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Fourier Analysis of VFIIX (Vanguard GNMA Fund)

VFIIX (Vanguard GNMA Fund) appears to have interesting cyclic behaviour every 192 weeks (.3465*sine), 174 weeks (.311*sine), and 174 weeks (.0374*cosine).

VFIIX (Vanguard GNMA Fund) has an average price of 4.88 (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 6/27/1980 to 3/13/2017 for VFIIX (Vanguard GNMA Fund), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
04.8798   0
1.62379 -3.42438 (1*2π)/19161,916 weeks
2.10953 -1.72339 (2*2π)/1916958 weeks
3-.02024 -1.16305 (3*2π)/1916639 weeks
4-.09547 -.75236 (4*2π)/1916479 weeks
5.03041 -.58992 (5*2π)/1916383 weeks
6.06743 -.56765 (6*2π)/1916319 weeks
7.00687 -.42232 (7*2π)/1916274 weeks
8.01233 -.44637 (8*2π)/1916240 weeks
9-.01212 -.36839 (9*2π)/1916213 weeks
10-.01553 -.34645 (10*2π)/1916192 weeks
11-.03739 -.31098 (11*2π)/1916174 weeks
12.00863 -.25348 (12*2π)/1916160 weeks
13-.01736 -.22596 (13*2π)/1916147 weeks
14.01518 -.21497 (14*2π)/1916137 weeks
15.00577 -.18605 (15*2π)/1916128 weeks
16.02068 -.21488 (16*2π)/1916120 weeks
17-.00312 -.19169 (17*2π)/1916113 weeks
18-.00752 -.17783 (18*2π)/1916106 weeks
19-.00572 -.18757 (19*2π)/1916101 weeks
20-.01659 -.15027 (20*2π)/191696 weeks
21-.01552 -.16285 (21*2π)/191691 weeks
22-.01229 -.14292 (22*2π)/191687 weeks
23-.01183 -.13553 (23*2π)/191683 weeks
24-.00705 -.12796 (24*2π)/191680 weeks
25-.01417 -.11851 (25*2π)/191677 weeks
26-.01487 -.12199 (26*2π)/191674 weeks
27-.00344 -.11124 (27*2π)/191671 weeks
28.00468 -.11187 (28*2π)/191668 weeks
29-.00548 -.11934 (29*2π)/191666 weeks
30-.02601 -.10507 (30*2π)/191664 weeks
31-.01635 -.09385 (31*2π)/191662 weeks
32-.00086 -.08319 (32*2π)/191660 weeks
33.00213 -.09226 (33*2π)/191658 weeks
34-.00854 -.08964 (34*2π)/191656 weeks
35-.01026 -.08101 (35*2π)/191655 weeks
36.00128 -.08172 (36*2π)/191653 weeks
37-.01334 -.09383 (37*2π)/191652 weeks
38-.00868 -.08053 (38*2π)/191650 weeks
39-.00126 -.07734 (39*2π)/191649 weeks
40.00206 -.07986 (40*2π)/191648 weeks
41-.01105 -.08274 (41*2π)/191647 weeks
42-.01074 -.07524 (42*2π)/191646 weeks
43-.01061 -.06485 (43*2π)/191645 weeks
44-.00436 -.06261 (44*2π)/191644 weeks
45.00528 -.06349 (45*2π)/191643 weeks
46-.00896 -.06926 (46*2π)/191642 weeks
47-.00403 -.06676 (47*2π)/191641 weeks
48-.00672 -.06834 (48*2π)/191640 weeks
49-.00545 -.05969 (49*2π)/191639 weeks
50-.00237 -.05586 (50*2π)/191638 weeks
51-.00597 -.06978 (51*2π)/191638 weeks
52-.00372 -.04874 (52*2π)/191637 weeks
53-.00241 -.05356 (53*2π)/191636 weeks
54-.00491 -.05611 (54*2π)/191635 weeks
