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# Fourier Analysis of IVOV (Vanguard S&P Mid-Cap 400 Value Index Fund)

IVOV (Vanguard S&P Mid-Cap 400 Value Index Fund) appears to have interesting cyclic behaviour every 40 weeks (2.5275*sine), 21 weeks (1.873*sine), and 31 weeks (1.8698*sine).

IVOV (Vanguard S&P Mid-Cap 400 Value Index Fund) has an average price of 81.62 (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 9/9/2010 to 4/23/2018 for IVOV (Vanguard S&P Mid-Cap 400 Value Index Fund), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
081.62058   0
1-.5192 -23.23818 (1*2π)/399399 weeks
25.88978 -12.93491 (2*2π)/399200 weeks
3-1.27064 -8.22589 (3*2π)/399133 weeks
4-1.28564 -3.81689 (4*2π)/399100 weeks
51.07832 -3.68669 (5*2π)/39980 weeks
6-.64626 -4.11061 (6*2π)/39967 weeks
7-1.59245 -2.80491 (7*2π)/39957 weeks
8-.68753 -4.30527 (8*2π)/39950 weeks
9-1.05605 -3.85812 (9*2π)/39944 weeks
10-.53175 -2.52749 (10*2π)/39940 weeks
11-.37999 -1.73362 (11*2π)/39936 weeks
12.47612 -1.32943 (12*2π)/39933 weeks
13-.57592 -1.86983 (13*2π)/39931 weeks
14-1.01192 -1.70909 (14*2π)/39929 weeks
15-.37331 -1.10066 (15*2π)/39927 weeks
16.12652 -1.22909 (16*2π)/39925 weeks
17-.74814 -1.05536 (17*2π)/39923 weeks
18.26357 -1.19895 (18*2π)/39922 weeks
19.36389 -1.87298 (19*2π)/39921 weeks
20-.47472 -1.01768 (20*2π)/39920 weeks
21-.2976 -.49861 (21*2π)/39919 weeks
22.33946 -.83853 (22*2π)/39918 weeks
23-.52784 -1.28784 (23*2π)/39917 weeks
24-.48833 -.73494 (24*2π)/39917 weeks
25-.08358 -.88323 (25*2π)/39916 weeks
26.1203 -.94982 (26*2π)/39915 weeks
27.1863 -.69694 (27*2π)/39915 weeks
28-.06082 -.88557 (28*2π)/39914 weeks
29.09152 -.87843 (29*2π)/39914 weeks
30-.55604 -.88611 (30*2π)/39913 weeks
31-.41347 -.63166 (31*2π)/39913 weeks
32-.25211 -1.02979 (32*2π)/39912 weeks
33-.18815 -.77223 (33*2π)/39912 weeks
34-.25408 -1.08676 (34*2π)/39912 weeks
35-.42528 -.21825 (35*2π)/39911 weeks
36-.33826 -.73787 (36*2π)/39911 weeks
37-.07876 -.38461 (37*2π)/39911 weeks
38-.09278 -.3752 (38*2π)/39911 weeks
39-.04943 -.47828 (39*2π)/39910 weeks
40-.1438 -.65177 (40*2π)/39910 weeks
41-.60815 -.49002 (41*2π)/39910 weeks
42-.06753 -.49235 (42*2π)/39910 weeks
43-.23873 -.38288 (43*2π)/3999 weeks
44-.2019 -.64186 (44*2π)/3999 weeks
45-.22265 -.64449 (45*2π)/3999 weeks
46-.01483 -.47952 (46*2π)/3999 weeks
47-.36341 -.25021 (47*2π)/3998 weeks
48.21081 -.29452 (48*2π)/3998 weeks
49-.35705 -.33586 (49*2π)/3998 weeks
50-.08844 -.5159 (50*2π)/3998 weeks
51-.17048 -.54691 (51*2π)/3998 weeks
52-.1177 -.40569 (52*2π)/3998 weeks
53.12572 -.69165 (53*2π)/3998 weeks
54.05274 -.48531 (54*2π)/3997 weeks
