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# Fourier Analysis of VSCPX (VANGUARD SMALL-CAP INDEX FUND INSTITUTIONAL PLUS SHARES)

VSCPX (VANGUARD SMALL-CAP INDEX FUND INSTITUTIONAL PLUS SHARES) appears to have interesting cyclic behaviour every 38 weeks (4.1593*sine), 32 weeks (3.8953*sine), and 35 weeks (3.1575*sine).

VSCPX (VANGUARD SMALL-CAP INDEX FUND INSTITUTIONAL PLUS SHARES) has an average price of 139.6 (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 12/13/2010 to 4/16/2018 for VSCPX (VANGUARD SMALL-CAP INDEX FUND INSTITUTIONAL PLUS SHARES), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0139.5977   0
1-2.35516 -36.05644 (1*2π)/384384 weeks
210.64349 -22.26293 (2*2π)/384192 weeks
3.26235 -13.8374 (3*2π)/384128 weeks
4-1.24877 -7.39611 (4*2π)/38496 weeks
53.81298 -6.87545 (5*2π)/38477 weeks
6-.20185 -7.08419 (6*2π)/38464 weeks
7-.35237 -3.31338 (7*2π)/38455 weeks
8-1.01479 -4.67935 (8*2π)/38448 weeks
9-2.2074 -4.75498 (9*2π)/38443 weeks
10-1.99158 -4.15932 (10*2π)/38438 weeks
11-1.57348 -3.15753 (11*2π)/38435 weeks
12.56319 -3.89533 (12*2π)/38432 weeks
13-.25024 -3.42516 (13*2π)/38430 weeks
14-.80224 -2.04889 (14*2π)/38427 weeks
15-.53895 -1.66066 (15*2π)/38426 weeks
16-.41847 -2.95398 (16*2π)/38424 weeks
17.12263 -1.19163 (17*2π)/38423 weeks
18.81378 -1.73838 (18*2π)/38421 weeks
19-1.05549 -2.31176 (19*2π)/38420 weeks
20-1.51693 -1.7412 (20*2π)/38419 weeks
21-.01273 -.85211 (21*2π)/38418 weeks
22-.38889 -2.60259 (22*2π)/38417 weeks
23-.77949 -1.64946 (23*2π)/38417 weeks
24-.03875 -1.42384 (24*2π)/38416 weeks
25.37429 -1.30135 (25*2π)/38415 weeks
26.18596 -.8634 (26*2π)/38415 weeks
27.03784 -1.33498 (27*2π)/38414 weeks
28.23659 -1.0561 (28*2π)/38414 weeks
29-.60812 -1.5114 (29*2π)/38413 weeks
30-.74633 -.76727 (30*2π)/38413 weeks
31-.56868 -1.5789 (31*2π)/38412 weeks
32-.29799 -1.29191 (32*2π)/38412 weeks
33-.7171 -2.0829 (33*2π)/38412 weeks
34-.28238 -.65389 (34*2π)/38411 weeks
35-.95899 -1.17137 (35*2π)/38411 weeks
36-.31822 -1.00887 (36*2π)/38411 weeks
37-.06822 -.8832 (37*2π)/38410 weeks
38.19234 -.98322 (38*2π)/38410 weeks
39-.04569 -1.47517 (39*2π)/38410 weeks
40-.44355 -.3215 (40*2π)/38410 weeks
41-.29974 -.85665 (41*2π)/3849 weeks
42.04546 -.55286 (42*2π)/3849 weeks
43-.18837 -.67619 (43*2π)/3849 weeks
44-.65234 -.31548 (44*2π)/3849 weeks
45-.65596 -.88933 (45*2π)/3849 weeks
46-.34469 -.0034 (46*2π)/3848 weeks
47-.53793 -.96766 (47*2π)/3848 weeks
48.0064 -.73172 (48*2π)/3848 weeks
49-.12508 -.7861 (49*2π)/3848 weeks
50-.15998 -.48686 (50*2π)/3848 weeks
