeks
135-.00431 -.02146 (135*2π)/193214 weeks
136-.00153 -.01699 (136*2π)/193214 weeks
137.00167 -.02574 (137*2π)/193214 weeks
138-.00614 -.02357 (138*2π)/193214 weeks
139-.00469 -.02066 (139*2π)/193214 weeks
140-.00451 -.02193 (140*2π)/193214 weeks
141-.00331 -.01859 (141*2π)/193214 weeks
142.00299 -.02381 (142*2π)/193214 weeks
143-.00598 -.02749 (143*2π)/193214 weeks
144-.00521 -.02507 (144*2π)/193213 weeks
145-.01055 -.02495 (145*2π)/193213 weeks
146-.01039 -.0154 (146*2π)/193213 weeks
147-.00352 -.01688 (147*2π)/193213 weeks
148-.00239 -.01787 (148*2π)/193213 weeks
149-.00083 -.02242 (149*2π)/193213 weeks
150-.0043 -.02281 (150*2π)/193213 weeks
151-.00708 -.02298 (151*2π)/193213 weeks
152-.00831 -.01805 (152*2π)/193213 weeks
153-.00357 -.01528 (153*2π)/193213 weeks
154-.00077 -.01916 (154*2π)/193213 weeks
155-.00328 -.02075 (155*2π)/193212 weeks
156-.00301 -.02078 (156*2π)/193212 weeks
157-.00541 -.0216 (157*2π)/193212 weeks
158-.00597 -.01774 (158*2π)/193212 weeks
159-.0023 -.02207 (159*2π)/193212 weeks
160-.00658 -.02132 (160*2π)/193212 weeks
161-.00873 -.02024 (161*2π)/193212 weeks
162-.00574 -.01501 (162*2π)/193212 weeks
163-.00251 -.01999 (163*2π)/193212 weeks
164-.00715 -.0204 (164*2π)/193212 weeks
165-.00711 -.01849 (165*2π)/193212 weeks
166-.01001 -.01663 (166*2π)/193212 weeks
167-.00404 -.01156 (167*2π)/193212 weeks
168-.00177 -.01726 (168*2π)/193212 weeks
169-.00329 -.01662 (169*2π)/193211 weeks
170-.00355 -.01524 (170*2π)/193211 weeks
171-.0013 -.01649 (171*2π)/193211 weeks
172-.00127 -.01827 (172*2π)/193211 weeks
173-.00045 -.02052 (173*2π)/193211 weeks
174-.00527 -.02039 (174*2π)/193211 weeks
175-.00384 -.01894 (175*2π)/193211 weeks
176-.00799 -.02087 (176*2π)/193211 weeks
177-.00592 -.01495 (177*2π)/193211 weeks
178-.005 -.01867 (178*2π)/193211 weeks
179-.00581 -.01388 (179*2π)/193211 weeks
180-.00121 -.01631 (180*2π)/193211 weeks
181-.00463 -.0189 (181*2π)/193211 weeks
182-.004 -.01701 (182*2π)/193211 weeks
183-.00375 -.02001 (183*2π)/193211 weeks
184-.00715 -.01827 (184*2π)/193211 weeks
185-.00589 -.01531 (185*2π)/193210 weeks
186-.00419 -.01826 (186*2π)/193210 weeks
187-.00712 -.01723 (187*2π)/193210 weeks
188-.0039 -.01636 (188*2π)/193210 weeks
189-.0067 -.01629 (189*2π)/193210 weeks
190-.00167 -.0161 (190*2π)/193210 weeks
191-.00621 -.01994 (191*2π)/193210 weeks
192-.00766 -.01767 (192*2π)/193210 weeks
193-.00833 -.0151 (193*2π)/193210 weeks
194-.00406 -.01445 (194*2π)/193210 weeks
195-.00517 -.01962 (195*2π)/193210 weeks
196-.00887 -.01856 (196*2π)/193210 weeks
197-.01178 -.0151 (197*2π)/193210 weeks
198-.00827 -.00998 (198*2π)/193210 weeks
199-.00476 -.01131 (199*2π)/193210 weeks
200-.00367 -.01432 (200*2π)/193210 weeks
201-.00723 -.01439 (201*2π)/193210 weeks
202-.00616 -.01279 (202*2π)/193210 weeks
203-.00431 -.01272 (203*2π)/193210 weeks
204-.00309 -.01475 (204*2π)/19329 weeks
205-.00668 -.01614 (205*2π)/19329 weeks
206-.0068 -.01304 (206*2π)/19329 weeks
207-.0064 -.01174 (207*2π)/19329 weeks
208-.00349 -.01196 (208*2π)/19329 weeks
209-.00411 -.01698 (209*2π)/19329 weeks
210-.009 -.01387 (210*2π)/19329 weeks
211-.00696 -.01018 (211*2π)/19329 weeks
212-.00448 -.00887 (212*2π)/19329 weeks
213-.00118 -.01186 (213*2π)/19329 weeks
