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# Fourier Analysis of VSGAX (VANGUARD SMALL-CAP GROWTH INDEX FUND ADMIRAL SHARES)

VSGAX (VANGUARD SMALL-CAP GROWTH INDEX FUND ADMIRAL SHARES) appears to have interesting cyclic behaviour every 31 weeks (1.1972*sine), 29 weeks (1.0483*sine), and 34 weeks (.8257*sine).

VSGAX (VANGUARD SMALL-CAP GROWTH INDEX FUND ADMIRAL SHARES) has an average price of 40.86 (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 9/27/2011 to 4/23/2018 for VSGAX (VANGUARD SMALL-CAP GROWTH INDEX FUND ADMIRAL SHARES), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
040.85926   0
1-1.22416 -7.19589 (1*2π)/344344 weeks
21.71065 -6.71045 (2*2π)/344172 weeks
3.00565 -4.04515 (3*2π)/344115 weeks
4.25306 -1.50832 (4*2π)/34486 weeks
5.0345 -2.98248 (5*2π)/34469 weeks
6-.53916 -1.47692 (6*2π)/34457 weeks
7-.04254 -1.65704 (7*2π)/34449 weeks
8-.34054 -1.72162 (8*2π)/34443 weeks
9-.41089 -1.34741 (9*2π)/34438 weeks
10-.39115 -.8257 (10*2π)/34434 weeks
11-.0885 -1.19722 (11*2π)/34431 weeks
12-.30163 -1.04831 (12*2π)/34429 weeks
13-.12849 -.89788 (13*2π)/34426 weeks
14.24004 -.83423 (14*2π)/34425 weeks
15-.10237 -.42097 (15*2π)/34423 weeks
16.24284 -.61154 (16*2π)/34422 weeks
17-.26089 -.75348 (17*2π)/34420 weeks
18-.48483 -.479 (18*2π)/34419 weeks
19.21205 -.47895 (19*2π)/34418 weeks
20-.28986 -.55359 (20*2π)/34417 weeks
21-.15179 -.32175 (21*2π)/34416 weeks
22-.01135 -.35471 (22*2π)/34416 weeks
23-.13445 -.42257 (23*2π)/34415 weeks
24-.09945 -.52576 (24*2π)/34414 weeks
25.00332 -.42386 (25*2π)/34414 weeks
26-.25501 -.52792 (26*2π)/34413 weeks
27-.06058 -.25693 (27*2π)/34413 weeks
28-.20261 -.36516 (28*2π)/34412 weeks
29-.10538 -.48222 (29*2π)/34412 weeks
30-.38345 -.16987 (30*2π)/34411 weeks
31-.24847 -.45249 (31*2π)/34411 weeks
32-.10081 -.27592 (32*2π)/34411 weeks
33-.06168 -.27645 (33*2π)/34410 weeks
34-.04501 -.34135 (34*2π)/34410 weeks
35-.24153 -.42677 (35*2π)/34410 weeks
36-.02178 -.14295 (36*2π)/34410 weeks
37-.16565 -.1621 (37*2π)/3449 weeks
38-.12943 -.27714 (38*2π)/3449 weeks
39-.24802 -.23843 (39*2π)/3449 weeks
40-.07495 -.27955 (40*2π)/3449 weeks
41-.01397 -.01773 (41*2π)/3448 weeks
42-.16171 -.28055 (42*2π)/3448 weeks
43-.01311 -.30289 (43*2π)/3448 weeks
44-.0953 -.22835 (44*2π)/3448 weeks
45-.00516 -.14519 (45*2π)/3448 weeks
46-.05958 -.34781 (46*2π)/3447 weeks
47-.13109 -.20829 (47*2π)/3447 weeks
48-.14676 -.31575 (48*2π)/3447 weeks
49-.04814 -.24708 (49*2π)/3447 weeks
50-.15347 -.27803 (50*2π)/3447 weeks
51-.06773 -.29855 (51*2π)/3447 weeks
52-.11671 -.36245 (52*2π)/3447 weeks
53-.16613 -.35024 (53*2π)/3446 weeks
54-.16323 -.25334 (54*2π)/3446 weeks
55-.03153 -.25548 (55*2π)/3446 weeks
56-.20939 -.30359 (56*2π)/3446 weeks