55-.0026 -.04862 (55*2π)/191635 weeks
56-.00246 -.05914 (56*2π)/191634 weeks
57-.00262 -.05907 (57*2π)/191634 weeks
58-.00657 -.05355 (58*2π)/191633 weeks
59-.0029 -.05107 (59*2π)/191632 weeks
60-.00952 -.05574 (60*2π)/191632 weeks
61-.00879 -.04787 (61*2π)/191631 weeks
62-.00403 -.04652 (62*2π)/191631 weeks
63-.0049 -.04109 (63*2π)/191630 weeks
64-.00214 -.04824 (64*2π)/191630 weeks
65-.00265 -.0454 (65*2π)/191629 weeks
66.00073 -.04872 (66*2π)/191629 weeks
67-.00166 -.04836 (67*2π)/191629 weeks
68-.00885 -.04584 (68*2π)/191628 weeks
69-.00541 -.04224 (69*2π)/191628 weeks
70-.00324 -.04513 (70*2π)/191627 weeks
71-.00797 -.043 (71*2π)/191627 weeks
72-.00682 -.04166 (72*2π)/191627 weeks
73.00218 -.03875 (73*2π)/191626 weeks
74-.00227 -.03985 (74*2π)/191626 weeks
75-.00393 -.04186 (75*2π)/191626 weeks
76.00124 -.04276 (76*2π)/191625 weeks
77-.00334 -.04455 (77*2π)/191625 weeks
78.00048 -.0417 (78*2π)/191625 weeks
79-.00704 -.0406 (79*2π)/191624 weeks
80-.00525 -.03932 (80*2π)/191624 weeks
81-.00445 -.03803 (81*2π)/191624 weeks
82-.00243 -.03671 (82*2π)/191623 weeks
83-.00659 -.03769 (83*2π)/191623 weeks
84-.00549 -.03204 (84*2π)/191623 weeks
85-.00302 -.03596 (85*2π)/191623 weeks
86-.00539 -.03896 (86*2π)/191622 weeks
87-.00598 -.03702 (87*2π)/191622 weeks
88-.00521 -.0377 (88*2π)/191622 weeks
89-.00741 -.03462 (89*2π)/191622 weeks
90-.00742 -.03001 (90*2π)/191621 weeks
91-.00757 -.03283 (91*2π)/191621 weeks
92-.0079 -.02815 (92*2π)/191621 weeks
93.00062 -.03183 (93*2π)/191621 weeks
94-.00427 -.03573 (94*2π)/191620 weeks
95-.00298 -.03296 (95*2π)/191620 weeks
96-.00443 -.0356 (96*2π)/191620 weeks
97-.00554 -.03341 (97*2π)/191620 weeks
98-.00235 -.03325 (98*2π)/191620 weeks
99-.00011 -.03383 (99*2π)/191619 weeks
100-.00676 -.03633 (100*2π)/191619 weeks
101-.00795 -.03156 (101*2π)/191619 weeks
102-.00457 -.03042 (102*2π)/191619 weeks
103-.00515 -.02848 (103*2π)/191619 weeks
104-.00245 -.03015 (104*2π)/191618 weeks
105-.00523 -.03271 (105*2π)/191618 weeks
106-.00459 -.02585 (106*2π)/191618 weeks
107-.00418 -.03076 (107*2π)/191618 weeks
108-.00461 -.03273 (108*2π)/191618 weeks
109-.00808 -.03031 (109*2π)/191618 weeks
110-.00733 -.02752 (110*2π)/191617 weeks
111-.00468 -.02345 (111*2π)/191617 weeks
112-.00447 -.02955 (112*2π)/191617 weeks
113-.00846 -.03003 (113*2π)/191617 weeks
114-.00537 -.02469 (114*2π)/191617 weeks
115-.00142 -.02606 (115*2π)/191617 weeks
116-.00702 -.02724 (116*2π)/191617 weeks
117-.0083 -.02668 (117*2π)/191616 weeks
118-.00819 -.02521 (118*2π)/191616 weeks
119-.00227 -.02438 (119*2π)/191616 weeks
120-.00433 -.02626 (120*2π)/191616 weeks
