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Fourier Analysis of VFIIX (Vanguard GNMA Fund)


VFIIX (Vanguard GNMA Fund) appears to have interesting cyclic behaviour every 191 weeks (.349*sine), 173 weeks (.3202*sine), and 173 weeks (.0326*cosine).

VFIIX (Vanguard GNMA Fund) has an average price of 4.87 (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 6/27/1980 to 1/9/2017 for VFIIX (Vanguard GNMA Fund), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
04.87187   0 
1.62788 -3.41256 (1*2π)/19071,907 weeks
2.11689 -1.71987 (2*2π)/1907954 weeks
3-.01232 -1.16631 (3*2π)/1907636 weeks
4-.09832 -.76045 (4*2π)/1907477 weeks
5.02445 -.58679 (5*2π)/1907381 weeks
6.07154 -.5606 (6*2π)/1907318 weeks
7.00627 -.41968 (7*2π)/1907272 weeks
8.02114 -.4424 (8*2π)/1907238 weeks
9-.00645 -.36955 (9*2π)/1907212 weeks
10-.00808 -.34899 (10*2π)/1907191 weeks
11-.03257 -.32018 (11*2π)/1907173 weeks
12.00675 -.256 (12*2π)/1907159 weeks
13-.02084 -.23147 (13*2π)/1907147 weeks
14.01173 -.21268 (14*2π)/1907136 weeks
15.00004 -.18268 (15*2π)/1907127 weeks
16.02615 -.20577 (16*2π)/1907119 weeks
17.0028 -.19013 (17*2π)/1907112 weeks
18-.00313 -.17704 (18*2π)/1907106 weeks
19.00471 -.18745 (19*2π)/1907100 weeks
20-.01407 -.155 (20*2π)/190795 weeks
21-.00844 -.16666 (21*2π)/190791 weeks
22-.00956 -.14809 (22*2π)/190787 weeks
23-.01001 -.14051 (23*2π)/190783 weeks
24-.00581 -.13117 (24*2π)/190779 weeks
25-.01445 -.12351 (25*2π)/190776 weeks
26-.01405 -.1273 (26*2π)/190773 weeks
27-.00677 -.11289 (27*2π)/190771 weeks
28.00461 -.10752 (28*2π)/190768 weeks
29.00413 -.11848 (29*2π)/190766 weeks
30-.01966 -.11761 (30*2π)/190764 weeks
31-.01889 -.10553 (31*2π)/190762 weeks
32-.01025 -.08649 (32*2π)/190760 weeks
33-.00014 -.08963 (33*2π)/190758 weeks
34-.00775 -.09237 (34*2π)/190756 weeks
35-.01437 -.0857 (35*2π)/190754 weeks
36-.00326 -.07723 (36*2π)/190753 weeks
37-.00709 -.09584 (37*2π)/190752 weeks
38-.01007 -.08534 (38*2π)/190750 weeks
39-.00525 -.07726 (39*2π)/190749 weeks
40.00235 -.07466 (40*2π)/190748 weeks
41-.00353 -.0851 (41*2π)/190747 weeks
42-.00647 -.08215 (42*2π)/190745 weeks
43-.01345 -.07463 (43*2π)/190744 weeks
44-.0119 -.06796 (44*2π)/190743 weeks
45-.00202 -.05843 (45*2π)/190742 weeks
46-.0075 -.07015 (46*2π)/190741 weeks
47-.00464 -.06628 (47*2π)/190741 weeks
48-.00357 -.07038 (48*2π)/190740 weeks
49-.00737 -.06428 (49*2π)/190739 weeks
50-.00856 -.0564 (50*2π)/190738 weeks
51.00099 -.07044 (51*2π)/190737 weeks
52-.01038 -.05512 (52*2π)/190737 weeks
53-.00762 -.05407 (53*2π)/190736 weeks
54-.00663 -.05746 (54*2π)/190735 weeks