55.05298 -.4172 (55*2π)/3997 weeks
56-.24923 -.23867 (56*2π)/3997 weeks
57-.08737 -.35251 (57*2π)/3997 weeks
58-.35546 -.39944 (58*2π)/3997 weeks
59-.15141 -.53002 (59*2π)/3997 weeks
60-.06251 -.70476 (60*2π)/3997 weeks
61-.14497 -.48189 (61*2π)/3997 weeks
62-.28197 -.45506 (62*2π)/3996 weeks
63-.37683 -.34841 (63*2π)/3996 weeks
64-.11332 -.40543 (64*2π)/3996 weeks
65-.34599 -.50643 (65*2π)/3996 weeks
66-.40431 -.28785 (66*2π)/3996 weeks
67-.28633 -.20658 (67*2π)/3996 weeks
68-.09962 -.29829 (68*2π)/3996 weeks
69-.08722 -.36745 (69*2π)/3996 weeks
70-.38772 -.33721 (70*2π)/3996 weeks
71-.26195 -.24062 (71*2π)/3996 weeks
72-.12544 -.26287 (72*2π)/3996 weeks
73-.3289 -.36193 (73*2π)/3995 weeks
74-.34334 -.13478 (74*2π)/3995 weeks
75-.13183 -.24986 (75*2π)/3995 weeks
76-.1098 -.22315 (76*2π)/3995 weeks
77-.35112 -.20959 (77*2π)/3995 weeks
78-.08773 -.20816 (78*2π)/3995 weeks
79-.19655 -.43479 (79*2π)/3995 weeks
80-.28598 -.19199 (80*2π)/3995 weeks
81-.17309 -.24174 (81*2π)/3995 weeks
82-.20801 -.29419 (82*2π)/3995 weeks
83-.1974 -.35125 (83*2π)/3995 weeks
84-.11089 -.15783 (84*2π)/3995 weeks
85-.09698 -.32474 (85*2π)/3995 weeks
86-.24134 -.25097 (86*2π)/3995 weeks
87-.22769 -.05655 (87*2π)/3995 weeks
88-.14698 -.2441 (88*2π)/3995 weeks
89-.17806 -.20312 (89*2π)/3994 weeks
90-.33429 -.20837 (90*2π)/3994 weeks
91-.05838 -.21097 (91*2π)/3994 weeks
92-.1517 -.35767 (92*2π)/3994 weeks
93-.23424 -.23366 (93*2π)/3994 weeks
94-.22971 -.25099 (94*2π)/3994 weeks
95-.1198 -.18457 (95*2π)/3994 weeks
96-.27129 -.35443 (96*2π)/3994 weeks
97-.34256 -.06732 (97*2π)/3994 weeks
98-.04074 -.09407 (98*2π)/3994 weeks
99-.23899 -.1762 (99*2π)/3994 weeks
100-.16006 -.03341 (100*2π)/3994 weeks
101-.14313 -.1447 (101*2π)/3994 weeks
102-.31824 -.25102 (102*2π)/3994 weeks
103-.26182 -.12014 (103*2π)/3994 weeks
104-.09976 -.02728 (104*2π)/3994 weeks
105-.05415 -.26269 (105*2π)/3994 weeks
106-.16137 -.17366 (106*2π)/3994 weeks
107-.10373 -.03908 (107*2π)/3994 weeks
108-.25919 -.07709 (108*2π)/3994 weeks
109-.20644 -.03636 (109*2π)/3994 weeks
110-.08537 -.1666 (110*2π)/3994 weeks
111-.07483 -.23952 (111*2π)/3994 weeks
112-.18757 -.20717 (112*2π)/3994 weeks
113-.14317 -.10015 (113*2π)/3994 weeks
114-.04526 -.10938 (114*2π)/3994 weeks
115-.1919 -.17564 (115*2π)/3993 weeks
116-.19066 -.2173 (116*2π)/3993 weeks
117-.18936 -.24082 (117*2π)/3993 weeks
118-.2478 -.21212 (118*2π)/3993 weeks
119-.18889 -.06364 (119*2π)/3993 weeks
120-.18233 -.24221 (120*2π)/3993 weeks
121-.16026 -.25307 (121*2π)/3993 weeks
122-.17492 -.2095 (122*2π)/3993 weeks
123-.19287 -.14757 (123*2π)/3993 weeks