51.49229 -.51939 (51*2π)/3848 weeks
52.09035 -.5602 (52*2π)/3847 weeks
53.11862 -.24037 (53*2π)/3847 weeks
54-.45184 -.32728 (54*2π)/3847 weeks
55-.16209 -.31041 (55*2π)/3847 weeks
56-.53203 -.57451 (56*2π)/3847 weeks
57-.20272 -.64172 (57*2π)/3847 weeks
58.01436 -.91375 (58*2π)/3847 weeks
59-.00467 -.88582 (59*2π)/3847 weeks
60-.23635 -.78861 (60*2π)/3846 weeks
61-.42281 -.48177 (61*2π)/3846 weeks
62-.03899 -.76319 (62*2π)/3846 weeks
63-.48593 -.93055 (63*2π)/3846 weeks
64-.62052 -.64184 (64*2π)/3846 weeks
65-.48254 -.3773 (65*2π)/3846 weeks
66-.2862 -.53864 (66*2π)/3846 weeks
67-.17409 -.79616 (67*2π)/3846 weeks
68-.40443 -.64073 (68*2π)/3846 weeks
69-.37551 -.47524 (69*2π)/3846 weeks
70-.15488 -.70439 (70*2π)/3845 weeks
71-.5748 -.61738 (71*2π)/3845 weeks
72-.41532 -.32816 (72*2π)/3845 weeks
73-.45061 -.37508 (73*2π)/3845 weeks
74-.45516 -.80802 (74*2π)/3845 weeks
75-.25921 -.25653 (75*2π)/3845 weeks
76-.06341 -.46741 (76*2π)/3845 weeks
77-.51462 -.5179 (77*2π)/3845 weeks
78-.36406 -.34402 (78*2π)/3845 weeks
79-.30481 -.55103 (79*2π)/3845 weeks
80-.20925 -.53513 (80*2π)/3845 weeks
81-.31224 -.22786 (81*2π)/3845 weeks
82-.01991 -.44678 (82*2π)/3845 weeks
83-.22557 -.6229 (83*2π)/3845 weeks
84-.52999 -.18672 (84*2π)/3845 weeks
85-.1751 -.36328 (85*2π)/3845 weeks
86-.18294 -.24988 (86*2π)/3844 weeks
87-.54589 -.28385 (87*2π)/3844 weeks
88-.11352 -.16941 (88*2π)/3844 weeks
89-.21959 -.52456 (89*2π)/3844 weeks
90-.26891 -.35568 (90*2π)/3844 weeks
91-.43522 -.4298 (91*2π)/3844 weeks
92-.10295 -.33519 (92*2π)/3844 weeks
93-.3681 -.72566 (93*2π)/3844 weeks
94-.70885 -.31213 (94*2π)/3844 weeks
95-.21958 -.45088 (95*2π)/3844 weeks
96-.51014 -.47697 (96*2π)/3844 weeks
97-.25229 -.31719 (97*2π)/3844 weeks
98.05053 -.41379 (98*2π)/3844 weeks
99-.35862 -.38852 (99*2π)/3844 weeks
100-.59788 -.14899 (100*2π)/3844 weeks
101-.17179 .06299 (101*2π)/3844 weeks
102-.26942 -.2705 (102*2π)/3844 weeks
103-.45191 -.13891 (103*2π)/3844 weeks
104-.33865 -.36561 (104*2π)/3844 weeks
105-.41949 -.31274 (105*2π)/3844 weeks
106-.24391 -.1091 (106*2π)/3844 weeks
107-.09103 -.02875 (107*2π)/3844 weeks
108-.22827 -.25429 (108*2π)/3844 weeks
109-.40158 -.14764 (109*2π)/3844 weeks
110-.23258 .10305 (110*2π)/3843 weeks
111-.35193 -.05427 (111*2π)/3843 weeks
112-.26937 -.14006 (112*2π)/3843 weeks
113-.18266 -.18553 (113*2π)/3843 weeks
114-.24489 -.32886 (114*2π)/3843 weeks
115-.33855 .00764 (115*2π)/3843 weeks
116-.29665 -.11715 (116*2π)/3843 weeks
117-.23567 -.22661 (117*2π)/3843 weeks