55-.01152 -.04902 (55*2π)/190735 weeks
56-.00387 -.05398 (56*2π)/190734 weeks
57-.00017 -.05475 (57*2π)/190733 weeks
58-.00496 -.05497 (58*2π)/190733 weeks
59-.00416 -.04909 (59*2π)/190732 weeks
60-.00286 -.05753 (60*2π)/190732 weeks
61-.00812 -.0552 (61*2π)/190731 weeks
62-.00644 -.05102 (62*2π)/190731 weeks
63-.01299 -.04673 (63*2π)/190730 weeks
64-.00669 -.04739 (64*2π)/190730 weeks
65-.00884 -.04565 (65*2π)/190729 weeks
66-.00323 -.04309 (66*2π)/190729 weeks
67-.0011 -.04263 (67*2π)/190728 weeks
68-.00548 -.04813 (68*2π)/190728 weeks
69-.00806 -.0447 (69*2π)/190728 weeks
70-.00388 -.04303 (70*2π)/190727 weeks
71-.00683 -.04645 (71*2π)/190727 weeks
72-.00843 -.04818 (72*2π)/190726 weeks
73-.00697 -.03792 (73*2π)/190726 weeks
74-.00824 -.03854 (74*2π)/190726 weeks
75-.00826 -.04117 (75*2π)/190725 weeks
76-.00465 -.03581 (76*2π)/190725 weeks
77-.00272 -.03987 (77*2π)/190725 weeks
78-.00089 -.03383 (78*2π)/190724 weeks
79-.00332 -.03907 (79*2π)/190724 weeks
80-.00355 -.03864 (80*2π)/190724 weeks
81-.00398 -.03796 (81*2π)/190724 weeks
82-.00398 -.03395 (82*2π)/190723 weeks
83-.00295 -.0376 (83*2π)/190723 weeks
84-.00918 -.03564 (84*2π)/190723 weeks
85-.00737 -.03267 (85*2π)/190722 weeks
86-.00403 -.03447 (86*2π)/190722 weeks
87-.00449 -.03485 (87*2π)/190722 weeks
88-.00153 -.03397 (88*2π)/190722 weeks
89-.00204 -.0354 (89*2π)/190721 weeks
90-.00714 -.0347 (90*2π)/190721 weeks
91-.00502 -.03619 (91*2π)/190721 weeks
92-.01166 -.03875 (92*2π)/190721 weeks
93-.01007 -.03013 (93*2π)/190721 weeks
94-.00628 -.03287 (94*2π)/190720 weeks
95-.00806 -.03061 (95*2π)/190720 weeks
96-.00506 -.0313 (96*2π)/190720 weeks
97-.00618 -.03334 (97*2π)/190720 weeks
98-.00628 -.03118 (98*2π)/190719 weeks
99-.00562 -.02505 (99*2π)/190719 weeks
100-.001 -.02885 (100*2π)/190719 weeks
101-.00292 -.03208 (101*2π)/190719 weeks
102-.00325 -.03006 (102*2π)/190719 weeks
103-.00612 -.03083 (103*2π)/190719 weeks
104-.00624 -.0271 (104*2π)/190718 weeks
105-.00123 -.02845 (105*2π)/190718 weeks
106-.00814 -.02791 (106*2π)/190718 weeks
107-.00658 -.02665 (107*2π)/190718 weeks
108-.00278 -.02463 (108*2π)/190718 weeks
109-.0015 -.02741 (109*2π)/190717 weeks
110-.0016 -.02896 (110*2π)/190717 weeks
111-.00844 -.02751 (111*2π)/190717 weeks
112-.00556 -.02462 (112*2π)/190717 weeks
113-.00106 -.02843 (113*2π)/190717 weeks
114-.00484 -.02903 (114*2π)/190717 weeks
115-.00629 -.02257 (115*2π)/190717 weeks
116-.00495 -.02414 (116*2π)/190716 weeks
117-.00389 -.02607 (117*2π)/190716 weeks
118-.0039 -.03001 (118*2π)/190716 weeks
119-.0069 -.0257 (119*2π)/190716 weeks
120-.00644 -.02637 (120*2π)/190716 weeks
