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Fourier Analysis of VIOG (Vanguard S&P Small-Cap 600 Grow)


VIOG (Vanguard S&P Small-Cap 600 Grow) appears to have interesting cyclic behaviour every 28 weeks (2.4655*sine), 26 weeks (2.4535*sine), and 30 weeks (1.989*sine).

VIOG (Vanguard S&P Small-Cap 600 Grow) has an average price of 86.27 (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 9/9/2010 to 1/9/2017 for VIOG (Vanguard S&P Small-Cap 600 Grow), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
086.26967   0 
1-2.12086 -24.43675 (1*2π)/332332 weeks
22.58813 -6.94189 (2*2π)/332166 weeks
3-.07057 -5.24789 (3*2π)/332111 weeks
42.89508 -5.04817 (4*2π)/33283 weeks
5-1.21998 -5.46582 (5*2π)/33266 weeks
6-1.71803 -3.93232 (6*2π)/33255 weeks
7-.82905 -4.15537 (7*2π)/33247 weeks
8.16365 -3.33537 (8*2π)/33242 weeks
9.17775 -2.44412 (9*2π)/33237 weeks
10.87388 -1.58043 (10*2π)/33233 weeks
11-.19135 -1.98899 (11*2π)/33230 weeks
12-.20056 -2.46546 (12*2π)/33228 weeks
13-.07633 -2.45352 (13*2π)/33226 weeks
14-.89058 -1.57997 (14*2π)/33224 weeks
15-.04487 -1.87602 (15*2π)/33222 weeks
16.90103 -1.73289 (16*2π)/33221 weeks
17.2772 -1.64588 (17*2π)/33220 weeks
18-.03547 -2.3823 (18*2π)/33218 weeks
19-1.12777 -1.76931 (19*2π)/33217 weeks
20-.59981 -1.2537 (20*2π)/33217 weeks
21-.23689 -1.64859 (21*2π)/33216 weeks
22.10347 -1.23302 (22*2π)/33215 weeks
23-.31485 -1.20118 (23*2π)/33214 weeks
24-.15156 -.89476 (24*2π)/33214 weeks
25-.58226 -1.24595 (25*2π)/33213 weeks
26-.9782 -.98408 (26*2π)/33213 weeks
27-.35765 -1.18377 (27*2π)/33212 weeks
28-.59209 -1.07755 (28*2π)/33212 weeks
29-.05546 -.44365 (29*2π)/33211 weeks
30-.40685 -1.16283 (30*2π)/33211 weeks
31-.24033 -.4863 (31*2π)/33211 weeks
32-.34976 -.58404 (32*2π)/33210 weeks
33-.6004 -.5825 (33*2π)/33210 weeks
34-.75954 -.27365 (34*2π)/33210 weeks
35-.11452 -.65254 (35*2π)/3329 weeks
36-.49323 -.56983 (36*2π)/3329 weeks
37-.25727 -.63388 (37*2π)/3329 weeks
38.11657 -.71161 (38*2π)/3329 weeks
39-.3261 -.27218 (39*2π)/3329 weeks
40.25775 -.45525 (40*2π)/3328 weeks
41-.4526 -.58364 (41*2π)/3328 weeks
42-.21189 -.61609 (42*2π)/3328 weeks
43-.09937 -.74369 (43*2π)/3328 weeks
44-.00991 -.97681 (44*2π)/3328 weeks
45-.05103 -.69746 (45*2π)/3327 weeks
46-.03107 -.20554 (46*2π)/3327 weeks
47-.3497 -.47921 (47*2π)/3327 weeks
48-.46292 -.26737 (48*2π)/3327 weeks
49-.22685 -.59549 (49*2π)/3327 weeks
50-.15715 -.65691 (50*2π)/3327 weeks
51-.15343 -.44602 (51*2π)/3327 weeks
52-.23392 -.50517 (52*2π)/3326 weeks
53-.30265 -.76074 (53*2π)/3326 weeks
54-.51904 -.55404 (54*2π)/3326 weeks
55-.43401 -.40669 (55*2π)/3326 weeks
