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# Fourier Analysis of VSIAX (VANGUARD SMALL-CAP VALUE INDEX FUND ADMIRAL SHARES)

VSIAX (VANGUARD SMALL-CAP VALUE INDEX FUND ADMIRAL SHARES) appears to have interesting cyclic behaviour every 28 weeks (1.2748*sine), 31 weeks (1.2225*sine), and 34 weeks (.7553*sine).

VSIAX (VANGUARD SMALL-CAP VALUE INDEX FUND ADMIRAL SHARES) has an average price of 40.01 (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 3/19/2018 for VSIAX (VANGUARD SMALL-CAP VALUE INDEX FUND ADMIRAL SHARES), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
040.00903   0
1-.95037 -8.81309 (1*2π)/339339 weeks
21.32322 -7.09729 (2*2π)/339170 weeks
3-.62414 -3.77648 (3*2π)/339113 weeks
4.18961 -1.68515 (4*2π)/33985 weeks
5.39453 -2.41256 (5*2π)/33968 weeks
6-.36522 -1.6688 (6*2π)/33957 weeks
7-.00106 -1.90442 (7*2π)/33948 weeks
8-.39019 -1.71738 (8*2π)/33942 weeks
9-.43295 -1.33606 (9*2π)/33938 weeks
10-.38169 -.75529 (10*2π)/33934 weeks
11-.00916 -1.22246 (11*2π)/33931 weeks
12-.25369 -1.27482 (12*2π)/33928 weeks
13-.2762 -.82313 (13*2π)/33926 weeks
14.1252 -.85222 (14*2π)/33924 weeks
15-.25351 -.4483 (15*2π)/33923 weeks
16.14901 -.36055 (16*2π)/33921 weeks
17-.10141 -.85518 (17*2π)/33920 weeks
18-.38498 -.67624 (18*2π)/33919 weeks
19-.01353 -.22747 (19*2π)/33918 weeks
20-.07165 -.68427 (20*2π)/33917 weeks
21-.21929 -.44442 (21*2π)/33916 weeks
22-.2079 -.3798 (22*2π)/33915 weeks
23-.2727 -.35025 (23*2π)/33915 weeks
24-.06621 -.35601 (24*2π)/33914 weeks
25.00949 -.22208 (25*2π)/33914 weeks
26-.00047 -.45542 (26*2π)/33913 weeks
27-.12403 -.24824 (27*2π)/33913 weeks
28-.12029 -.37767 (28*2π)/33912 weeks
29.0829 -.2329 (29*2π)/33912 weeks
30-.25443 -.48105 (30*2π)/33911 weeks
31-.02963 -.55198 (31*2π)/33911 weeks
32-.13088 -.40908 (32*2π)/33911 weeks
33-.19846 -.34549 (33*2π)/33910 weeks
34-.15789 -.20185 (34*2π)/33910 weeks
35.07945 -.41053 (35*2π)/33910 weeks
36-.109 -.25081 (36*2π)/3399 weeks
37-.19376 -.30413 (37*2π)/3399 weeks
38-.12026 -.24063 (38*2π)/3399 weeks
39-.11778 -.35716 (39*2π)/3399 weeks
40.06208 -.29373 (40*2π)/3398 weeks
41-.26699 -.29529 (41*2π)/3398 weeks
42-.09548 -.36874 (42*2π)/3398 weeks
43-.12501 -.26409 (43*2π)/3398 weeks
44-.07268 -.28259 (44*2π)/3398 weeks
45-.25395 -.30083 (45*2π)/3398 weeks
46-.16127 -.24036 (46*2π)/3397 weeks
47-.22131 -.22832 (47*2π)/3397 weeks
48-.09286 -.3015 (48*2π)/3397 weeks
49-.20515 -.22096 (49*2π)/3397 weeks
50-.16171 -.30505 (50*2π)/3397 weeks
51-.23552 -.2894 (51*2π)/3397 weeks
52-.20184 -.23891 (52*2π)/3397 weeks
53-.17115 -.18163 (53*2π)/3396 weeks
54-.06257 -.21646 (54*2π)/3396 weeks
55-.21254 -.19432 (55*2π)/3396 weeks