121-.00902 -.01946 (121*2π)/190716 weeks
122-.0022 -.02212 (122*2π)/190716 weeks
123-.00178 -.02624 (123*2π)/190716 weeks
124-.00376 -.02658 (124*2π)/190715 weeks
125-.00543 -.0217 (125*2π)/190715 weeks
126-.00318 -.02336 (126*2π)/190715 weeks
127-.00203 -.02539 (127*2π)/190715 weeks
128-.00429 -.02469 (128*2π)/190715 weeks
129-.00462 -.02559 (129*2π)/190715 weeks
130-.0064 -.02332 (130*2π)/190715 weeks
131-.00544 -.0239 (131*2π)/190715 weeks
132-.00362 -.02304 (132*2π)/190714 weeks
133-.00925 -.02355 (133*2π)/190714 weeks
134-.00274 -.01761 (134*2π)/190714 weeks
135-.00291 -.02144 (135*2π)/190714 weeks
136-.00208 -.02128 (136*2π)/190714 weeks
137-.00163 -.02377 (137*2π)/190714 weeks
138-.00729 -.02501 (138*2π)/190714 weeks
139-.00575 -.02057 (139*2π)/190714 weeks
140-.00553 -.0225 (140*2π)/190714 weeks
141-.00574 -.02054 (141*2π)/190714 weeks
142-.00562 -.0214 (142*2π)/190713 weeks
143-.00484 -.019 (143*2π)/190713 weeks
144-.00381 -.02057 (144*2π)/190713 weeks
145-.00467 -.01908 (145*2π)/190713 weeks
146-.00379 -.01977 (146*2π)/190713 weeks
147-.0034 -.01906 (147*2π)/190713 weeks
148-.00032 -.02031 (148*2π)/190713 weeks
149-.00209 -.02432 (149*2π)/190713 weeks
150-.00393 -.02112 (150*2π)/190713 weeks
151-.00496 -.02297 (151*2π)/190713 weeks
152-.00465 -.02127 (152*2π)/190713 weeks
153-.0057 -.02059 (153*2π)/190712 weeks
154-.0025 -.01958 (154*2π)/190712 weeks
155-.00513 -.02031 (155*2π)/190712 weeks
156-.00573 -.01928 (156*2π)/190712 weeks
157-.00562 -.01929 (157*2π)/190712 weeks
158-.00328 -.01706 (158*2π)/190712 weeks
159-.0019 -.01947 (159*2π)/190712 weeks
160-.00772 -.02044 (160*2π)/190712 weeks
161-.0057 -.01668 (161*2π)/190712 weeks
162-.00367 -.01787 (162*2π)/190712 weeks
163-.00398 -.01873 (163*2π)/190712 weeks
164-.0057 -.01947 (164*2π)/190712 weeks
165-.0057 -.01761 (165*2π)/190712 weeks
166-.00633 -.01809 (166*2π)/190711 weeks
167-.00556 -.01868 (167*2π)/190711 weeks
168-.00397 -.01787 (168*2π)/190711 weeks
169-.00335 -.01745 (169*2π)/190711 weeks
170-.00432 -.01794 (170*2π)/190711 weeks
171-.00421 -.02009 (171*2π)/190711 weeks
172-.00781 -.021 (172*2π)/190711 weeks
173-.00664 -.01739 (173*2π)/190711 weeks
174-.00553 -.01516 (174*2π)/190711 weeks
175-.00373 -.01603 (175*2π)/190711 weeks
176-.00413 -.01769 (176*2π)/190711 weeks
177-.00604 -.01816 (177*2π)/190711 weeks
178-.00441 -.01638 (178*2π)/190711 weeks
179-.0044 -.01704 (179*2π)/190711 weeks
180-.00503 -.01651 (180*2π)/190711 weeks
181-.00447 -.0179 (181*2π)/190711 weeks
182-.00546 -.01781 (182*2π)/190710 weeks
183-.00437 -.01589 (183*2π)/190710 weeks
