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# Fourier Analysis of VGRNX (VANGUARD GLOBAL EX-U.S. REAL ESTATE INDEX FUND INSTITUTIONAL)

VGRNX (VANGUARD GLOBAL EX-U.S. REAL ESTATE INDEX FUND INSTITUTIONAL) appears to have interesting cyclic behaviour every 39 weeks (2.5566*sine), 35 weeks (1.6104*sine), and 35 weeks (1.0102*cosine).

VGRNX (VANGUARD GLOBAL EX-U.S. REAL ESTATE INDEX FUND INSTITUTIONAL) has an average price of 93.39 (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 11/2/2010 to 4/16/2018 for VGRNX (VANGUARD GLOBAL EX-U.S. REAL ESTATE INDEX FUND INSTITUTIONAL), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
093.39498   0
1-1.95958 -12.15952 (1*2π)/390390 weeks
24.81358 -10.0786 (2*2π)/390195 weeks
33.56117 -6.38637 (3*2π)/390130 weeks
41.14906 -1.46689 (4*2π)/39098 weeks
5-.45149 -3.80218 (5*2π)/39078 weeks
6-1.22558 -3.48397 (6*2π)/39065 weeks
7-1.38341 -.33416 (7*2π)/39056 weeks
8.08433 -2.21033 (8*2π)/39049 weeks
9-.68455 -2.88438 (9*2π)/39043 weeks
10.74053 -2.55664 (10*2π)/39039 weeks
11-1.01024 -1.61038 (11*2π)/39035 weeks
12.85937 -1.18911 (12*2π)/39033 weeks
13-.20669 -.32058 (13*2π)/39030 weeks
14-.85797 -1.14614 (14*2π)/39028 weeks
15.16782 -1.36502 (15*2π)/39026 weeks
16-.58454 -1.23985 (16*2π)/39024 weeks
17-.71991 -.3881 (17*2π)/39023 weeks
18.57783 -.14296 (18*2π)/39022 weeks
19-.72722 -1.00348 (19*2π)/39021 weeks
20-.71716 -1.18776 (20*2π)/39020 weeks
21.10074 -.44705 (21*2π)/39019 weeks
22.345 -.40223 (22*2π)/39018 weeks
23-.1111 -.64956 (23*2π)/39017 weeks
24.13433 -.21187 (24*2π)/39016 weeks
25.06766 -.35555 (25*2π)/39016 weeks
26-.36108 -.79743 (26*2π)/39015 weeks
27.06068 -.94692 (27*2π)/39014 weeks
28.04051 -.53329 (28*2π)/39014 weeks
29-.31657 -.98033 (29*2π)/39013 weeks
30.68361 -.80403 (30*2π)/39013 weeks
31.00831 -.51994 (31*2π)/39013 weeks
32-.09203 -.24259 (32*2π)/39012 weeks
33.19581 -.85235 (33*2π)/39012 weeks
34-.54001 -.2899 (34*2π)/39011 weeks
35.30051 -.79485 (35*2π)/39011 weeks
36-.02593 -.58154 (36*2π)/39011 weeks
37-.44963 -.30854 (37*2π)/39011 weeks
38-.16997 -.44868 (38*2π)/39010 weeks
39.04748 -.46181 (39*2π)/39010 weeks
40-.46716 -.47599 (40*2π)/39010 weeks
41.00015 -.30788 (41*2π)/39010 weeks
42-.1955 -.41668 (42*2π)/3909 weeks
43-.29339 -.38023 (43*2π)/3909 weeks
44-.02433 -.51446 (44*2π)/3909 weeks
45.04558 -.35342 (45*2π)/3909 weeks
46-.24947 -.14564 (46*2π)/3908 weeks
47.02522 .06822 (47*2π)/3908 weeks