121-.00138 -.02672 (121*2π)/191616 weeks
122-.00946 -.03038 (122*2π)/191616 weeks
123-.00983 -.02541 (123*2π)/191616 weeks
124-.00601 -.02351 (124*2π)/191615 weeks
125-.00311 -.02438 (125*2π)/191615 weeks
126-.00783 -.02522 (126*2π)/191615 weeks
127-.00772 -.02365 (127*2π)/191615 weeks
128-.00502 -.02169 (128*2π)/191615 weeks
129-.00534 -.02238 (129*2π)/191615 weeks
130-.00339 -.02274 (130*2π)/191615 weeks
131-.00546 -.02407 (131*2π)/191615 weeks
132-.00478 -.02436 (132*2π)/191615 weeks
133-.00394 -.02138 (133*2π)/191614 weeks
134-.00461 -.02849 (134*2π)/191614 weeks
135-.00885 -.02175 (135*2π)/191614 weeks
136-.00708 -.0216 (136*2π)/191614 weeks
137-.00714 -.01959 (137*2π)/191614 weeks
138-.00385 -.01777 (138*2π)/191614 weeks
139-.00314 -.02358 (139*2π)/191614 weeks
140-.00619 -.02166 (140*2π)/191614 weeks
141-.0046 -.02244 (141*2π)/191614 weeks
142-.00621 -.02198 (142*2π)/191613 weeks
143-.00545 -.02282 (143*2π)/191613 weeks
144-.00745 -.02117 (144*2π)/191613 weeks
145-.00578 -.02071 (145*2π)/191613 weeks
146-.00752 -.02045 (146*2π)/191613 weeks
147-.00702 -.02004 (147*2π)/191613 weeks
148-.00814 -.0192 (148*2π)/191613 weeks
149-.00586 -.0159 (149*2π)/191613 weeks
150-.00192 -.0186 (150*2π)/191613 weeks
151-.00424 -.01817 (151*2π)/191613 weeks
152-.00314 -.02045 (152*2π)/191613 weeks
153-.00358 -.01986 (153*2π)/191613 weeks
154-.0049 -.02089 (154*2π)/191612 weeks
155-.00344 -.01754 (155*2π)/191612 weeks
156-.00395 -.01936 (156*2π)/191612 weeks
157-.00517 -.01955 (157*2π)/191612 weeks
158-.00544 -.02017 (158*2π)/191612 weeks
159-.00589 -.01668 (159*2π)/191612 weeks
160-.00247 -.01577 (160*2π)/191612 weeks
161-.00503 -.021 (161*2π)/191612 weeks
162-.00702 -.0179 (162*2π)/191612 weeks
163-.00521 -.01667 (163*2π)/191612 weeks
164-.00434 -.01685 (164*2π)/191612 weeks
165-.00464 -.01872 (165*2π)/191612 weeks
166-.00586 -.01753 (166*2π)/191612 weeks
167-.00651 -.01824 (167*2π)/191611 weeks
168-.00586 -.01862 (168*2π)/191611 weeks
169-.00501 -.01713 (169*2π)/191611 weeks
170-.00442 -.01587 (170*2π)/191611 weeks
171-.00473 -.01617 (171*2π)/191611 weeks
172-.00285 -.01763 (172*2π)/191611 weeks
173-.00481 -.02146 (173*2π)/191611 weeks
174-.00613 -.01897 (174*2π)/191611 weeks
175-.00699 -.01624 (175*2π)/191611 weeks
176-.00522 -.01522 (176*2π)/191611 weeks
177-.00428 -.01641 (177*2π)/191611 weeks
178-.00555 -.01814 (178*2π)/191611 weeks
179-.0051 -.01597 (179*2π)/191611 weeks
180-.00461 -.01629 (180*2π)/191611 weeks
181-.00539 -.01596 (181*2π)/191611 weeks
182-.00418 -.01693 (182*2π)/191611 weeks
183-.00495 -.01762 (183*2π)/191610 weeks