56-.42475 -.39394 (56*2π)/3326 weeks
57-.29211 -.30303 (57*2π)/3326 weeks
58-.36003 -.20616 (58*2π)/3326 weeks
59-.313 -.23814 (59*2π)/3326 weeks
60-.15459 -.23145 (60*2π)/3326 weeks
61-.24964 -.46314 (61*2π)/3325 weeks
62-.29983 -.35646 (62*2π)/3325 weeks
63-.20499 -.37261 (63*2π)/3325 weeks
64-.52694 -.17658 (64*2π)/3325 weeks
65-.16497 -.27338 (65*2π)/3325 weeks
66-.06838 -.33924 (66*2π)/3325 weeks
67-.27006 -.46498 (67*2π)/3325 weeks
68-.38914 -.34823 (68*2π)/3325 weeks
69-.24972 -.41291 (69*2π)/3325 weeks
70-.16945 -.16492 (70*2π)/3325 weeks
71-.02268 -.273 (71*2π)/3325 weeks
72.09534 -.30145 (72*2π)/3325 weeks
73-.20236 -.51928 (73*2π)/3325 weeks
74-.25568 -.27641 (74*2π)/3324 weeks
75-.42618 -.33992 (75*2π)/3324 weeks
76-.23076 -.15877 (76*2π)/3324 weeks
77-.07253 -.29738 (77*2π)/3324 weeks
78-.21825 -.33963 (78*2π)/3324 weeks
79-.06311 -.28617 (79*2π)/3324 weeks
80-.09823 -.44657 (80*2π)/3324 weeks
81-.31172 -.47012 (81*2π)/3324 weeks
82-.30019 -.04202 (82*2π)/3324 weeks
83-.08745 -.10458 (83*2π)/3324 weeks
84-.25123 -.23866 (84*2π)/3324 weeks
85-.33557 -.4898 (85*2π)/3324 weeks
86-.34245 -.44989 (86*2π)/3324 weeks
87-.43328 -.36292 (87*2π)/3324 weeks
88-.34088 -.11589 (88*2π)/3324 weeks
89-.19739 -.0917 (89*2π)/3324 weeks
90-.374 -.2605 (90*2π)/3324 weeks
91-.38963 -.26694 (91*2π)/3324 weeks
92-.30167 -.24156 (92*2π)/3324 weeks
93-.38064 -.08734 (93*2π)/3324 weeks
94-.27271 -.0282 (94*2π)/3324 weeks
95-.16094 .01206 (95*2π)/3323 weeks
96-.33492 -.16924 (96*2π)/3323 weeks
97-.29399 -.15771 (97*2π)/3323 weeks
98-.30589 -.16249 (98*2π)/3323 weeks
99-.25026 -.00648 (99*2π)/3323 weeks
100-.23809 -.19518 (100*2π)/3323 weeks
101-.18914 -.20683 (101*2π)/3323 weeks
102-.19804 -.1827 (102*2π)/3323 weeks
103-.30212 -.08912 (103*2π)/3323 weeks
104-.16094 -.14183 (104*2π)/3323 weeks
105-.17075 -.23978 (105*2π)/3323 weeks
106-.27216 -.19778 (106*2π)/3323 weeks
107-.32033 -.12499 (107*2π)/3323 weeks
108-.27339 -.21526 (108*2π)/3323 weeks
109-.21986 -.0752 (109*2π)/3323 weeks
110-.12932 -.12515 (110*2π)/3323 weeks
111-.30369 -.25392 (111*2π)/3323 weeks
112-.20961 -.20864 (112*2π)/3323 weeks
113-.22522 -.07746 (113*2π)/3323 weeks
114-.18255 -.15471 (114*2π)/3323 weeks
115-.31064 -.1111 (115*2π)/3323 weeks
116-.31837 -.15287 (116*2π)/3323 weeks
117-.15316 -.19996 (117*2π)/3323 weeks
118-.10608 -.22088 (118*2π)/3323 weeks
119-.25352 .03077 (119*2π)/3323 weeks
120-.2175 -.1385 (120*2π)/3323 weeks
121-.371 -.08583 (121*2π)/3323 weeks
122-.40413 -.32717 (122*2π)/3323 weeks
123-.26874 -.16076 (123*2π)/3323 weeks
124-.19828 .00677 (124*2π)/3323 weeks
125-.17917 -.13986 (125*2π)/3323 weeks