48-.21511 -.08419 (48*2π)/3908 weeks
49-.15598 -.16859 (49*2π)/3908 weeks
50-.02253 -.29247 (50*2π)/3908 weeks
51.00932 -.32037 (51*2π)/3908 weeks
52.1855 -.42974 (52*2π)/3908 weeks
53-.05268 -.34715 (53*2π)/3907 weeks
54.13293 -.34603 (54*2π)/3907 weeks
55.05447 .0772 (55*2π)/3907 weeks
56-.00511 -.09439 (56*2π)/3907 weeks
57-.18262 .03983 (57*2π)/3907 weeks
58-.33587 -.25082 (58*2π)/3907 weeks
59-.06555 -.40492 (59*2π)/3907 weeks
60-.02412 -.50029 (60*2π)/3907 weeks
61.17285 -.43942 (61*2π)/3906 weeks
62-.18157 -.33494 (62*2π)/3906 weeks
63-.00974 -.24995 (63*2π)/3906 weeks
64-.07167 -.38595 (64*2π)/3906 weeks
65-.25941 -.24476 (65*2π)/3906 weeks
66-.19589 -.15484 (66*2π)/3906 weeks
67-.21649 -.35494 (67*2π)/3906 weeks
68.01621 -.21093 (68*2π)/3906 weeks
69-.23919 -.22888 (69*2π)/3906 weeks
70-.00861 -.13885 (70*2π)/3906 weeks
71.09409 -.31687 (71*2π)/3905 weeks
72-.28821 -.42614 (72*2π)/3905 weeks
73-.22414 -.0487 (73*2π)/3905 weeks
74-.12845 -.10235 (74*2π)/3905 weeks
75-.04436 -.29072 (75*2π)/3905 weeks
76-.17248 -.15066 (76*2π)/3905 weeks
77-.15332 -.13701 (77*2π)/3905 weeks
78-.26649 -.26478 (78*2π)/3905 weeks
79-.27006 -.0018 (79*2π)/3905 weeks
80.06081 -.15432 (80*2π)/3905 weeks
81.11269 -.08222 (81*2π)/3905 weeks
82-.29108 -.12307 (82*2π)/3905 weeks
83-.01761 -.08639 (83*2π)/3905 weeks
84-.11993 -.0547 (84*2π)/3905 weeks
85-.28737 -.08292 (85*2π)/3905 weeks
86.05254 -.09106 (86*2π)/3905 weeks
87-.05255 -.16857 (87*2π)/3904 weeks
88-.2565 -.33564 (88*2π)/3904 weeks
89-.00267 -.11689 (89*2π)/3904 weeks
90.06022 -.18857 (90*2π)/3904 weeks
91-.03777 -.13743 (91*2π)/3904 weeks
92.01062 -.18194 (92*2π)/3904 weeks
93-.15518 -.05623 (93*2π)/3904 weeks
94.01709 -.07435 (94*2π)/3904 weeks
95-.14004 -.15984 (95*2π)/3904 weeks
96.01147 -.05562 (96*2π)/3904 weeks
97-.11618 -.19176 (97*2π)/3904 weeks
98-.1539 -.09582 (98*2π)/3904 weeks
99-.08567 -.00246 (99*2π)/3904 weeks
100-.20576 -.24121 (100*2π)/3904 weeks
101-.18751 -.20945 (101*2π)/3904 weeks
102-.21139 -.11206 (102*2π)/3904 weeks
103-.06946 -.24434 (103*2π)/3904 weeks
104-.14208 -.1783 (104*2π)/3904 weeks
105-.15702 -.0027 (105*2π)/3904 weeks
106-.24157 -.01573 (106*2π)/3904 weeks
107-.21721 -.01952 (107*2π)/3904 weeks
108-.23694 -.05884 (108*2π)/3904 weeks
109-.09683 -.12433 (109*2π)/3904 weeks
110-.06783 -.11308 (110*2π)/3904 weeks
111-.16028 -.0999 (111*2π)/3904 weeks
112-.08042 -.05789 (112*2π)/3903 weeks