184-.00516 -.01829 (184*2π)/190710 weeks
185-.0063 -.01493 (185*2π)/190710 weeks
186-.00527 -.01637 (186*2π)/190710 weeks
187-.00497 -.01582 (187*2π)/190710 weeks
188-.0042 -.01669 (188*2π)/190710 weeks
189-.0037 -.0155 (189*2π)/190710 weeks
190-.0055 -.01807 (190*2π)/190710 weeks
191-.00661 -.01484 (191*2π)/190710 weeks
192-.00421 -.01571 (192*2π)/190710 weeks
193-.00518 -.01504 (193*2π)/190710 weeks
194-.00296 -.01512 (194*2π)/190710 weeks
195-.00485 -.01582 (195*2π)/190710 weeks
196-.00471 -.01576 (196*2π)/190710 weeks
197-.00583 -.01584 (197*2π)/190710 weeks
198-.00522 -.01314 (198*2π)/190710 weeks
199-.00314 -.01596 (199*2π)/190710 weeks
200-.00256 -.01545 (200*2π)/190710 weeks
201-.0064 -.01724 (201*2π)/19079 weeks
202-.0045 -.01414 (202*2π)/19079 weeks
203-.00403 -.01684 (203*2π)/19079 weeks
204-.00579 -.01535 (204*2π)/19079 weeks
205-.00512 -.01412 (205*2π)/19079 weeks
206-.00465 -.01614 (206*2π)/19079 weeks
207-.00518 -.01406 (207*2π)/19079 weeks
208-.0059 -.01449 (208*2π)/19079 weeks
209-.00538 -.01386 (209*2π)/19079 weeks
210-.00468 -.01366 (210*2π)/19079 weeks
211-.00377 -.01457 (211*2π)/19079 weeks
212-.00594 -.01655 (212*2π)/19079 weeks
213-.00552 -.01415 (213*2π)/19079 weeks
214-.00461 -.01409 (214*2π)/19079 weeks
215-.00541 -.01437 (215*2π)/19079 weeks
216-.00675 -.01544 (216*2π)/19079 weeks
217-.00836 -.01318 (217*2π)/19079 weeks
218-.00503 -.00998 (218*2π)/19079 weeks
219-.0034 -.01301 (219*2π)/19079 weeks
220-.00406 -.01468 (220*2π)/19079 weeks
221-.00645 -.0134 (221*2π)/19079 weeks
222-.00537 -.01172 (222*2π)/19079 weeks
223-.00354 -.01196 (223*2π)/19079 weeks
224-.0039 -.01461 (224*2π)/19079 weeks
225-.00528 -.01451 (225*2π)/19078 weeks
226-.00696 -.01394 (226*2π)/19078 weeks
227-.00501 -.01312 (227*2π)/19078 weeks
228-.00522 -.01454 (228*2π)/19078 weeks
229-.0051 -.01194 (229*2π)/19078 weeks
230-.00452 -.01346 (230*2π)/19078 weeks
231-.0041 -.01317 (231*2π)/19078 weeks
232-.00399 -.01396 (232*2π)/19078 weeks
233-.00503 -.01364 (233*2π)/19078 weeks
234-.00486 -.01306 (234*2π)/19078 weeks
235-.00616 -.01235 (235*2π)/19078 weeks
236-.00403 -.01292 (236*2π)/19078 weeks
237-.00709 -.01351 (237*2π)/19078 weeks
238-.00508 -.01337 (238*2π)/19078 weeks
239-.0072 -.01115 (239*2π)/19078 weeks
240-.00486 -.0106 (240*2π)/19078 weeks
241-.00484 -.01163 (241*2π)/19078 weeks
242-.0044 -.01079 (242*2π)/19078 weeks
243-.00401 -.01273 (243*2π)/19078 weeks
244-.004 -.01174 (244*2π)/19078 weeks
245-.00401 -.01415 (245*2π)/19078 weeks
246-.0061 -.01283 (246*2π)/19078 weeks
247-.00582 -.0126 (247*2π)/19078 weeks
248-.00535 -.01174 (248*2π)/19078 weeks