126-.25176 -.09319 (126*2π)/3323 weeks
127-.23531 -.06695 (127*2π)/3323 weeks
128-.19106 -.15156 (128*2π)/3323 weeks
129-.29532 -.21447 (129*2π)/3323 weeks
130-.21814 -.10089 (130*2π)/3323 weeks
131-.20843 -.07678 (131*2π)/3323 weeks
132-.15485 -.07008 (132*2π)/3323 weeks
133-.20204 -.05511 (133*2π)/3322 weeks
134-.19173 .03151 (134*2π)/3322 weeks
135-.20637 -.06422 (135*2π)/3322 weeks
136-.33833 -.0413 (136*2π)/3322 weeks
137-.24092 -.13106 (137*2π)/3322 weeks
138-.15745 -.23799 (138*2π)/3322 weeks
139-.35397 -.22825 (139*2π)/3322 weeks
140-.32968 -.03931 (140*2π)/3322 weeks
141-.29455 -.0235 (141*2π)/3322 weeks
142-.33825 -.03424 (142*2π)/3322 weeks
143-.30571 -.01994 (143*2π)/3322 weeks
144-.37973 -.28351 (144*2π)/3322 weeks
145-.16818 .02061 (145*2π)/3322 weeks
146-.29751 .04028 (146*2π)/3322 weeks
147-.38535 .01485 (147*2π)/3322 weeks
148-.30887 -.00535 (148*2π)/3322 weeks
149-.33445 .02473 (149*2π)/3322 weeks
150-.12873 -.02325 (150*2π)/3322 weeks
151-.29296 -.03326 (151*2π)/3322 weeks
152-.20217 .11453 (152*2π)/3322 weeks
153-.23047 -.05538 (153*2π)/3322 weeks
154-.37069 .12103 (154*2π)/3322 weeks
155-.29614 -.01232 (155*2π)/3322 weeks
156-.36922 .03347 (156*2π)/3322 weeks
157-.09963 .0875 (157*2π)/3322 weeks
158-.25213 .04568 (158*2π)/3322 weeks
159-.13468 -.00573 (159*2π)/3322 weeks
160-.15643 -.011 (160*2π)/3322 weeks
161-.34049 -.046 (161*2π)/3322 weeks
162-.28616 .08034 (162*2π)/3322 weeks
163-.09028 .13181 (163*2π)/3322 weeks
164-.01703 -.03116 (164*2π)/3322 weeks
165-.22777 .04211 (165*2π)/3322 weeks
166-.23664   (166*2π)/3322 weeks
167-.22777 -.04211 (167*2π)/3322 weeks
168-.01703 .03116 (168*2π)/3322 weeks
169-.09028 -.13181 (169*2π)/3322 weeks
170-.28616 -.08034 (170*2π)/3322 weeks
171-.34049 .046 (171*2π)/3322 weeks
172-.15643 .011 (172*2π)/3322 weeks
173-.13468 .00573 (173*2π)/3322 weeks
174-.25213 -.04568 (174*2π)/3322 weeks
175-.09963 -.0875 (175*2π)/3322 weeks
176-.36922 -.03347 (176*2π)/3322 weeks
177-.29614 .01232 (177*2π)/3322 weeks
178-.37069 -.12103 (178*2π)/3322 weeks
179-.23047 .05538 (179*2π)/3322 weeks
180-.20217 -.11453 (180*2π)/3322 weeks
181-.29296 .03326 (181*2π)/3322 weeks
182-.12873 .02325 (182*2π)/3322 weeks
183-.33445 -.02473 (183*2π)/3322 weeks
184-.30887 .00535 (184*2π)/3322 weeks
185-.38535 -.01485 (185*2π)/3322 weeks
186-.29751 -.04028 (186*2π)/3322 weeks
187-.16818 -.02061 (187*2π)/3322 weeks
188-.37973 .28351 (188*2π)/3322 weeks
189-.30571 .01994 (189*2π)/3322 weeks
190-.33825 .03424 (190*2π)/3322 weeks
191-.29455 .0235 (191*2π)/3322 weeks
192-.32968 .03931 (192*2π)/3322 weeks
193-.35397 .22825 (193*2π)/3322 weeks
194-.15745 .23799 (194*2π)/3322 weeks