56-.12282 -.08515 (56*2π)/3396 weeks
57-.04006 -.11811 (57*2π)/3396 weeks
58-.07505 -.21729 (58*2π)/3396 weeks
59-.16784 -.23731 (59*2π)/3396 weeks
60-.11338 -.12787 (60*2π)/3396 weeks
61-.05679 -.15271 (61*2π)/3396 weeks
62-.17221 -.1773 (62*2π)/3395 weeks
63-.09501 -.07817 (63*2π)/3395 weeks
64-.08598 -.16114 (64*2π)/3395 weeks
65-.09586 -.23868 (65*2π)/3395 weeks
66.00038 -.10217 (66*2π)/3395 weeks
67-.03572 -.22001 (67*2π)/3395 weeks
68-.12044 -.09605 (68*2π)/3395 weeks
69-.0565 -.11766 (69*2π)/3395 weeks
70-.08925 -.11469 (70*2π)/3395 weeks
71-.13934 -.10612 (71*2π)/3395 weeks
72-.02101 -.15162 (72*2π)/3395 weeks
73-.1202 -.18556 (73*2π)/3395 weeks
74-.16351 -.06398 (74*2π)/3395 weeks
75-.08123 -.14583 (75*2π)/3395 weeks
76-.0637 -.13369 (76*2π)/3394 weeks
77-.12209 -.04121 (77*2π)/3394 weeks
78-.02974 -.13085 (78*2π)/3394 weeks
79-.12096 -.13788 (79*2π)/3394 weeks
80-.11119 -.15181 (80*2π)/3394 weeks
81-.06249 -.09488 (81*2π)/3394 weeks
82-.11868 -.22001 (82*2π)/3394 weeks
83-.21154 -.06492 (83*2π)/3394 weeks
84-.09193 -.1302 (84*2π)/3394 weeks
85-.18082 -.08302 (85*2π)/3394 weeks
86-.11685 -.05503 (86*2π)/3394 weeks
87-.12997 -.18502 (87*2π)/3394 weeks
88-.18937 -.14552 (88*2π)/3394 weeks
89-.13509 -.01004 (89*2π)/3394 weeks
90-.08891 -.10993 (90*2π)/3394 weeks
91-.15591 -.07739 (91*2π)/3394 weeks
92-.1311 -.14053 (92*2π)/3394 weeks
93-.18738 -.10487 (93*2π)/3394 weeks
94-.15039 -.06469 (94*2π)/3394 weeks
95-.08075 -.07955 (95*2π)/3394 weeks
96-.12006 -.11745 (96*2π)/3394 weeks
97-.17356 -.03522 (97*2π)/3393 weeks
98-.13678 -.07325 (98*2π)/3393 weeks
99-.11003 -.06266 (99*2π)/3393 weeks
100-.07692 -.06139 (100*2π)/3393 weeks
101-.09776 -.14206 (101*2π)/3393 weeks
102-.1103 -.04897 (102*2π)/3393 weeks
103-.10736 -.01994 (103*2π)/3393 weeks
104-.0946 -.03369 (104*2π)/3393 weeks
105-.11719 -.02384 (105*2π)/3393 weeks
106-.11505 -.09856 (106*2π)/3393 weeks
107-.11753 -.01886 (107*2π)/3393 weeks
108-.08194 -.04536 (108*2π)/3393 weeks
109-.11932 -.04455 (109*2π)/3393 weeks
110-.09111 -.03992 (110*2π)/3393 weeks
111-.06548 -.03329 (111*2π)/3393 weeks
112-.08226 -.05407 (112*2π)/3393 weeks
113-.03491 -.01566 (113*2π)/3393 weeks
114-.08624 -.05807 (114*2π)/3393 weeks
115-.12827 -.03042 (115*2π)/3393 weeks
116-.07431 -.05224 (116*2π)/3393 weeks
117-.09789 .01074 (117*2π)/3393 weeks
118-.06375 -.02043 (118*2π)/3393 weeks
119-.09149 -.00999 (119*2π)/3393 weeks
120-.06001 -.02249 (120*2π)/3393 weeks
121-.13438 -.06024 (121*2π)/3393 weeks
122-.09384 -.07131 (122*2π)/3393 weeks
123-.07113 -.02967 (123*2π)/3393 weeks
124-.09707 -.05272 (124*2π)/3393 weeks
125-.13257 -.10539 (125*2π)/3393 weeks
126-.12253 -.07486 (126*2π)/3393 weeks