124-.25643 -.15606 (124*2π)/3993 weeks
125-.13673 -.10885 (125*2π)/3993 weeks
126-.2518 -.18296 (126*2π)/3993 weeks
127-.29199 -.14843 (127*2π)/3993 weeks
128-.24325 -.16914 (128*2π)/3993 weeks
129-.25025 -.1759 (129*2π)/3993 weeks
130-.2614 -.16542 (130*2π)/3993 weeks
131-.2571 -.09011 (131*2π)/3993 weeks
132-.23491 -.07424 (132*2π)/3993 weeks
133-.36466 -.05299 (133*2π)/3993 weeks
134-.22566 -.10522 (134*2π)/3993 weeks
135-.13616 -.15417 (135*2π)/3993 weeks
136-.26438 -.08559 (136*2π)/3993 weeks
137-.17853 -.08822 (137*2π)/3993 weeks
138-.29037 -.03704 (138*2π)/3993 weeks
139-.25072 .00113 (139*2π)/3993 weeks
140-.26853 -.06487 (140*2π)/3993 weeks
141-.22035 -.05133 (141*2π)/3993 weeks
142-.02861 .00287 (142*2π)/3993 weeks
143-.18114 .04115 (143*2π)/3993 weeks
144-.20473 -.02163 (144*2π)/3993 weeks
145-.17024 .04732 (145*2π)/3993 weeks
146-.18485 -.0483 (146*2π)/3993 weeks
147-.09027 -.16366 (147*2π)/3993 weeks
148-.10608 -.09985 (148*2π)/3993 weeks
149-.09223 -.00141 (149*2π)/3993 weeks
150-.13317 -.12683 (150*2π)/3993 weeks
151-.20184 -.03131 (151*2π)/3993 weeks
152-.17258 -.06918 (152*2π)/3993 weeks
153-.1969 -.05864 (153*2π)/3993 weeks
154-.16083 -.06949 (154*2π)/3993 weeks
155-.1516 -.184 (155*2π)/3993 weeks
156-.01948 -.058 (156*2π)/3993 weeks
157-.12544 -.07412 (157*2π)/3993 weeks
158-.16833 -.09334 (158*2π)/3993 weeks
159-.17909 -.04196 (159*2π)/3993 weeks
160-.16828 -.03034 (160*2π)/3992 weeks
161-.18655 .0626 (161*2π)/3992 weeks
162-.20715 -.03806 (162*2π)/3992 weeks
163-.17109 -.03466 (163*2π)/3992 weeks
164-.24019 -.09525 (164*2π)/3992 weeks
165-.19495 -.04945 (165*2π)/3992 weeks
166-.09506 -.08189 (166*2π)/3992 weeks
167-.25915 -.07968 (167*2π)/3992 weeks
168-.18906 .09062 (168*2π)/3992 weeks
169-.11037 -.01959 (169*2π)/3992 weeks
170-.1664 -.06783 (170*2π)/3992 weeks
171-.15058 -.11859 (171*2π)/3992 weeks
172-.19483 -.05933 (172*2π)/3992 weeks
173-.29039 -.135 (173*2π)/3992 weeks
174-.08909 .0004 (174*2π)/3992 weeks
175-.11637 .0159 (175*2π)/3992 weeks
176-.20331 -.06436 (176*2π)/3992 weeks
177-.21706 -.09483 (177*2π)/3992 weeks
178-.2566 -.05739 (178*2π)/3992 weeks
179-.23204 -.00357 (179*2π)/3992 weeks
180-.0764 -.11588 (180*2π)/3992 weeks
181-.18964 .05658 (181*2π)/3992 weeks
182-.12733 -.06843 (182*2π)/3992 weeks
183-.18626 -.00104 (183*2π)/3992 weeks
184-.12886 -.10678 (184*2π)/3992 weeks
185-.27294 -.00344 (185*2π)/3992 weeks
186-.21981 -.09135 (186*2π)/3992 weeks
187-.19015 -.09628 (187*2π)/3992 weeks
188-.16109 -.12825 (188*2π)/3992 weeks
189-.22549 .0169 (189*2π)/3992 weeks
190-.26021 .09936 (190*2π)/3992 weeks
191-.09403 -.11067 (191*2π)/3992 weeks