195-.24092 .13106 (195*2π)/3322 weeks
196-.33833 .0413 (196*2π)/3322 weeks
197-.20637 .06422 (197*2π)/3322 weeks
198-.19173 -.03151 (198*2π)/3322 weeks
199-.20204 .05511 (199*2π)/3322 weeks
200-.15485 .07008 (200*2π)/3322 weeks
201-.20843 .07678 (201*2π)/3322 weeks
202-.21814 .10089 (202*2π)/3322 weeks
203-.29532 .21447 (203*2π)/3322 weeks
204-.19106 .15156 (204*2π)/3322 weeks
205-.23531 .06695 (205*2π)/3322 weeks
206-.25176 .09319 (206*2π)/3322 weeks
207-.17917 .13986 (207*2π)/3322 weeks
208-.19828 -.00677 (208*2π)/3322 weeks
209-.26874 .16076 (209*2π)/3322 weeks
210-.40413 .32717 (210*2π)/3322 weeks
211-.371 .08583 (211*2π)/3322 weeks
212-.2175 .1385 (212*2π)/3322 weeks
213-.25352 -.03077 (213*2π)/3322 weeks
214-.10608 .22088 (214*2π)/3322 weeks
215-.15316 .19996 (215*2π)/3322 weeks
216-.31837 .15287 (216*2π)/3322 weeks
217-.31064 .1111 (217*2π)/3322 weeks
218-.18255 .15471 (218*2π)/3322 weeks
219-.22522 .07746 (219*2π)/3322 weeks
220-.20961 .20864 (220*2π)/3322 weeks
221-.30369 .25392 (221*2π)/3322 weeks
222-.12932 .12515 (222*2π)/3321 weeks
223-.21986 .0752 (223*2π)/3321 weeks
224-.27339 .21526 (224*2π)/3321 weeks
225-.32033 .12499 (225*2π)/3321 weeks
226-.27216 .19778 (226*2π)/3321 weeks
227-.17075 .23978 (227*2π)/3321 weeks
228-.16094 .14183 (228*2π)/3321 weeks
229-.30212 .08912 (229*2π)/3321 weeks
230-.19804 .1827 (230*2π)/3321 weeks
231-.18914 .20683 (231*2π)/3321 weeks
232-.23809 .19518 (232*2π)/3321 weeks
233-.25026 .00648 (233*2π)/3321 weeks
234-.30589 .16249 (234*2π)/3321 weeks
235-.29399 .15771 (235*2π)/3321 weeks
236-.33492 .16924 (236*2π)/3321 weeks
237-.16094 -.01206 (237*2π)/3321 weeks
238-.27271 .0282 (238*2π)/3321 weeks
239-.38064 .08734 (239*2π)/3321 weeks
240-.30167 .24156 (240*2π)/3321 weeks
241-.38963 .26694 (241*2π)/3321 weeks
242-.374 .2605 (242*2π)/3321 weeks
243-.19739 .0917 (243*2π)/3321 weeks
244-.34088 .11589 (244*2π)/3321 weeks
245-.43328 .36292 (245*2π)/3321 weeks
246-.34245 .44989 (246*2π)/3321 weeks
247-.33557 .4898 (247*2π)/3321 weeks
248-.25123 .23866 (248*2π)/3321 weeks
249-.08745 .10458 (249*2π)/3321 weeks
250-.30019 .04202 (250*2π)/3321 weeks
251-.31172 .47012 (251*2π)/3321 weeks
252-.09823 .44657 (252*2π)/3321 weeks
253-.06311 .28617 (253*2π)/3321 weeks
254-.21825 .33963 (254*2π)/3321 weeks
255-.07253 .29738 (255*2π)/3321 weeks
256-.23076 .15877 (256*2π)/3321 weeks
257-.42618 .33992 (257*2π)/3321 weeks
258-.25568 .27641 (258*2π)/3321 weeks
259-.20236 .51928 (259*2π)/3321 weeks
260.09534 .30145 (260*2π)/3321 weeks
261-.02268 .273 (261*2π)/3321 weeks
262-.16945 .16492 (262*2π)/3321 weeks
263-.24972 .41291 (263*2π)/3321 weeks