127-.08084 -.1137 (127*2π)/3393 weeks
128-.13023 -.05967 (128*2π)/3393 weeks
129-.11202 -.071 (129*2π)/3393 weeks
130-.11954 -.04315 (130*2π)/3393 weeks
131-.08281 -.06883 (131*2π)/3393 weeks
132-.13074 -.04435 (132*2π)/3393 weeks
133-.10684 -.08664 (133*2π)/3393 weeks
134-.119 -.08668 (134*2π)/3393 weeks
135-.13537 -.05963 (135*2π)/3393 weeks
136-.13448 -.06816 (136*2π)/3392 weeks
137-.08967 -.03977 (137*2π)/3392 weeks
138-.11556 -.05868 (138*2π)/3392 weeks
139-.08293 -.08098 (139*2π)/3392 weeks
140-.11505 -.04497 (140*2π)/3392 weeks
141-.07374 -.03184 (141*2π)/3392 weeks
142-.16463 -.08384 (142*2π)/3392 weeks
143-.12774 .01437 (143*2π)/3392 weeks
144-.08005 -.02537 (144*2π)/3392 weeks
145-.0722 -.03801 (145*2π)/3392 weeks
146-.11547 -.06488 (146*2π)/3392 weeks
147-.09675 -.13081 (147*2π)/3392 weeks
148-.09009 -.00898 (148*2π)/3392 weeks
149-.06676 .00082 (149*2π)/3392 weeks
150-.07032 -.01296 (150*2π)/3392 weeks
151-.09692 -.04434 (151*2π)/3392 weeks
152-.15399 -.05253 (152*2π)/3392 weeks
153-.07277 .01511 (153*2π)/3392 weeks
154-.15427 -.00054 (154*2π)/3392 weeks
155-.08449 -.01387 (155*2π)/3392 weeks
156-.11681 .02955 (156*2π)/3392 weeks
157-.08646 -.06479 (157*2π)/3392 weeks
158-.08936 -.00294 (158*2π)/3392 weeks
159-.09908 -.00848 (159*2π)/3392 weeks
160-.04442 -.01376 (160*2π)/3392 weeks
161-.09286 -.02688 (161*2π)/3392 weeks
162-.17897 .02206 (162*2π)/3392 weeks
163-.08615 .01095 (163*2π)/3392 weeks
164-.10735 -.05452 (164*2π)/3392 weeks
165-.08874 .0163 (165*2π)/3392 weeks
166-.0894 -.04983 (166*2π)/3392 weeks
167-.17413 -.01792 (167*2π)/3392 weeks
168-.06639 .02318 (168*2π)/3392 weeks
169-.05334 -.00229 (169*2π)/3392 weeks
170-.05334 .00229 (170*2π)/3392 weeks
171-.06639 -.02318 (171*2π)/3392 weeks
172-.17413 .01792 (172*2π)/3392 weeks
173-.0894 .04983 (173*2π)/3392 weeks
174-.08874 -.0163 (174*2π)/3392 weeks
175-.10735 .05452 (175*2π)/3392 weeks
176-.08615 -.01095 (176*2π)/3392 weeks
177-.17897 -.02206 (177*2π)/3392 weeks
178-.09286 .02688 (178*2π)/3392 weeks
179-.04442 .01376 (179*2π)/3392 weeks
180-.09908 .00848 (180*2π)/3392 weeks
181-.08936 .00294 (181*2π)/3392 weeks
182-.08646 .06479 (182*2π)/3392 weeks
183-.11681 -.02955 (183*2π)/3392 weeks
184-.08449 .01387 (184*2π)/3392 weeks
185-.15427 .00054 (185*2π)/3392 weeks
186-.07277 -.01511 (186*2π)/3392 weeks
187-.15399 .05253 (187*2π)/3392 weeks
188-.09692 .04434 (188*2π)/3392 weeks
189-.07032 .01296 (189*2π)/3392 weeks
190-.06676 -.00082 (190*2π)/3392 weeks
191-.09009 .00898 (191*2π)/3392 weeks
192-.09675 .13081 (192*2π)/3392 weeks
193-.11547 .06488 (193*2π)/3392 weeks
194-.0722 .03801 (194*2π)/3392 weeks
195-.08005 .02537 (195*2π)/3392 weeks
196-.12774 -.01437 (196*2π)/3392 weeks