118-.1907 -.25754 (118*2π)/3843 weeks
119-.12453 -.19647 (119*2π)/3843 weeks
120-.36223 -.19114 (120*2π)/3843 weeks
121-.11345 -.12152 (121*2π)/3843 weeks
122-.14353 -.31201 (122*2π)/3843 weeks
123-.24108 -.22746 (123*2π)/3843 weeks
124-.10479 -.23456 (124*2π)/3843 weeks
125-.17139 -.25738 (125*2π)/3843 weeks
126-.30905 -.34143 (126*2π)/3843 weeks
127-.30127 -.22883 (127*2π)/3843 weeks
128-.28871 -.4699 (128*2π)/3843 weeks
129-.30385 -.20266 (129*2π)/3843 weeks
130-.28746 -.09978 (130*2π)/3843 weeks
131-.34975 -.31635 (131*2π)/3843 weeks
132-.29974 -.17158 (132*2π)/3843 weeks
133-.41847 -.36247 (133*2π)/3843 weeks
134-.45271 -.32439 (134*2π)/3843 weeks
135-.35332 -.39526 (135*2π)/3843 weeks
136-.38169 -.34909 (136*2π)/3843 weeks
137-.20508 -.02648 (137*2π)/3843 weeks
138-.42083 -.03305 (138*2π)/3843 weeks
139-.35353 -.13049 (139*2π)/3843 weeks
140-.54575 .01162 (140*2π)/3843 weeks
141-.69117 -.08533 (141*2π)/3843 weeks
142-.42596 -.15654 (142*2π)/3843 weeks
143-.37496 -.24171 (143*2π)/3843 weeks
144-.39706 -.00278 (144*2π)/3843 weeks
145-.27902 -.15014 (145*2π)/3843 weeks
146-.28881 -.05026 (146*2π)/3843 weeks
147-.22439 -.1033 (147*2π)/3843 weeks
148-.40589 -.06851 (148*2π)/3843 weeks
149-.27216 .06963 (149*2π)/3843 weeks
150-.44012 -.04999 (150*2π)/3843 weeks
151-.36072 -.00168 (151*2π)/3843 weeks
152-.31103 -.00328 (152*2π)/3843 weeks
153-.35764 -.1046 (153*2π)/3843 weeks
154-.33437 -.0452 (154*2π)/3842 weeks
155-.44473 -.12265 (155*2π)/3842 weeks
156-.34429 -.08796 (156*2π)/3842 weeks
157-.39762 -.14604 (157*2π)/3842 weeks
158-.19666 -.16726 (158*2π)/3842 weeks
159-.2274 -.16102 (159*2π)/3842 weeks
160-.27017 .09361 (160*2π)/3842 weeks
161-.10432 -.21021 (161*2π)/3842 weeks
162-.45776 -.1345 (162*2π)/3842 weeks
163-.42335 .03735 (163*2π)/3842 weeks
164-.4047 .03635 (164*2π)/3842 weeks
165-.2719 .02356 (165*2π)/3842 weeks
166-.36273 .03583 (166*2π)/3842 weeks
167-.2437 -.41658 (167*2π)/3842 weeks
168-.229 -.1108 (168*2π)/3842 weeks
169-.2235 .08515 (169*2π)/3842 weeks
170-.28421 .13482 (170*2π)/3842 weeks
171-.22584 .04199 (171*2π)/3842 weeks
172-.22428 -.12456 (172*2π)/3842 weeks
173-.53604 -.02208 (173*2π)/3842 weeks
174-.24718 -.14379 (174*2π)/3842 weeks
175-.42166 .03748 (175*2π)/3842 weeks
176-.28794 -.11241 (176*2π)/3842 weeks
177-.38741 .08808 (177*2π)/3842 weeks
178-.15213 -.17739 (178*2π)/3842 weeks
179-.22253 .04443 (179*2π)/3842 weeks
180-.25916 .03271 (180*2π)/3842 weeks
181-.20054 .16733 (181*2π)/3842 weeks
182-.26135 -.04968 (182*2π)/3842 weeks
183-.26594 -.19303 (183*2π)/3842 weeks