184-.00475 -.01535 (184*2π)/191610 weeks
185-.00425 -.01792 (185*2π)/191610 weeks
186-.00673 -.01543 (186*2π)/191610 weeks
187-.00552 -.01619 (187*2π)/191610 weeks
188-.00547 -.01555 (188*2π)/191610 weeks
189-.00435 -.01609 (189*2π)/191610 weeks
190-.004 -.01465 (190*2π)/191610 weeks
191-.00467 -.01779 (191*2π)/191610 weeks
192-.00695 -.01533 (192*2π)/191610 weeks
193-.00456 -.01533 (193*2π)/191610 weeks
194-.00563 -.01492 (194*2π)/191610 weeks
195-.00336 -.01426 (195*2π)/191610 weeks
196-.0048 -.01538 (196*2π)/191610 weeks
197-.00467 -.01537 (197*2π)/191610 weeks
198-.00578 -.01583 (198*2π)/191610 weeks
199-.00594 -.01296 (199*2π)/191610 weeks
200-.00331 -.01515 (200*2π)/191610 weeks
201-.00253 -.01459 (201*2π)/191610 weeks
202-.00597 -.01713 (202*2π)/19169 weeks
203-.00472 -.01384 (203*2π)/19169 weeks
204-.0038 -.01642 (204*2π)/19169 weeks
205-.00573 -.01527 (205*2π)/19169 weeks
206-.00527 -.01392 (206*2π)/19169 weeks
207-.0046 -.01589 (207*2π)/19169 weeks
208-.00528 -.0139 (208*2π)/19169 weeks
209-.006 -.01433 (209*2π)/19169 weeks
210-.00553 -.01367 (210*2π)/19169 weeks
211-.00484 -.01342 (211*2π)/19169 weeks
212-.0039 -.01431 (212*2π)/19169 weeks
213-.00608 -.0163 (213*2π)/19169 weeks
214-.00565 -.01391 (214*2π)/19169 weeks
215-.00477 -.01387 (215*2π)/19169 weeks
216-.00561 -.01411 (216*2π)/19169 weeks
217-.00701 -.01502 (217*2π)/19169 weeks
218-.00835 -.01258 (218*2π)/19169 weeks
219-.00467 -.00979 (219*2π)/19169 weeks
220-.00343 -.0131 (220*2π)/19169 weeks
221-.00442 -.0146 (221*2π)/19169 weeks
222-.00657 -.01293 (222*2π)/19169 weeks
223-.00514 -.01152 (223*2π)/19169 weeks
224-.00347 -.01224 (224*2π)/19169 weeks
225-.00447 -.01477 (225*2π)/19169 weeks
226-.00587 -.01423 (226*2π)/19168 weeks
227-.00722 -.01327 (227*2π)/19168 weeks
228-.00505 -.01293 (228*2π)/19168 weeks
229-.00562 -.01416 (229*2π)/19168 weeks
230-.00487 -.0117 (230*2π)/19168 weeks
231-.00475 -.01345 (231*2π)/19168 weeks
232-.00441 -.01323 (232*2π)/19168 weeks
233-.0047 -.0139 (233*2π)/19168 weeks
234-.00563 -.01312 (234*2π)/19168 weeks
235-.0053 -.01255 (235*2π)/19168 weeks
236-.00621 -.01159 (236*2π)/19168 weeks
237-.00455 -.01287 (237*2π)/19168 weeks
238-.00753 -.01219 (238*2π)/19168 weeks
239-.00535 -.01256 (239*2π)/19168 weeks
240-.0063 -.00981 (240*2π)/19168 weeks
241-.00391 -.01072 (241*2π)/19168 weeks
242-.00456 -.01177 (242*2π)/19168 weeks
243-.004 -.01135 (243*2π)/19168 weeks
244-.00471 -.01321 (244*2π)/19168 weeks
245-.0045 -.0122 (245*2π)/19168 weeks
246-.00583 -.01394 (246*2π)/19168 weeks
247-.00679 -.01141 (247*2π)/19168 weeks
248-.00611 -.01142 (248*2π)/19168 weeks