197-.16463 .08384 (197*2π)/3392 weeks
198-.07374 .03184 (198*2π)/3392 weeks
199-.11505 .04497 (199*2π)/3392 weeks
200-.08293 .08098 (200*2π)/3392 weeks
201-.11556 .05868 (201*2π)/3392 weeks
202-.08967 .03977 (202*2π)/3392 weeks
203-.13448 .06816 (203*2π)/3392 weeks
204-.13537 .05963 (204*2π)/3392 weeks
205-.119 .08668 (205*2π)/3392 weeks
206-.10684 .08664 (206*2π)/3392 weeks
207-.13074 .04435 (207*2π)/3392 weeks
208-.08281 .06883 (208*2π)/3392 weeks
209-.11954 .04315 (209*2π)/3392 weeks
210-.11202 .071 (210*2π)/3392 weeks
211-.13023 .05967 (211*2π)/3392 weeks
212-.08084 .1137 (212*2π)/3392 weeks
213-.12253 .07486 (213*2π)/3392 weeks
214-.13257 .10539 (214*2π)/3392 weeks
215-.09707 .05272 (215*2π)/3392 weeks
216-.07113 .02967 (216*2π)/3392 weeks
217-.09384 .07131 (217*2π)/3392 weeks
218-.13438 .06024 (218*2π)/3392 weeks
219-.06001 .02249 (219*2π)/3392 weeks
220-.09149 .00999 (220*2π)/3392 weeks
221-.06375 .02043 (221*2π)/3392 weeks
222-.09789 -.01074 (222*2π)/3392 weeks
223-.07431 .05224 (223*2π)/3392 weeks
224-.12827 .03042 (224*2π)/3392 weeks
225-.08624 .05807 (225*2π)/3392 weeks
226-.03491 .01566 (226*2π)/3392 weeks
227-.08226 .05407 (227*2π)/3391 weeks
228-.06548 .03329 (228*2π)/3391 weeks
229-.09111 .03992 (229*2π)/3391 weeks
230-.11932 .04455 (230*2π)/3391 weeks
231-.08194 .04536 (231*2π)/3391 weeks
232-.11753 .01886 (232*2π)/3391 weeks
233-.11505 .09856 (233*2π)/3391 weeks
234-.11719 .02384 (234*2π)/3391 weeks
235-.0946 .03369 (235*2π)/3391 weeks
236-.10736 .01994 (236*2π)/3391 weeks
237-.1103 .04897 (237*2π)/3391 weeks
238-.09776 .14206 (238*2π)/3391 weeks
239-.07692 .06139 (239*2π)/3391 weeks
240-.11003 .06266 (240*2π)/3391 weeks
241-.13678 .07325 (241*2π)/3391 weeks
242-.17356 .03522 (242*2π)/3391 weeks
243-.12006 .11745 (243*2π)/3391 weeks
244-.08075 .07955 (244*2π)/3391 weeks
245-.15039 .06469 (245*2π)/3391 weeks
246-.18738 .10487 (246*2π)/3391 weeks
247-.1311 .14053 (247*2π)/3391 weeks
248-.15591 .07739 (248*2π)/3391 weeks
249-.08891 .10993 (249*2π)/3391 weeks
250-.13509 .01004 (250*2π)/3391 weeks
251-.18937 .14552 (251*2π)/3391 weeks
252-.12997 .18502 (252*2π)/3391 weeks
253-.11685 .05503 (253*2π)/3391 weeks
254-.18082 .08302 (254*2π)/3391 weeks
255-.09193 .1302 (255*2π)/3391 weeks
256-.21154 .06492 (256*2π)/3391 weeks
257-.11868 .22001 (257*2π)/3391 weeks
258-.06249 .09488 (258*2π)/3391 weeks
259-.11119 .15181 (259*2π)/3391 weeks
260-.12096 .13788 (260*2π)/3391 weeks
261-.02974 .13085 (261*2π)/3391 weeks
262-.12209 .04121 (262*2π)/3391 weeks
263-.0637 .13369 (263*2π)/3391 weeks
264-.08123 .14583 (264*2π)/3391 weeks
265-.16351 .06398 (265*2π)/3391 weeks
266-.1202 .18556 (266*2π)/3391 weeks