57-.18868 -.16045 (57*2π)/3446 weeks
58-.09763 -.13189 (58*2π)/3446 weeks
59-.10071 -.2159 (59*2π)/3446 weeks
60-.13647 -.25047 (60*2π)/3446 weeks
61-.13062 -.18181 (61*2π)/3446 weeks
62-.08655 -.18305 (62*2π)/3446 weeks
63-.20929 -.21121 (63*2π)/3445 weeks
64-.12632 -.0985 (64*2π)/3445 weeks
65-.12226 -.15948 (65*2π)/3445 weeks
66-.14114 -.22234 (66*2π)/3445 weeks
67-.01687 -.09324 (67*2π)/3445 weeks
68-.07142 -.18772 (68*2π)/3445 weeks
69-.12498 -.07263 (69*2π)/3445 weeks
70-.0431 -.1242 (70*2π)/3445 weeks
71-.1124 -.10893 (71*2π)/3445 weeks
72-.13047 -.09938 (72*2π)/3445 weeks
73-.04784 -.16444 (73*2π)/3445 weeks
74-.15188 -.17114 (74*2π)/3445 weeks
75-.13241 -.00232 (75*2π)/3445 weeks
76-.0814 -.16753 (76*2π)/3445 weeks
77-.07355 -.14354 (77*2π)/3444 weeks
78-.08324 -.03349 (78*2π)/3444 weeks
79-.07826 -.19618 (79*2π)/3444 weeks
80-.15728 -.09509 (80*2π)/3444 weeks
81-.15279 -.12801 (81*2π)/3444 weeks
82-.0636 -.08713 (82*2π)/3444 weeks
83-.21314 -.13524 (83*2π)/3444 weeks
84-.16433 .03352 (84*2π)/3444 weeks
85-.11613 -.12962 (85*2π)/3444 weeks
86-.13513 -.00916 (86*2π)/3444 weeks
87-.10464 -.07751 (87*2π)/3444 weeks
88-.20401 -.13673 (88*2π)/3444 weeks
89-.16752 -.02305 (89*2π)/3444 weeks
90-.00725 -.01709 (90*2π)/3444 weeks
91-.11653 -.12699 (91*2π)/3444 weeks
92-.11582 -.04274 (92*2π)/3444 weeks
93-.12737 -.10269 (93*2π)/3444 weeks
94-.13188 -.05823 (94*2π)/3444 weeks
95-.07653 -.09254 (95*2π)/3444 weeks
96-.08408 -.1597 (96*2π)/3444 weeks
97-.13206 -.06232 (97*2π)/3444 weeks
98-.06127 -.0384 (98*2π)/3444 weeks
99-.10595 -.11202 (99*2π)/3443 weeks
100-.08489 -.12254 (100*2π)/3443 weeks
101-.08659 -.13031 (101*2π)/3443 weeks
102-.13377 -.12192 (102*2π)/3443 weeks
103-.04275 -.09095 (103*2π)/3443 weeks
104-.08184 -.09998 (104*2π)/3443 weeks
105-.09237 -.0836 (105*2π)/3443 weeks
106-.11352 -.08375 (106*2π)/3443 weeks
107-.14786 -.07801 (107*2π)/3443 weeks
108-.07419 -.11238 (108*2π)/3443 weeks
109-.15887 -.12873 (109*2π)/3443 weeks
110-.13468 -.0737 (110*2π)/3443 weeks
111-.13848 -.12103 (111*2π)/3443 weeks
112-.1554 -.0834 (112*2π)/3443 weeks
113-.14308 -.01845 (113*2π)/3443 weeks
114-.12181 -.07162 (114*2π)/3443 weeks
115-.1197 .02824 (115*2π)/3443 weeks
116-.12371 -.00895 (116*2π)/3443 weeks
117-.16683 -.04203 (117*2π)/3443 weeks
118-.10627 -.02592 (118*2π)/3443 weeks
119-.14377 .0154 (119*2π)/3443 weeks
120-.11314 .01071 (120*2π)/3443 weeks
121-.12578 .01901 (121*2π)/3443 weeks
122-.09687 .04488 (122*2π)/3443 weeks
123-.14327 -.03049 (123*2π)/3443 weeks
124-.09582 -.05468 (124*2π)/3443 weeks
125-.1056 .02338 (125*2π)/3443 weeks
126-.12394 .00706 (126*2π)/3443 weeks
127-.09485 -.07219 (127*2π)/3443 weeks
128-.11978 -.05045 (128*2π)/3443 weeks