249-.00535 -.01094 (249*2π)/19168 weeks
250-.00653 -.01072 (250*2π)/19168 weeks
251-.00524 -.01034 (251*2π)/19168 weeks
252-.00449 -.01084 (252*2π)/19168 weeks
253-.005 -.01063 (253*2π)/19168 weeks
254-.00505 -.01198 (254*2π)/19168 weeks
255-.00476 -.01141 (255*2π)/19168 weeks
256-.00367 -.0116 (256*2π)/19167 weeks
257-.00655 -.01191 (257*2π)/19167 weeks
258-.00461 -.01164 (258*2π)/19167 weeks
259-.00574 -.01107 (259*2π)/19167 weeks
260-.0046 -.00914 (260*2π)/19167 weeks
261-.0037 -.01134 (261*2π)/19167 weeks
262-.00403 -.01146 (262*2π)/19167 weeks
263-.00526 -.01235 (263*2π)/19167 weeks
264-.00723 -.01121 (264*2π)/19167 weeks
265-.00672 -.00946 (265*2π)/19167 weeks
266-.00477 -.01045 (266*2π)/19167 weeks
267-.00493 -.0105 (267*2π)/19167 weeks
268-.00449 -.01088 (268*2π)/19167 weeks
269-.00483 -.0106 (269*2π)/19167 weeks
270-.00593 -.01027 (270*2π)/19167 weeks
271-.00487 -.00951 (271*2π)/19167 weeks
272-.00528 -.00955 (272*2π)/19167 weeks
273-.00412 -.01059 (273*2π)/19167 weeks
274-.00521 -.01155 (274*2π)/19167 weeks
275-.00547 -.00971 (275*2π)/19167 weeks
276-.00599 -.01113 (276*2π)/19167 weeks
277-.00556 -.01023 (277*2π)/19167 weeks
278-.00521 -.00957 (278*2π)/19167 weeks
279-.00596 -.00977 (279*2π)/19167 weeks
280-.0044 -.00884 (280*2π)/19167 weeks
281-.00508 -.0091 (281*2π)/19167 weeks
282-.0046 -.00982 (282*2π)/19167 weeks
283-.0059 -.01107 (283*2π)/19167 weeks
284-.00531 -.00996 (284*2π)/19167 weeks
285-.00518 -.00952 (285*2π)/19167 weeks
286-.0042 -.00977 (286*2π)/19167 weeks
287-.0039 -.01058 (287*2π)/19167 weeks
288-.00656 -.00972 (288*2π)/19167 weeks
289-.00456 -.00958 (289*2π)/19167 weeks
290-.00465 -.00921 (290*2π)/19167 weeks
291-.00442 -.00902 (291*2π)/19167 weeks
292-.00525 -.01016 (292*2π)/19167 weeks
293-.00551 -.01026 (293*2π)/19167 weeks
294-.00552 -.00873 (294*2π)/19167 weeks
295-.00504 -.00946 (295*2π)/19166 weeks
296-.00577 -.00952 (296*2π)/19166 weeks
297-.00644 -.00862 (297*2π)/19166 weeks
298-.00473 -.00843 (298*2π)/19166 weeks
299-.00446 -.00927 (299*2π)/19166 weeks
300-.00447 -.00961 (300*2π)/19166 weeks
301-.00519 -.00815 (301*2π)/19166 weeks
302-.00567 -.0102 (302*2π)/19166 weeks
303-.00427 -.0094 (303*2π)/19166 weeks
304-.00465 -.01015 (304*2π)/19166 weeks
305-.00451 -.00967 (305*2π)/19166 weeks
306-.00594 -.00852 (306*2π)/19166 weeks
307-.00543 -.00912 (307*2π)/19166 weeks
308-.00453 -.00851 (308*2π)/19166 weeks
309-.00501 -.00935 (309*2π)/19166 weeks
310-.00541 -.0081 (310*2π)/19166 weeks
311-.0052 -.00843 (311*2π)/19166 weeks
312-.00454 -.00884 (312*2π)/19166 weeks
313-.00466 -.009 (313*2π)/19166 weeks