184-.34686 .15755 (184*2π)/3842 weeks
185-.20264 .11338 (185*2π)/3842 weeks
186-.31675 -.12611 (186*2π)/3842 weeks
187-.24077 .07332 (187*2π)/3842 weeks
188-.15132 -.08737 (188*2π)/3842 weeks
189-.4117 -.11244 (189*2π)/3842 weeks
190-.23402 .26852 (190*2π)/3842 weeks
191-.24702 .12903 (191*2π)/3842 weeks
192-.30252   (192*2π)/3842 weeks
193-.24702 -.12903 (193*2π)/3842 weeks
194-.23402 -.26852 (194*2π)/3842 weeks
195-.4117 .11244 (195*2π)/3842 weeks
196-.15132 .08737 (196*2π)/3842 weeks
197-.24077 -.07332 (197*2π)/3842 weeks
198-.31675 .12611 (198*2π)/3842 weeks
199-.20264 -.11338 (199*2π)/3842 weeks
200-.34686 -.15755 (200*2π)/3842 weeks
201-.26594 .19303 (201*2π)/3842 weeks
202-.26135 .04968 (202*2π)/3842 weeks
203-.20054 -.16733 (203*2π)/3842 weeks
204-.25916 -.03271 (204*2π)/3842 weeks
205-.22253 -.04443 (205*2π)/3842 weeks
206-.15213 .17739 (206*2π)/3842 weeks
207-.38741 -.08808 (207*2π)/3842 weeks
208-.28794 .11241 (208*2π)/3842 weeks
209-.42166 -.03748 (209*2π)/3842 weeks
210-.24718 .14379 (210*2π)/3842 weeks
211-.53604 .02208 (211*2π)/3842 weeks
212-.22428 .12456 (212*2π)/3842 weeks
213-.22584 -.04199 (213*2π)/3842 weeks
214-.28421 -.13482 (214*2π)/3842 weeks
215-.2235 -.08515 (215*2π)/3842 weeks
216-.229 .1108 (216*2π)/3842 weeks
217-.2437 .41658 (217*2π)/3842 weeks
218-.36273 -.03583 (218*2π)/3842 weeks
219-.2719 -.02356 (219*2π)/3842 weeks
220-.4047 -.03635 (220*2π)/3842 weeks
221-.42335 -.03735 (221*2π)/3842 weeks
222-.45776 .1345 (222*2π)/3842 weeks
223-.10432 .21021 (223*2π)/3842 weeks
224-.27017 -.09361 (224*2π)/3842 weeks
225-.2274 .16102 (225*2π)/3842 weeks
226-.19666 .16726 (226*2π)/3842 weeks
227-.39762 .14604 (227*2π)/3842 weeks
228-.34429 .08796 (228*2π)/3842 weeks
229-.44473 .12265 (229*2π)/3842 weeks
230-.33437 .0452 (230*2π)/3842 weeks
231-.35764 .1046 (231*2π)/3842 weeks
232-.31103 .00328 (232*2π)/3842 weeks
233-.36072 .00168 (233*2π)/3842 weeks
234-.44012 .04999 (234*2π)/3842 weeks
235-.27216 -.06963 (235*2π)/3842 weeks
236-.40589 .06851 (236*2π)/3842 weeks
237-.22439 .1033 (237*2π)/3842 weeks
238-.28881 .05026 (238*2π)/3842 weeks
239-.27902 .15014 (239*2π)/3842 weeks
240-.39706 .00278 (240*2π)/3842 weeks
241-.37496 .24171 (241*2π)/3842 weeks
242-.42596 .15654 (242*2π)/3842 weeks
243-.69117 .08533 (243*2π)/3842 weeks
244-.54575 -.01162 (244*2π)/3842 weeks
245-.35353 .13049 (245*2π)/3842 weeks
246-.42083 .03305 (246*2π)/3842 weeks
247-.20508 .02648 (247*2π)/3842 weeks
248-.38169 .34909 (248*2π)/3842 weeks
249-.35332 .39526 (249*2π)/3842 weeks