267-.02101 .15162 (267*2π)/3391 weeks
268-.13934 .10612 (268*2π)/3391 weeks
269-.08925 .11469 (269*2π)/3391 weeks
270-.0565 .11766 (270*2π)/3391 weeks
271-.12044 .09605 (271*2π)/3391 weeks
272-.03572 .22001 (272*2π)/3391 weeks
273.00038 .10217 (273*2π)/3391 weeks
274-.09586 .23868 (274*2π)/3391 weeks
275-.08598 .16114 (275*2π)/3391 weeks
276-.09501 .07817 (276*2π)/3391 weeks
277-.17221 .1773 (277*2π)/3391 weeks
278-.05679 .15271 (278*2π)/3391 weeks
279-.11338 .12787 (279*2π)/3391 weeks
280-.16784 .23731 (280*2π)/3391 weeks
281-.07505 .21729 (281*2π)/3391 weeks
282-.04006 .11811 (282*2π)/3391 weeks
283-.12282 .08515 (283*2π)/3391 weeks
284-.21254 .19432 (284*2π)/3391 weeks
285-.06257 .21646 (285*2π)/3391 weeks
286-.17115 .18163 (286*2π)/3391 weeks
287-.20184 .23891 (287*2π)/3391 weeks
288-.23552 .2894 (288*2π)/3391 weeks
289-.16171 .30505 (289*2π)/3391 weeks
290-.20515 .22096 (290*2π)/3391 weeks
291-.09286 .3015 (291*2π)/3391 weeks
292-.22131 .22832 (292*2π)/3391 weeks
293-.16127 .24036 (293*2π)/3391 weeks
294-.25395 .30083 (294*2π)/3391 weeks
295-.07268 .28259 (295*2π)/3391 weeks
296-.12501 .26409 (296*2π)/3391 weeks
297-.09548 .36874 (297*2π)/3391 weeks
298-.26699 .29529 (298*2π)/3391 weeks
299.06208 .29373 (299*2π)/3391 weeks
300-.11778 .35716 (300*2π)/3391 weeks
301-.12026 .24063 (301*2π)/3391 weeks
302-.19376 .30413 (302*2π)/3391 weeks
303-.109 .25081 (303*2π)/3391 weeks
304.07945 .41053 (304*2π)/3391 weeks
305-.15789 .20185 (305*2π)/3391 weeks
306-.19846 .34549 (306*2π)/3391 weeks
307-.13088 .40908 (307*2π)/3391 weeks
308-.02963 .55198 (308*2π)/3391 weeks
309-.25443 .48105 (309*2π)/3391 weeks
310.0829 .2329 (310*2π)/3391 weeks
311-.12029 .37767 (311*2π)/3391 weeks
312-.12403 .24824 (312*2π)/3391 weeks
313-.00047 .45542 (313*2π)/3391 weeks
314.00949 .22208 (314*2π)/3391 weeks
315-.06621 .35601 (315*2π)/3391 weeks
316-.2727 .35025 (316*2π)/3391 weeks
317-.2079 .3798 (317*2π)/3391 weeks
318-.21929 .44442 (318*2π)/3391 weeks
319-.07165 .68427 (319*2π)/3391 weeks
320-.01353 .22747 (320*2π)/3391 weeks
321-.38498 .67624 (321*2π)/3391 weeks
322-.10141 .85518 (322*2π)/3391 weeks
323.14901 .36055 (323*2π)/3391 weeks
324-.25351 .4483 (324*2π)/3391 weeks
325.1252 .85222 (325*2π)/3391 weeks
326-.2762 .82313 (326*2π)/3391 weeks
327-.25369 1.27482 (327*2π)/3391 weeks
328-.00916 1.22246 (328*2π)/3391 weeks
329-.38169 .75529 (329*2π)/3391 weeks
330-.43295 1.33606 (330*2π)/3391 weeks
331-.39019 1.71738 (331*2π)/3391 weeks
332-.00106 1.90442 (332*2π)/3391 weeks
333-.36522 1.6688 (333*2π)/3391 weeks
334.39453 2.41256 (334*2π)/3391 weeks
335.18961 1.68515 (335*2π)/3391 weeks
336-.62414 3.77648 (336*2π)/3391 weeks
3371.32322 7.09729 (337*2π)/3391 weeks