314-.00456 -.00884 (314*2π)/19166 weeks
315-.0045 -.00944 (315*2π)/19166 weeks
316-.00528 -.0097 (316*2π)/19166 weeks
317-.00547 -.00908 (317*2π)/19166 weeks
318-.00644 -.00881 (318*2π)/19166 weeks
319-.00435 -.00761 (319*2π)/19166 weeks
320-.00461 -.00991 (320*2π)/19166 weeks
321-.00529 -.00865 (321*2π)/19166 weeks
322-.00613 -.0084 (322*2π)/19166 weeks
323-.00507 -.00739 (323*2π)/19166 weeks
324-.00335 -.00933 (324*2π)/19166 weeks
325-.00734 -.0085 (325*2π)/19166 weeks
326-.0054 -.00725 (326*2π)/19166 weeks
327-.00468 -.00783 (327*2π)/19166 weeks
328-.00462 -.00818 (328*2π)/19166 weeks
329-.00545 -.00831 (329*2π)/19166 weeks
330-.00597 -.00779 (330*2π)/19166 weeks
331-.00587 -.00708 (331*2π)/19166 weeks
332-.00403 -.00762 (332*2π)/19166 weeks
333-.00533 -.00886 (333*2π)/19166 weeks
334-.0048 -.00794 (334*2π)/19166 weeks
335-.00504 -.0083 (335*2π)/19166 weeks
336-.00518 -.00761 (336*2π)/19166 weeks
337-.00518 -.00819 (337*2π)/19166 weeks
338-.00516 -.00785 (338*2π)/19166 weeks
339-.00505 -.00829 (339*2π)/19166 weeks
340-.00438 -.00659 (340*2π)/19166 weeks
341-.00465 -.00911 (341*2π)/19166 weeks
342-.00528 -.00805 (342*2π)/19166 weeks
343-.00392 -.00768 (343*2π)/19166 weeks
344-.00466 -.00852 (344*2π)/19166 weeks
345-.00513 -.00699 (345*2π)/19166 weeks
346-.00479 -.00745 (346*2π)/19166 weeks
347-.00433 -.00758 (347*2π)/19166 weeks
348-.00539 -.0083 (348*2π)/19166 weeks
349-.00404 -.00755 (349*2π)/19165 weeks
350-.00437 -.00743 (350*2π)/19165 weeks
351-.00529 -.00842 (351*2π)/19165 weeks
352-.00583 -.00708 (352*2π)/19165 weeks
353-.00422 -.00738 (353*2π)/19165 weeks
354-.00469 -.00794 (354*2π)/19165 weeks
355-.00474 -.0081 (355*2π)/19165 weeks
356-.00565 -.00773 (356*2π)/19165 weeks
357-.00576 -.00662 (357*2π)/19165 weeks
358-.00389 -.0073 (358*2π)/19165 weeks
359-.0045 -.00729 (359*2π)/19165 weeks
360-.0035 -.00664 (360*2π)/19165 weeks
361-.00388 -.00805 (361*2π)/19165 weeks
362-.00517 -.00802 (362*2π)/19165 weeks
363-.00479 -.00779 (363*2π)/19165 weeks
364-.00521 -.00766 (364*2π)/19165 weeks
365-.00483 -.00598 (365*2π)/19165 weeks
366-.00472 -.00695 (366*2π)/19165 weeks
367-.00414 -.00693 (367*2π)/19165 weeks
368-.00477 -.00839 (368*2π)/19165 weeks
369-.00512 -.00618 (369*2π)/19165 weeks
370-.00299 -.00717 (370*2π)/19165 weeks
371-.00474 -.00797 (371*2π)/19165 weeks
372-.00478 -.00703 (372*2π)/19165 weeks
373-.00509 -.00695 (373*2π)/19165 weeks
374-.00404 -.0068 (374*2π)/19165 weeks
375-.00382 -.00701 (375*2π)/19165 weeks
376-.00479 -.00746 (376*2π)/19165 weeks
377-.00486 -.00627 (377*2π)/19165 weeks
378-.00456 -.00653 (378*2π)/19165 weeks
379-.00473 -.00756