264-.38914 .34823 (264*2π)/3321 weeks
265-.27006 .46498 (265*2π)/3321 weeks
266-.06838 .33924 (266*2π)/3321 weeks
267-.16497 .27338 (267*2π)/3321 weeks
268-.52694 .17658 (268*2π)/3321 weeks
269-.20499 .37261 (269*2π)/3321 weeks
270-.29983 .35646 (270*2π)/3321 weeks
271-.24964 .46314 (271*2π)/3321 weeks
272-.15459 .23145 (272*2π)/3321 weeks
273-.313 .23814 (273*2π)/3321 weeks
274-.36003 .20616 (274*2π)/3321 weeks
275-.29211 .30303 (275*2π)/3321 weeks
276-.42475 .39394 (276*2π)/3321 weeks
277-.43401 .40669 (277*2π)/3321 weeks
278-.51904 .55404 (278*2π)/3321 weeks
279-.30265 .76074 (279*2π)/3321 weeks
280-.23392 .50517 (280*2π)/3321 weeks
281-.15343 .44602 (281*2π)/3321 weeks
282-.15715 .65691 (282*2π)/3321 weeks
283-.22685 .59549 (283*2π)/3321 weeks
284-.46292 .26737 (284*2π)/3321 weeks
285-.3497 .47921 (285*2π)/3321 weeks
286-.03107 .20554 (286*2π)/3321 weeks
287-.05103 .69746 (287*2π)/3321 weeks
288-.00991 .97681 (288*2π)/3321 weeks
289-.09937 .74369 (289*2π)/3321 weeks
290-.21189 .61609 (290*2π)/3321 weeks
291-.4526 .58364 (291*2π)/3321 weeks
292.25775 .45525 (292*2π)/3321 weeks
293-.3261 .27218 (293*2π)/3321 weeks
294.11657 .71161 (294*2π)/3321 weeks
295-.25727 .63388 (295*2π)/3321 weeks
296-.49323 .56983 (296*2π)/3321 weeks
297-.11452 .65254 (297*2π)/3321 weeks
298-.75954 .27365 (298*2π)/3321 weeks
299-.6004 .5825 (299*2π)/3321 weeks
300-.34976 .58404 (300*2π)/3321 weeks
301-.24033 .4863 (301*2π)/3321 weeks
302-.40685 1.16283 (302*2π)/3321 weeks
303-.05546 .44365 (303*2π)/3321 weeks
304-.59209 1.07755 (304*2π)/3321 weeks
305-.35765 1.18377 (305*2π)/3321 weeks
306-.9782 .98408 (306*2π)/3321 weeks
307-.58226 1.24595 (307*2π)/3321 weeks
308-.15156 .89476 (308*2π)/3321 weeks
309-.31485 1.20118 (309*2π)/3321 weeks
310.10347 1.23302 (310*2π)/3321 weeks
311-.23689 1.64859 (311*2π)/3321 weeks
312-.59981 1.2537 (312*2π)/3321 weeks
313-1.12777 1.76931 (313*2π)/3321 weeks
314-.03547 2.3823 (314*2π)/3321 weeks
315.2772 1.64588 (315*2π)/3321 weeks
316.90103 1.73289 (316*2π)/3321 weeks
317-.04487 1.87602 (317*2π)/3321 weeks
318-.89058 1.57997 (318*2π)/3321 weeks
319-.07633 2.45352 (319*2π)/3321 weeks
320-.20056 2.46546 (320*2π)/3321 weeks
321-.19135 1.98899 (321*2π)/3321 weeks
322.87388 1.58043 (322*2π)/3321 weeks
323.17775 2.44412 (323*2π)/3321 weeks
324.16365 3.33537 (324*2π)/3321 weeks
325-.82905 4.15537 (325*2π)/3321 weeks
326-1.71803 3.93232 (326*2π)/3321 weeks
327-1.21998 5.46582 (327*2π)/3321 weeks
3282.89508 5.04817 (328*2π)/3321 weeks
329-.07057 5.24789 (329*2π)/3321 weeks
3302.58813 6.94189 (330*2π)/3321 weeks

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