249-.00665 -.01218 (249*2π)/19078 weeks
250-.00613 -.01116 (250*2π)/19078 weeks
251-.00517 -.01092 (251*2π)/19078 weeks
252-.00569 -.01073 (252*2π)/19078 weeks
253-.00499 -.01189 (253*2π)/19078 weeks
254-.00501 -.01142 (254*2π)/19078 weeks
255-.00361 -.01061 (255*2π)/19077 weeks
256-.0056 -.01272 (256*2π)/19077 weeks
257-.00425 -.01172 (257*2π)/19077 weeks
258-.00531 -.01226 (258*2π)/19077 weeks
259-.00619 -.00983 (259*2π)/19077 weeks
260-.00415 -.01028 (260*2π)/19077 weeks
261-.00372 -.01019 (261*2π)/19077 weeks
262-.00331 -.01162 (262*2π)/19077 weeks
263-.00526 -.01282 (263*2π)/19077 weeks
264-.00694 -.01175 (264*2π)/19077 weeks
265-.00533 -.01097 (265*2π)/19077 weeks
266-.00529 -.01092 (266*2π)/19077 weeks
267-.00447 -.01075 (267*2π)/19077 weeks
268-.00446 -.01065 (268*2π)/19077 weeks
269-.00539 -.01147 (269*2π)/19077 weeks
270-.00549 -.01024 (270*2π)/19077 weeks
271-.00617 -.01026 (271*2π)/19077 weeks
272-.00474 -.0096 (272*2π)/19077 weeks
273-.00394 -.01102 (273*2π)/19077 weeks
274-.00539 -.01013 (274*2π)/19077 weeks
275-.00467 -.01156 (275*2π)/19077 weeks
276-.00487 -.01123 (276*2π)/19077 weeks
277-.00516 -.01048 (277*2π)/19077 weeks
278-.00555 -.01148 (278*2π)/19077 weeks
279-.00564 -.00966 (279*2π)/19077 weeks
280-.00615 -.00978 (280*2π)/19077 weeks
281-.00555 -.00921 (281*2π)/19077 weeks
282-.00481 -.01112 (282*2π)/19077 weeks
283-.00514 -.01071 (283*2π)/19077 weeks
284-.00571 -.01058 (284*2π)/19077 weeks
285-.0053 -.00966 (285*2π)/19077 weeks
286-.00374 -.00894 (286*2π)/19077 weeks
287-.00537 -.01122 (287*2π)/19077 weeks
288-.00486 -.01001 (288*2π)/19077 weeks
289-.00514 -.00966 (289*2π)/19077 weeks
290-.0055 -.00875 (290*2π)/19077 weeks
291-.0048 -.00953 (291*2π)/19077 weeks
292-.00411 -.01015 (292*2π)/19077 weeks
293-.00548 -.00985 (293*2π)/19077 weeks
294-.00489 -.00939 (294*2π)/19076 weeks
295-.00461 -.00996 (295*2π)/19076 weeks
296-.00577 -.01111 (296*2π)/19076 weeks
297-.00615 -.00989 (297*2π)/19076 weeks
298-.00557 -.00946 (298*2π)/19076 weeks
299-.00465 -.00915 (299*2π)/19076 weeks
300-.00657 -.00898 (300*2π)/19076 weeks
301-.00522 -.01041 (301*2π)/19076 weeks
302-.00541 -.00913 (302*2π)/19076 weeks
303-.00445 -.00928 (303*2π)/19076 weeks
304-.00392 -.00856 (304*2π)/19076 weeks
305-.00524 -.00964 (305*2π)/19076 weeks
306-.00482 -.00998 (306*2π)/19076 weeks
307-.00538 -.00894 (307*2π)/19076 weeks
308-.00435 -.0091 (308*2π)/19076 weeks
309-.00546 -.00942 (309*2π)/19076 weeks
310-.00574 -.00964 (310*2π)/19076 weeks
311-.00554 -.00907 (311*2π)/19076 weeks
312-.00535 -.00898 (312*2π)/19076 weeks
313-.00568 -.00869 (313*2π)/19076 weeks