250-.45271 .32439 (250*2π)/3842 weeks
251-.41847 .36247 (251*2π)/3842 weeks
252-.29974 .17158 (252*2π)/3842 weeks
253-.34975 .31635 (253*2π)/3842 weeks
254-.28746 .09978 (254*2π)/3842 weeks
255-.30385 .20266 (255*2π)/3842 weeks
256-.28871 .4699 (256*2π)/3842 weeks
257-.30127 .22883 (257*2π)/3841 weeks
258-.30905 .34143 (258*2π)/3841 weeks
259-.17139 .25738 (259*2π)/3841 weeks
260-.10479 .23456 (260*2π)/3841 weeks
261-.24108 .22746 (261*2π)/3841 weeks
262-.14353 .31201 (262*2π)/3841 weeks
263-.11345 .12152 (263*2π)/3841 weeks
264-.36223 .19114 (264*2π)/3841 weeks
265-.12453 .19647 (265*2π)/3841 weeks
266-.1907 .25754 (266*2π)/3841 weeks
267-.23567 .22661 (267*2π)/3841 weeks
268-.29665 .11715 (268*2π)/3841 weeks
269-.33855 -.00764 (269*2π)/3841 weeks
270-.24489 .32886 (270*2π)/3841 weeks
271-.18266 .18553 (271*2π)/3841 weeks
272-.26937 .14006 (272*2π)/3841 weeks
273-.35193 .05427 (273*2π)/3841 weeks
274-.23258 -.10305 (274*2π)/3841 weeks
275-.40158 .14764 (275*2π)/3841 weeks
276-.22827 .25429 (276*2π)/3841 weeks
277-.09103 .02875 (277*2π)/3841 weeks
278-.24391 .1091 (278*2π)/3841 weeks
279-.41949 .31274 (279*2π)/3841 weeks
280-.33865 .36561 (280*2π)/3841 weeks
281-.45191 .13891 (281*2π)/3841 weeks
282-.26942 .2705 (282*2π)/3841 weeks
283-.17179 -.06299 (283*2π)/3841 weeks
284-.59788 .14899 (284*2π)/3841 weeks
285-.35862 .38852 (285*2π)/3841 weeks
286.05053 .41379 (286*2π)/3841 weeks
287-.25229 .31719 (287*2π)/3841 weeks
288-.51014 .47697 (288*2π)/3841 weeks
289-.21958 .45088 (289*2π)/3841 weeks
290-.70885 .31213 (290*2π)/3841 weeks
291-.3681 .72566 (291*2π)/3841 weeks
292-.10295 .33519 (292*2π)/3841 weeks
293-.43522 .4298 (293*2π)/3841 weeks
294-.26891 .35568 (294*2π)/3841 weeks
295-.21959 .52456 (295*2π)/3841 weeks
296-.11352 .16941 (296*2π)/3841 weeks
297-.54589 .28385 (297*2π)/3841 weeks
298-.18294 .24988 (298*2π)/3841 weeks
299-.1751 .36328 (299*2π)/3841 weeks
300-.52999 .18672 (300*2π)/3841 weeks
301-.22557 .6229 (301*2π)/3841 weeks
302-.01991 .44678 (302*2π)/3841 weeks
303-.31224 .22786 (303*2π)/3841 weeks
304-.20925 .53513 (304*2π)/3841 weeks
305-.30481 .55103 (305*2π)/3841 weeks
306-.36406 .34402 (306*2π)/3841 weeks
307-.51462 .5179 (307*2π)/3841 weeks
308-.06341 .46741 (308*2π)/3841 weeks
309-.25921 .25653 (309*2π)/3841 weeks
310-.45516 .80802 (310*2π)/3841 weeks
311-.45061 .37508 (311*2π)/3841 weeks
312-.41532 .32816 (312*2π)/3841 weeks
313-.5748 .61738 (313*2π)/3841 weeks
314-.15488 .70439 (314*2π)/3841 weeks
315-.37551 .47524 (315*2π)/3841 weeks
316-.40443 .64073 (316*2π)/3841 weeks