192-.2209 -.08793 (192*2π)/3992 weeks
193-.24929 .03395 (193*2π)/3992 weeks
194-.16778 -.07278 (194*2π)/3992 weeks
195-.28625 -.02614 (195*2π)/3992 weeks
196-.18607 .03673 (196*2π)/3992 weeks
197-.06284 -.08024 (197*2π)/3992 weeks
198-.20853 .00005 (198*2π)/3992 weeks
199-.29341 .01357 (199*2π)/3992 weeks
200-.29341 -.01357 (200*2π)/3992 weeks
201-.20853 -.00005 (201*2π)/3992 weeks
202-.06284 .08024 (202*2π)/3992 weeks
203-.18607 -.03673 (203*2π)/3992 weeks
204-.28625 .02614 (204*2π)/3992 weeks
205-.16778 .07278 (205*2π)/3992 weeks
206-.24929 -.03395 (206*2π)/3992 weeks
207-.2209 .08793 (207*2π)/3992 weeks
208-.09403 .11067 (208*2π)/3992 weeks
209-.26021 -.09936 (209*2π)/3992 weeks
210-.22549 -.0169 (210*2π)/3992 weeks
211-.16109 .12825 (211*2π)/3992 weeks
212-.19015 .09628 (212*2π)/3992 weeks
213-.21981 .09135 (213*2π)/3992 weeks
214-.27294 .00344 (214*2π)/3992 weeks
215-.12886 .10678 (215*2π)/3992 weeks
216-.18626 .00104 (216*2π)/3992 weeks
217-.12733 .06843 (217*2π)/3992 weeks
218-.18964 -.05658 (218*2π)/3992 weeks
219-.0764 .11588 (219*2π)/3992 weeks
220-.23204 .00357 (220*2π)/3992 weeks
221-.2566 .05739 (221*2π)/3992 weeks
222-.21706 .09483 (222*2π)/3992 weeks
223-.20331 .06436 (223*2π)/3992 weeks
224-.11637 -.0159 (224*2π)/3992 weeks
225-.08909 -.0004 (225*2π)/3992 weeks
226-.29039 .135 (226*2π)/3992 weeks
227-.19483 .05933 (227*2π)/3992 weeks
228-.15058 .11859 (228*2π)/3992 weeks
229-.1664 .06783 (229*2π)/3992 weeks
230-.11037 .01959 (230*2π)/3992 weeks
231-.18906 -.09062 (231*2π)/3992 weeks
232-.25915 .07968 (232*2π)/3992 weeks
233-.09506 .08189 (233*2π)/3992 weeks
234-.19495 .04945 (234*2π)/3992 weeks
235-.24019 .09525 (235*2π)/3992 weeks
236-.17109 .03466 (236*2π)/3992 weeks
237-.20715 .03806 (237*2π)/3992 weeks
238-.18655 -.0626 (238*2π)/3992 weeks
239-.16828 .03034 (239*2π)/3992 weeks
240-.17909 .04196 (240*2π)/3992 weeks
241-.16833 .09334 (241*2π)/3992 weeks
242-.12544 .07412 (242*2π)/3992 weeks
243-.01948 .058 (243*2π)/3992 weeks
244-.1516 .184 (244*2π)/3992 weeks
245-.16083 .06949 (245*2π)/3992 weeks
246-.1969 .05864 (246*2π)/3992 weeks
247-.17258 .06918 (247*2π)/3992 weeks
248-.20184 .03131 (248*2π)/3992 weeks
249-.13317 .12683 (249*2π)/3992 weeks
250-.09223 .00141 (250*2π)/3992 weeks
251-.10608 .09985 (251*2π)/3992 weeks
252-.09027 .16366 (252*2π)/3992 weeks
253-.18485 .0483 (253*2π)/3992 weeks
254-.17024 -.04732 (254*2π)/3992 weeks
255-.20473 .02163 (255*2π)/3992 weeks
256-.18114 -.04115 (256*2π)/3992 weeks
257-.02861 -.00287 (257*2π)/3992 weeks
258-.22035 .05133 (258*2π)/3992 weeks
259-.26853 .06487 (259*2π)/3992 weeks
260-.25072 -.00113 (260*2π)/3992 weeks