129-.04964 -.07017 (129*2π)/3443 weeks
130-.09274 -.04925 (130*2π)/3443 weeks
131-.08898 -.08285 (131*2π)/3443 weeks
132-.12955 -.04076 (132*2π)/3443 weeks
133-.05564 -.05538 (133*2π)/3443 weeks
134-.12692 -.04844 (134*2π)/3443 weeks
135-.08783 -.0645 (135*2π)/3443 weeks
136-.09621 -.07858 (136*2π)/3443 weeks
137-.10772 -.04621 (137*2π)/3443 weeks
138-.09544 -.08212 (138*2π)/3442 weeks
139-.09027 -.05739 (139*2π)/3442 weeks
140-.1155 -.07398 (140*2π)/3442 weeks
141-.08261 -.07594 (141*2π)/3442 weeks
142-.1045 -.05241 (142*2π)/3442 weeks
143-.06243 -.02903 (143*2π)/3442 weeks
144-.17685 -.06437 (144*2π)/3442 weeks
145-.07745 .01843 (145*2π)/3442 weeks
146-.0637 -.04531 (146*2π)/3442 weeks
147-.07262 -.05733 (147*2π)/3442 weeks
148-.11571 -.0655 (148*2π)/3442 weeks
149-.12891 -.11392 (149*2π)/3442 weeks
150-.03606 -.00464 (150*2π)/3442 weeks
151-.04462 -.02708 (151*2π)/3442 weeks
152-.06656 -.02375 (152*2π)/3442 weeks
153-.11216 -.04656 (153*2π)/3442 weeks
154-.14237 -.00809 (154*2π)/3442 weeks
155-.03968 -.00259 (155*2π)/3442 weeks
156-.12188 .01562 (156*2π)/3442 weeks
157-.0974 -.05779 (157*2π)/3442 weeks
158-.08228 .00379 (158*2π)/3442 weeks
159-.13055 -.08379 (159*2π)/3442 weeks
160-.05655 -.02588 (160*2π)/3442 weeks
161-.08463 -.01618 (161*2π)/3442 weeks
162-.09132 -.05994 (162*2π)/3442 weeks
163-.09724 .00555 (163*2π)/3442 weeks
164-.10644 .04438 (164*2π)/3442 weeks
165-.0954 -.04723 (165*2π)/3442 weeks
166-.15513 -.03364 (166*2π)/3442 weeks
167-.07672 -.01316 (167*2π)/3442 weeks
168-.13202 -.03144 (168*2π)/3442 weeks
169-.09767 .04051 (169*2π)/3442 weeks
170-.06407 -.08767 (170*2π)/3442 weeks
171-.1062 -.02524 (171*2π)/3442 weeks
172-.10506   (172*2π)/3442 weeks
173-.1062 .02524 (173*2π)/3442 weeks
174-.06407 .08767 (174*2π)/3442 weeks
175-.09767 -.04051 (175*2π)/3442 weeks
176-.13202 .03144 (176*2π)/3442 weeks
177-.07672 .01316 (177*2π)/3442 weeks
178-.15513 .03364 (178*2π)/3442 weeks
179-.0954 .04723 (179*2π)/3442 weeks
180-.10644 -.04438 (180*2π)/3442 weeks
181-.09724 -.00555 (181*2π)/3442 weeks
182-.09132 .05994 (182*2π)/3442 weeks
183-.08463 .01618 (183*2π)/3442 weeks
184-.05655 .02588 (184*2π)/3442 weeks
185-.13055 .08379 (185*2π)/3442 weeks
186-.08228 -.00379 (186*2π)/3442 weeks
187-.0974 .05779 (187*2π)/3442 weeks
188-.12188 -.01562 (188*2π)/3442 weeks
189-.03968 .00259 (189*2π)/3442 weeks
190-.14237 .00809 (190*2π)/3442 weeks
191-.11216 .04656 (191*2π)/3442 weeks
192-.06656 .02375 (192*2π)/3442 weeks
193-.04462 .02708 (193*2π)/3442 weeks
194-.03606 .00464 (194*2π)/3442 weeks
195-.12891 .11392 (195*2π)/3442 weeks
196-.11571 .0655 (196*2π)/3442 weeks
197-.07262 .05733 (197*2π)/3442 weeks
198-.0637 .04531 (198*2π)/3442 weeks
199-.07745 -.01843 (199*2π)/3442 weeks