317-.17409 .79616 (317*2π)/3841 weeks
318-.2862 .53864 (318*2π)/3841 weeks
319-.48254 .3773 (319*2π)/3841 weeks
320-.62052 .64184 (320*2π)/3841 weeks
321-.48593 .93055 (321*2π)/3841 weeks
322-.03899 .76319 (322*2π)/3841 weeks
323-.42281 .48177 (323*2π)/3841 weeks
324-.23635 .78861 (324*2π)/3841 weeks
325-.00467 .88582 (325*2π)/3841 weeks
326.01436 .91375 (326*2π)/3841 weeks
327-.20272 .64172 (327*2π)/3841 weeks
328-.53203 .57451 (328*2π)/3841 weeks
329-.16209 .31041 (329*2π)/3841 weeks
330-.45184 .32728 (330*2π)/3841 weeks
331.11862 .24037 (331*2π)/3841 weeks
332.09035 .5602 (332*2π)/3841 weeks
333.49229 .51939 (333*2π)/3841 weeks
334-.15998 .48686 (334*2π)/3841 weeks
335-.12508 .7861 (335*2π)/3841 weeks
336.0064 .73172 (336*2π)/3841 weeks
337-.53793 .96766 (337*2π)/3841 weeks
338-.34469 .0034 (338*2π)/3841 weeks
339-.65596 .88933 (339*2π)/3841 weeks
340-.65234 .31548 (340*2π)/3841 weeks
341-.18837 .67619 (341*2π)/3841 weeks
342.04546 .55286 (342*2π)/3841 weeks
343-.29974 .85665 (343*2π)/3841 weeks
344-.44355 .3215 (344*2π)/3841 weeks
345-.04569 1.47517 (345*2π)/3841 weeks
346.19234 .98322 (346*2π)/3841 weeks
347-.06822 .8832 (347*2π)/3841 weeks
348-.31822 1.00887 (348*2π)/3841 weeks
349-.95899 1.17137 (349*2π)/3841 weeks
350-.28238 .65389 (350*2π)/3841 weeks
351-.7171 2.0829 (351*2π)/3841 weeks
352-.29799 1.29191 (352*2π)/3841 weeks
353-.56868 1.5789 (353*2π)/3841 weeks
354-.74633 .76727 (354*2π)/3841 weeks
355-.60812 1.5114 (355*2π)/3841 weeks
356.23659 1.0561 (356*2π)/3841 weeks
357.03784 1.33498 (357*2π)/3841 weeks
358.18596 .8634 (358*2π)/3841 weeks
359.37429 1.30135 (359*2π)/3841 weeks
360-.03875 1.42384 (360*2π)/3841 weeks
361-.77949 1.64946 (361*2π)/3841 weeks
362-.38889 2.60259 (362*2π)/3841 weeks
363-.01273 .85211 (363*2π)/3841 weeks
364-1.51693 1.7412 (364*2π)/3841 weeks
365-1.05549 2.31176 (365*2π)/3841 weeks
366.81378 1.73838 (366*2π)/3841 weeks
367.12263 1.19163 (367*2π)/3841 weeks
368-.41847 2.95398 (368*2π)/3841 weeks
369-.53895 1.66066 (369*2π)/3841 weeks
370-.80224 2.04889 (370*2π)/3841 weeks
371-.25024 3.42516 (371*2π)/3841 weeks
372.56319 3.89533 (372*2π)/3841 weeks
373-1.57348 3.15753 (373*2π)/3841 weeks
374-1.99158 4.15932 (374*2π)/3841 weeks
375-2.2074 4.75498 (375*2π)/3841 weeks
376-1.01479 4.67935 (376*2π)/3841 weeks
377-.35237 3.31338 (377*2π)/3841 weeks
378-.20185 7.08419 (378*2π)/3841 weeks
3793.81298 6.87545 (379*2π)/3841 weeks
380-1.24877 7.39611 (380*2π)/3841 weeks
381.26235 13.8374 (381*2π)/3841 weeks
38210.64349 22.26293 (382*2π)/3841 weeks