261-.29037 .03704 (261*2π)/3992 weeks
262-.17853 .08822 (262*2π)/3992 weeks
263-.26438 .08559 (263*2π)/3992 weeks
264-.13616 .15417 (264*2π)/3992 weeks
265-.22566 .10522 (265*2π)/3992 weeks
266-.36466 .05299 (266*2π)/3992 weeks
267-.23491 .07424 (267*2π)/3991 weeks
268-.2571 .09011 (268*2π)/3991 weeks
269-.2614 .16542 (269*2π)/3991 weeks
270-.25025 .1759 (270*2π)/3991 weeks
271-.24325 .16914 (271*2π)/3991 weeks
272-.29199 .14843 (272*2π)/3991 weeks
273-.2518 .18296 (273*2π)/3991 weeks
274-.13673 .10885 (274*2π)/3991 weeks
275-.25643 .15606 (275*2π)/3991 weeks
276-.19287 .14757 (276*2π)/3991 weeks
277-.17492 .2095 (277*2π)/3991 weeks
278-.16026 .25307 (278*2π)/3991 weeks
279-.18233 .24221 (279*2π)/3991 weeks
280-.18889 .06364 (280*2π)/3991 weeks
281-.2478 .21212 (281*2π)/3991 weeks
282-.18936 .24082 (282*2π)/3991 weeks
283-.19066 .2173 (283*2π)/3991 weeks
284-.1919 .17564 (284*2π)/3991 weeks
285-.04526 .10938 (285*2π)/3991 weeks
286-.14317 .10015 (286*2π)/3991 weeks
287-.18757 .20717 (287*2π)/3991 weeks
288-.07483 .23952 (288*2π)/3991 weeks
289-.08537 .1666 (289*2π)/3991 weeks
290-.20644 .03636 (290*2π)/3991 weeks
291-.25919 .07709 (291*2π)/3991 weeks
292-.10373 .03908 (292*2π)/3991 weeks
293-.16137 .17366 (293*2π)/3991 weeks
294-.05415 .26269 (294*2π)/3991 weeks
295-.09976 .02728 (295*2π)/3991 weeks
296-.26182 .12014 (296*2π)/3991 weeks
297-.31824 .25102 (297*2π)/3991 weeks
298-.14313 .1447 (298*2π)/3991 weeks
299-.16006 .03341 (299*2π)/3991 weeks
300-.23899 .1762 (300*2π)/3991 weeks
301-.04074 .09407 (301*2π)/3991 weeks
302-.34256 .06732 (302*2π)/3991 weeks
303-.27129 .35443 (303*2π)/3991 weeks
304-.1198 .18457 (304*2π)/3991 weeks
305-.22971 .25099 (305*2π)/3991 weeks
306-.23424 .23366 (306*2π)/3991 weeks
307-.1517 .35767 (307*2π)/3991 weeks
308-.05838 .21097 (308*2π)/3991 weeks
309-.33429 .20837 (309*2π)/3991 weeks
310-.17806 .20312 (310*2π)/3991 weeks
311-.14698 .2441 (311*2π)/3991 weeks
312-.22769 .05655 (312*2π)/3991 weeks
313-.24134 .25097 (313*2π)/3991 weeks
314-.09698 .32474 (314*2π)/3991 weeks
315-.11089 .15783 (315*2π)/3991 weeks
316-.1974 .35125 (316*2π)/3991 weeks
317-.20801 .29419 (317*2π)/3991 weeks
318-.17309 .24174 (318*2π)/3991 weeks
319-.28598 .19199 (319*2π)/3991 weeks
320-.19655 .43479 (320*2π)/3991 weeks
321-.08773 .20816 (321*2π)/3991 weeks
322-.35112 .20959 (322*2π)/3991 weeks
323-.1098 .22315 (323*2π)/3991 weeks
324-.13183 .24986 (324*2π)/3991 weeks
325-.34334 .13478 (325*2π)/3991 weeks
326-.3289 .36193 (326*2π)/3991 weeks
327-.12544 .26287 (327*2π)/3991 weeks
328-.26195 .24062 (328*2π)/3991 weeks
329-.38772 .33721 (329*2π)/3991 weeks