214-.00336 -.01433 (214*2π)/19329 weeks
215-.00443 -.01492 (215*2π)/19329 weeks
216-.0058 -.01282 (216*2π)/19329 weeks
217-.00441 -.01324 (217*2π)/19329 weeks
218-.00599 -.01177 (218*2π)/19329 weeks
219-.00309 -.01107 (219*2π)/19329 weeks
220-.00235 -.01279 (220*2π)/19329 weeks
221-.00129 -.01394 (221*2π)/19329 weeks
222-.00166 -.01686 (222*2π)/19329 weeks
223-.0082 -.01784 (223*2π)/19329 weeks
224-.00637 -.01261 (224*2π)/19329 weeks
225-.00737 -.01548 (225*2π)/19329 weeks
226-.00823 -.00979 (226*2π)/19329 weeks
227-.0038 -.01254 (227*2π)/19329 weeks
228-.00621 -.01122 (228*2π)/19328 weeks
229-.00356 -.01245 (229*2π)/19328 weeks
230-.00601 -.01303 (230*2π)/19328 weeks
231-.00607 -.01227 (231*2π)/19328 weeks
232-.00567 -.01017 (232*2π)/19328 weeks
233-.00332 -.01052 (233*2π)/19328 weeks
234-.00285 -.01149 (234*2π)/19328 weeks
235-.00172 -.01382 (235*2π)/19328 weeks
236-.00512 -.01578 (236*2π)/19328 weeks
237-.00786 -.0146 (237*2π)/19328 weeks
238-.00839 -.01146 (238*2π)/19328 weeks
239-.00679 -.01094 (239*2π)/19328 weeks
240-.00632 -.00866 (240*2π)/19328 weeks
241-.00446 -.01073 (241*2π)/19328 weeks
242-.00446 -.00857 (242*2π)/19328 weeks
243-.00151 -.01197 (243*2π)/19328 weeks
244-.00442 -.01297 (244*2π)/19328 weeks
245-.00548 -.01343 (245*2π)/19328 weeks
246-.00827 -.01045 (246*2π)/19328 weeks
247-.00494 -.00676 (247*2π)/19328 weeks
248-.00033 -.00841 (248*2π)/19328 weeks
249-.00087 -.01405 (249*2π)/19328 weeks
250-.0059 -.01485 (250*2π)/19328 weeks
251-.00805 -.01006 (251*2π)/19328 weeks
252-.00336 -.0086 (252*2π)/19328 weeks
253-.00094 -.01104 (253*2π)/19328 weeks
254-.00374 -.0147 (254*2π)/19328 weeks
255-.00599 -.01262 (255*2π)/19328 weeks
256-.00635 -.0108 (256*2π)/19328 weeks
257-.00342 -.01057 (257*2π)/19328 weeks
258-.00377 -.01339 (258*2π)/19327 weeks
259-.00644 -.01426 (259*2π)/19327 weeks
260-.00971 -.0098 (260*2π)/19327 weeks
261-.00482 -.0072 (261*2π)/19327 weeks
262-.00215 -.00958 (262*2π)/19327 weeks
263-.00256 -.01199 (263*2π)/19327 weeks
264-.00478 -.01318 (264*2π)/19327 weeks
265-.00769 -.01238 (265*2π)/19327 weeks
266-.00829 -.00802 (266*2π)/19327 weeks
267-.00325 -.0066 (267*2π)/19327 weeks
268-.0029 -.00932 (268*2π)/19327 weeks
269-.00168 -.01039 (269*2π)/19327 weeks
270-.00306 -.01224 (270*2π)/19327 weeks
271-.00416 -.01353 (271*2π)/19327 weeks
272-.00762 -.01197 (272*2π)/19327 weeks
273-.00697 -.00931 (273*2π)/19327 weeks
274-.00486 -.00744 (274*2π)/19327 weeks
275-.00262 -.00879 (275*2π)/19327 weeks
276-.00248 -.01192 (276*2π)/19327 weeks
277-.00449 -.01334 (277*2π)/19327 weeks
278-.00845 -.01105 (278*2π)/19327 weeks
279-.00531 -.00861 (279*2π)/19327 weeks
280-.00565 -.01007 (280*2π)/19327 weeks
281-.00476 -.00894 (281*2π)/19327 weeks
282-.0058 -.01005 (282*2π)/19327 weeks
283-.00432 -.00754 (283*2π)/19327 weeks
284-.00359 -.01113 (284*2π)/19327 weeks
285-.00487 -.01048 (285*2π)/19327 weeks
286-.007 -.01061 (286*2π)/19327 weeks
287-.00628 -.00654 (287*2π)/19327 weeks
288-.00338 -.00736 (288*2π)/19327 weeks
289-.00297 -.00829 (289*2π)/19327 weeks
290-.00252 -.00853 (290*2π)/19327 weeks
291-.00326 -.0104 (291*2π)/19327 weeks
292-.00467 -.00959 (292*2π)/19327 weeks
293-.00436 -.00854 (293*2π)/19327 weeks
294-.00394 -.01018 (294*2π)/19327 weeks