200-.17685 .06437 (200*2π)/3442 weeks
201-.06243 .02903 (201*2π)/3442 weeks
202-.1045 .05241 (202*2π)/3442 weeks
203-.08261 .07594 (203*2π)/3442 weeks
204-.1155 .07398 (204*2π)/3442 weeks
205-.09027 .05739 (205*2π)/3442 weeks
206-.09544 .08212 (206*2π)/3442 weeks
207-.10772 .04621 (207*2π)/3442 weeks
208-.09621 .07858 (208*2π)/3442 weeks
209-.08783 .0645 (209*2π)/3442 weeks
210-.12692 .04844 (210*2π)/3442 weeks
211-.05564 .05538 (211*2π)/3442 weeks
212-.12955 .04076 (212*2π)/3442 weeks
213-.08898 .08285 (213*2π)/3442 weeks
214-.09274 .04925 (214*2π)/3442 weeks
215-.04964 .07017 (215*2π)/3442 weeks
216-.11978 .05045 (216*2π)/3442 weeks
217-.09485 .07219 (217*2π)/3442 weeks
218-.12394 -.00706 (218*2π)/3442 weeks
219-.1056 -.02338 (219*2π)/3442 weeks
220-.09582 .05468 (220*2π)/3442 weeks
221-.14327 .03049 (221*2π)/3442 weeks
222-.09687 -.04488 (222*2π)/3442 weeks
223-.12578 -.01901 (223*2π)/3442 weeks
224-.11314 -.01071 (224*2π)/3442 weeks
225-.14377 -.0154 (225*2π)/3442 weeks
226-.10627 .02592 (226*2π)/3442 weeks
227-.16683 .04203 (227*2π)/3442 weeks
228-.12371 .00895 (228*2π)/3442 weeks
229-.1197 -.02824 (229*2π)/3442 weeks
230-.12181 .07162 (230*2π)/3441 weeks
231-.14308 .01845 (231*2π)/3441 weeks
232-.1554 .0834 (232*2π)/3441 weeks
233-.13848 .12103 (233*2π)/3441 weeks
234-.13468 .0737 (234*2π)/3441 weeks
235-.15887 .12873 (235*2π)/3441 weeks
236-.07419 .11238 (236*2π)/3441 weeks
237-.14786 .07801 (237*2π)/3441 weeks
238-.11352 .08375 (238*2π)/3441 weeks
239-.09237 .0836 (239*2π)/3441 weeks
240-.08184 .09998 (240*2π)/3441 weeks
241-.04275 .09095 (241*2π)/3441 weeks
242-.13377 .12192 (242*2π)/3441 weeks
243-.08659 .13031 (243*2π)/3441 weeks
244-.08489 .12254 (244*2π)/3441 weeks
245-.10595 .11202 (245*2π)/3441 weeks
246-.06127 .0384 (246*2π)/3441 weeks
247-.13206 .06232 (247*2π)/3441 weeks
248-.08408 .1597 (248*2π)/3441 weeks
249-.07653 .09254 (249*2π)/3441 weeks
250-.13188 .05823 (250*2π)/3441 weeks
251-.12737 .10269 (251*2π)/3441 weeks
252-.11582 .04274 (252*2π)/3441 weeks
253-.11653 .12699 (253*2π)/3441 weeks
254-.00725 .01709 (254*2π)/3441 weeks
255-.16752 .02305 (255*2π)/3441 weeks
256-.20401 .13673 (256*2π)/3441 weeks
257-.10464 .07751 (257*2π)/3441 weeks
258-.13513 .00916 (258*2π)/3441 weeks
259-.11613 .12962 (259*2π)/3441 weeks
260-.16433 -.03352 (260*2π)/3441 weeks
261-.21314 .13524 (261*2π)/3441 weeks
262-.0636 .08713 (262*2π)/3441 weeks
263-.15279 .12801 (263*2π)/3441 weeks
264-.15728 .09509 (264*2π)/3441 weeks
265-.07826 .19618 (265*2π)/3441 weeks
266-.08324 .03349 (266*2π)/3441 weeks
267-.07355 .14354 (267*2π)/3441 weeks
268-.0814 .16753 (268*2π)/3441 weeks
269-.13241 .00232 (269*2π)/3441 weeks
270-.15188 .17114 (270*2π)/3441 weeks