330-.08722 .36745 (330*2π)/3991 weeks
331-.09962 .29829 (331*2π)/3991 weeks
332-.28633 .20658 (332*2π)/3991 weeks
333-.40431 .28785 (333*2π)/3991 weeks
334-.34599 .50643 (334*2π)/3991 weeks
335-.11332 .40543 (335*2π)/3991 weeks
336-.37683 .34841 (336*2π)/3991 weeks
337-.28197 .45506 (337*2π)/3991 weeks
338-.14497 .48189 (338*2π)/3991 weeks
339-.06251 .70476 (339*2π)/3991 weeks
340-.15141 .53002 (340*2π)/3991 weeks
341-.35546 .39944 (341*2π)/3991 weeks
342-.08737 .35251 (342*2π)/3991 weeks
343-.24923 .23867 (343*2π)/3991 weeks
344.05298 .4172 (344*2π)/3991 weeks
345.05274 .48531 (345*2π)/3991 weeks
346.12572 .69165 (346*2π)/3991 weeks
347-.1177 .40569 (347*2π)/3991 weeks
348-.17048 .54691 (348*2π)/3991 weeks
349-.08844 .5159 (349*2π)/3991 weeks
350-.35705 .33586 (350*2π)/3991 weeks
351.21081 .29452 (351*2π)/3991 weeks
352-.36341 .25021 (352*2π)/3991 weeks
353-.01483 .47952 (353*2π)/3991 weeks
354-.22265 .64449 (354*2π)/3991 weeks
355-.2019 .64186 (355*2π)/3991 weeks
356-.23873 .38288 (356*2π)/3991 weeks
357-.06753 .49235 (357*2π)/3991 weeks
358-.60815 .49002 (358*2π)/3991 weeks
359-.1438 .65177 (359*2π)/3991 weeks
360-.04943 .47828 (360*2π)/3991 weeks
361-.09278 .3752 (361*2π)/3991 weeks
362-.07876 .38461 (362*2π)/3991 weeks
363-.33826 .73787 (363*2π)/3991 weeks
364-.42528 .21825 (364*2π)/3991 weeks
365-.25408 1.08676 (365*2π)/3991 weeks
366-.18815 .77223 (366*2π)/3991 weeks
367-.25211 1.02979 (367*2π)/3991 weeks
368-.41347 .63166 (368*2π)/3991 weeks
369-.55604 .88611 (369*2π)/3991 weeks
370.09152 .87843 (370*2π)/3991 weeks
371-.06082 .88557 (371*2π)/3991 weeks
372.1863 .69694 (372*2π)/3991 weeks
373.1203 .94982 (373*2π)/3991 weeks
374-.08358 .88323 (374*2π)/3991 weeks
375-.48833 .73494 (375*2π)/3991 weeks
376-.52784 1.28784 (376*2π)/3991 weeks
377.33946 .83853 (377*2π)/3991 weeks
378-.2976 .49861 (378*2π)/3991 weeks
379-.47472 1.01768 (379*2π)/3991 weeks
380.36389 1.87298 (380*2π)/3991 weeks
381.26357 1.19895 (381*2π)/3991 weeks
382-.74814 1.05536 (382*2π)/3991 weeks
383.12652 1.22909 (383*2π)/3991 weeks
384-.37331 1.10066 (384*2π)/3991 weeks
385-1.01192 1.70909 (385*2π)/3991 weeks
386-.57592 1.86983 (386*2π)/3991 weeks
387.47612 1.32943 (387*2π)/3991 weeks
388-.37999 1.73362 (388*2π)/3991 weeks
389-.53175 2.52749 (389*2π)/3991 weeks
390-1.05605 3.85812 (390*2π)/3991 weeks
391-.68753 4.30527 (391*2π)/3991 weeks
392-1.59245 2.80491 (392*2π)/3991 weeks
393-.64626 4.11061 (393*2π)/3991 weeks
3941.07832 3.68669 (394*2π)/3991 weeks
395-1.28564 3.81689 (395*2π)/3991 weeks
396-1.27064 8.22589 (396*2π)/3991 weeks
3975.88978 12.93491 (397*2π)/3991 weeks