295-.00524 -.00761 (295*2π)/19327 weeks
296-.00155 -.00734 (296*2π)/19327 weeks
297-.00109 -.00998 (297*2π)/19327 weeks
298-.00149 -.01098 (298*2π)/19326 weeks
299-.00251 -.01368 (299*2π)/19326 weeks
300-.00781 -.01245 (300*2π)/19326 weeks
301-.00536 -.0072 (301*2π)/19326 weeks
302-.00269 -.00921 (302*2π)/19326 weeks
303-.00289 -.00995 (303*2π)/19326 weeks
304-.00386 -.01192 (304*2π)/19326 weeks
305-.00537 -.00973 (305*2π)/19326 weeks
306-.00307 -.00912 (306*2π)/19326 weeks
307-.00225 -.01028 (307*2π)/19326 weeks
308-.00311 -.01282 (308*2π)/19326 weeks
309-.00653 -.01206 (309*2π)/19326 weeks
310-.00596 -.01039 (310*2π)/19326 weeks
311-.00486 -.01061 (311*2π)/19326 weeks
312-.00577 -.01114 (312*2π)/19326 weeks
313-.00573 -.01103 (313*2π)/19326 weeks
314-.00753 -.01116 (314*2π)/19326 weeks
315-.0069 -.00785 (315*2π)/19326 weeks
316-.00562 -.0092 (316*2π)/19326 weeks
317-.00578 -.0087 (317*2π)/19326 weeks
318-.00534 -.00955 (318*2π)/19326 weeks
319-.00616 -.00927 (319*2π)/19326 weeks
320-.00651 -.00958 (320*2π)/19326 weeks
321-.00661 -.00719 (321*2π)/19326 weeks
322-.00519 -.00838 (322*2π)/19326 weeks
323-.00564 -.00796 (323*2π)/19326 weeks
324-.00521 -.00767 (324*2π)/19326 weeks
325-.0046 -.00835 (325*2π)/19326 weeks
326-.00496 -.00897 (326*2π)/19326 weeks
327-.0061 -.00862 (327*2π)/19326 weeks
328-.00593 -.00863 (328*2π)/19326 weeks
329-.00637 -.00683 (329*2π)/19326 weeks
330-.00456 -.00663 (330*2π)/19326 weeks
331-.00407 -.0067 (331*2π)/19326 weeks
332-.0029 -.00835 (332*2π)/19326 weeks
333-.00446 -.01029 (333*2π)/19326 weeks
334-.00541 -.00938 (334*2π)/19326 weeks
335-.00699 -.00998 (335*2π)/19326 weeks
336-.00729 -.00635 (336*2π)/19326 weeks
337-.00478 -.00585 (337*2π)/19326 weeks
338-.00383 -.00766 (338*2π)/19326 weeks
339-.00493 -.00837 (339*2π)/19326 weeks
340-.00562 -.00823 (340*2π)/19326 weeks
341-.00513 -.00657 (341*2π)/19326 weeks
342-.00374 -.0075 (342*2π)/19326 weeks
343-.00464 -.00792 (343*2π)/19326 weeks
344-.00453 -.00804 (344*2π)/19326 weeks
345-.00594 -.0068 (345*2π)/19326 weeks
346-.00321 -.00643 (346*2π)/19326 weeks
347-.00435 -.00801 (347*2π)/19326 weeks
348-.00477 -.00752 (348*2π)/19326 weeks
349-.0049 -.00671 (349*2π)/19326 weeks
350-.00371 -.00639 (350*2π)/19326 weeks
351-.0036 -.00709 (351*2π)/19326 weeks
352-.00307 -.00795 (352*2π)/19325 weeks
353-.00443 -.00812 (353*2π)/19325 weeks
354-.00323 -.00734 (354*2π)/19325 weeks
355-.00363 -.00852 (355*2π)/19325 weeks
356-.00387 -.00851 (356*2π)/19325 weeks
357-.00365 -.00915 (357*2π)/19325 weeks
358-.00552 -.00875 (358*2π)/19325 weeks
359-.00387 -.00735 (359*2π)/19325 weeks
360-.00384 -.00971 (360*2π)/19325 weeks
361-.00526 -.00837 (361*2π)/19325 weeks
362-.00436 -.00991 (362*2π)/19325 weeks
363-.00697 -.008 (363*2π)/19325 weeks
364-.00445 -.00725 (364*2π)/19325 weeks
365-.00509 -.00845 (365*2π)/19325 weeks
366-.00553 -.00827 (366*2π)/19325 weeks
367-.00621 -.0078 (367*2π)/19325 weeks
368-.00535 -.00601 (368*2π)/19325 weeks
369-.00388 -.00732 (369*2π)/19325 weeks
370-.00396 -.0097 (370*2π)/19325 weeks
371-.00857 -.01007 (371*2π)/19325 weeks
372-.00773 -.00571 (372*2π)/19325 weeks
373-.00576 -.00541 (373*2π)/19325 weeks
374-.00475 -.00596 (374*2π)/19325 weeks
375-.00559