314-.00522 -.00808 (314*2π)/19076 weeks
315-.00446 -.00842 (315*2π)/19076 weeks
316-.00447 -.00836 (316*2π)/19076 weeks
317-.00425 -.01023 (317*2π)/19076 weeks
318-.00622 -.0088 (318*2π)/19076 weeks
319-.00415 -.00818 (319*2π)/19076 weeks
320-.0044 -.00817 (320*2π)/19076 weeks
321-.00418 -.00948 (321*2π)/19076 weeks
322-.0059 -.00968 (322*2π)/19076 weeks
323-.0045 -.00621 (323*2π)/19076 weeks
324-.0038 -.00955 (324*2π)/19076 weeks
325-.00504 -.00947 (325*2π)/19076 weeks
326-.00524 -.00884 (326*2π)/19076 weeks
327-.00516 -.00803 (327*2π)/19076 weeks
328-.00466 -.0081 (328*2π)/19076 weeks
329-.0045 -.00878 (329*2π)/19076 weeks
330-.00531 -.01008 (330*2π)/19076 weeks
331-.00621 -.0084 (331*2π)/19076 weeks
332-.00477 -.00885 (332*2π)/19076 weeks
333-.0053 -.00855 (333*2π)/19076 weeks
334-.00476 -.00839 (334*2π)/19076 weeks
335-.00539 -.00865 (335*2π)/19076 weeks
336-.00495 -.00861 (336*2π)/19076 weeks
337-.00518 -.00884 (337*2π)/19076 weeks
338-.00403 -.00886 (338*2π)/19076 weeks
339-.00655 -.00899 (339*2π)/19076 weeks
340-.00488 -.00811 (340*2π)/19076 weeks
341-.0045 -.00915 (341*2π)/19076 weeks
342-.00549 -.0082 (342*2π)/19076 weeks
343-.00425 -.00756 (343*2π)/19076 weeks
344-.00502 -.00842 (344*2π)/19076 weeks
345-.00511 -.0086 (345*2π)/19076 weeks
346-.00583 -.00793 (346*2π)/19076 weeks
347-.00446 -.00874 (347*2π)/19075 weeks
348-.00504 -.00799 (348*2π)/19075 weeks
349-.006 -.00763 (349*2π)/19075 weeks
350-.0047 -.00715 (350*2π)/19075 weeks
351-.00466 -.00886 (351*2π)/19075 weeks
352-.00548 -.00819 (352*2π)/19075 weeks
353-.00536 -.00799 (353*2π)/19075 weeks
354-.00516 -.00716 (354*2π)/19075 weeks
355-.00427 -.00728 (355*2π)/19075 weeks
356-.00428 -.00919 (356*2π)/19075 weeks
357-.00476 -.00821 (357*2π)/19075 weeks
358-.00412 -.00856 (358*2π)/19075 weeks
359-.00579 -.00853 (359*2π)/19075 weeks
360-.00596 -.00733 (360*2π)/19075 weeks
361-.00519 -.00764 (361*2π)/19075 weeks
362-.00512 -.00724 (362*2π)/19075 weeks
363-.00384 -.00689 (363*2π)/19075 weeks
364-.00495 -.00787 (364*2π)/19075 weeks
365-.00471 -.00814 (365*2π)/19075 weeks
366-.00596 -.00821 (366*2π)/19075 weeks
367-.00427 -.00674 (367*2π)/19075 weeks
368-.0042 -.00898 (368*2π)/19075 weeks
369-.00599 -.00766 (369*2π)/19075 weeks
370-.00499 -.00707 (370*2π)/19075 weeks
371-.00511 -.00709 (371*2π)/19075 weeks
372-.00437 -.00778 (372*2π)/19075 weeks
373-.00472 -.00783 (373*2π)/19075 weeks
374-.00566 -.00731 (374*2π)/19075 weeks
375-.00482 -.00658 (375*2π)/19075 weeks
376-.00502 -.00728 (376*2π)/19075 weeks
377-.00576 -.00786 (377*2π)/19075 weeks
378-.00515 -.00741