271-.04784 .16444 (271*2π)/3441 weeks
272-.13047 .09938 (272*2π)/3441 weeks
273-.1124 .10893 (273*2π)/3441 weeks
274-.0431 .1242 (274*2π)/3441 weeks
275-.12498 .07263 (275*2π)/3441 weeks
276-.07142 .18772 (276*2π)/3441 weeks
277-.01687 .09324 (277*2π)/3441 weeks
278-.14114 .22234 (278*2π)/3441 weeks
279-.12226 .15948 (279*2π)/3441 weeks
280-.12632 .0985 (280*2π)/3441 weeks
281-.20929 .21121 (281*2π)/3441 weeks
282-.08655 .18305 (282*2π)/3441 weeks
283-.13062 .18181 (283*2π)/3441 weeks
284-.13647 .25047 (284*2π)/3441 weeks
285-.10071 .2159 (285*2π)/3441 weeks
286-.09763 .13189 (286*2π)/3441 weeks
287-.18868 .16045 (287*2π)/3441 weeks
288-.20939 .30359 (288*2π)/3441 weeks
289-.03153 .25548 (289*2π)/3441 weeks
290-.16323 .25334 (290*2π)/3441 weeks
291-.16613 .35024 (291*2π)/3441 weeks
292-.11671 .36245 (292*2π)/3441 weeks
293-.06773 .29855 (293*2π)/3441 weeks
294-.15347 .27803 (294*2π)/3441 weeks
295-.04814 .24708 (295*2π)/3441 weeks
296-.14676 .31575 (296*2π)/3441 weeks
297-.13109 .20829 (297*2π)/3441 weeks
298-.05958 .34781 (298*2π)/3441 weeks
299-.00516 .14519 (299*2π)/3441 weeks
300-.0953 .22835 (300*2π)/3441 weeks
301-.01311 .30289 (301*2π)/3441 weeks
302-.16171 .28055 (302*2π)/3441 weeks
303-.01397 .01773 (303*2π)/3441 weeks
304-.07495 .27955 (304*2π)/3441 weeks
305-.24802 .23843 (305*2π)/3441 weeks
306-.12943 .27714 (306*2π)/3441 weeks
307-.16565 .1621 (307*2π)/3441 weeks
308-.02178 .14295 (308*2π)/3441 weeks
309-.24153 .42677 (309*2π)/3441 weeks
310-.04501 .34135 (310*2π)/3441 weeks
311-.06168 .27645 (311*2π)/3441 weeks
312-.10081 .27592 (312*2π)/3441 weeks
313-.24847 .45249 (313*2π)/3441 weeks
314-.38345 .16987 (314*2π)/3441 weeks
315-.10538 .48222 (315*2π)/3441 weeks
316-.20261 .36516 (316*2π)/3441 weeks
317-.06058 .25693 (317*2π)/3441 weeks
318-.25501 .52792 (318*2π)/3441 weeks
319.00332 .42386 (319*2π)/3441 weeks
320-.09945 .52576 (320*2π)/3441 weeks
321-.13445 .42257 (321*2π)/3441 weeks
322-.01135 .35471 (322*2π)/3441 weeks
323-.15179 .32175 (323*2π)/3441 weeks
324-.28986 .55359 (324*2π)/3441 weeks
325.21205 .47895 (325*2π)/3441 weeks
326-.48483 .479 (326*2π)/3441 weeks
327-.26089 .75348 (327*2π)/3441 weeks
328.24284 .61154 (328*2π)/3441 weeks
329-.10237 .42097 (329*2π)/3441 weeks
330.24004 .83423 (330*2π)/3441 weeks
331-.12849 .89788 (331*2π)/3441 weeks
332-.30163 1.04831 (332*2π)/3441 weeks
333-.0885 1.19722 (333*2π)/3441 weeks
334-.39115 .8257 (334*2π)/3441 weeks
335-.41089 1.34741 (335*2π)/3441 weeks
336-.34054 1.72162 (336*2π)/3441 weeks
337-.04254 1.65704 (337*2π)/3441 weeks
338-.53916 1.47692 (338*2π)/3441 weeks
339.0345 2.98248 (339*2π)/3441 weeks
340.25306 1.50832 (340*2π)/3441 weeks
341.00565 4.04515 (341*2π)/3441 weeks
3421.71065 6.71045 (342*2π)/3441 weeks