113-.08227 .13719 (113*2π)/3903 weeks
114-.06141 -.00664 (114*2π)/3903 weeks
115-.11935 -.01199 (115*2π)/3903 weeks
116-.05991 -.10892 (116*2π)/3903 weeks
117-.07056 .03042 (117*2π)/3903 weeks
118-.16945 .00985 (118*2π)/3903 weeks
119-.08966 .01502 (119*2π)/3903 weeks
120-.13849 -.09254 (120*2π)/3903 weeks
121-.0131 -.06548 (121*2π)/3903 weeks
122-.14565 .02765 (122*2π)/3903 weeks
123.06539 -.07739 (123*2π)/3903 weeks
124.04516 -.18624 (124*2π)/3903 weeks
125-.09418 -.09219 (125*2π)/3903 weeks
126-.06703 -.06419 (126*2π)/3903 weeks
127-.03955 -.0296 (127*2π)/3903 weeks
128-.08602 -.15659 (128*2π)/3903 weeks
129-.14928 -.16321 (129*2π)/3903 weeks
130-.08574 -.13276 (130*2π)/3903 weeks
131-.1946 -.11509 (131*2π)/3903 weeks
132-.08499 -.11486 (132*2π)/3903 weeks
133-.16515 -.13761 (133*2π)/3903 weeks
134-.24639 -.05519 (134*2π)/3903 weeks
135-.13084 -.18335 (135*2π)/3903 weeks
136-.22842 -.11508 (136*2π)/3903 weeks
137-.07576 -.08209 (137*2π)/3903 weeks
138-.13062 -.18381 (138*2π)/3903 weeks
139-.23092 .10139 (139*2π)/3903 weeks
140-.17817 -.02145 (140*2π)/3903 weeks
141-.18516 -.01319 (141*2π)/3903 weeks
142-.24153 -.06087 (142*2π)/3903 weeks
143-.16002 -.15889 (143*2π)/3903 weeks
144-.09771 -.17819 (144*2π)/3903 weeks
145-.10735 -.04683 (145*2π)/3903 weeks
146-.10776 -.00426 (146*2π)/3903 weeks
147-.11578 -.00293 (147*2π)/3903 weeks
148-.12859 -.07975 (148*2π)/3903 weeks
149-.22865 -.03075 (149*2π)/3903 weeks
150-.11163 -.03179 (150*2π)/3903 weeks
151-.19644 -.00753 (151*2π)/3903 weeks
152-.09677 -.16046 (152*2π)/3903 weeks
153-.08449 -.03887 (153*2π)/3903 weeks
154-.02369 -.02766 (154*2π)/3903 weeks
155-.15643 -.02235 (155*2π)/3903 weeks
156-.03862 .05233 (156*2π)/3903 weeks
157-.10458 -.0931 (157*2π)/3902 weeks
158-.08077 -.05196 (158*2π)/3902 weeks
159-.1067 .02604 (159*2π)/3902 weeks
160-.07979 .03219 (160*2π)/3902 weeks
161-.11333 .00931 (161*2π)/3902 weeks
162-.16844 .03771 (162*2π)/3902 weeks
163-.10397 -.05255 (163*2π)/3902 weeks
164-.12946 -.0501 (164*2π)/3902 weeks
165-.11218 -.0851 (165*2π)/3902 weeks
166-.16279 .00296 (166*2π)/3902 weeks
167-.06652 -.05324 (167*2π)/3902 weeks
168-.09672 -.00188 (168*2π)/3902 weeks
169-.11934 -.01962 (169*2π)/3902 weeks
170-.25663 -.02334 (170*2π)/3902 weeks
171-.17421 .02234 (171*2π)/3902 weeks
172-.08601 -.09356 (172*2π)/3902 weeks
173-.07993 -.0306 (173*2π)/3902 weeks
174-.00745 -.03867 (174*2π)/3902 weeks
175-.06778 -.07797 (175*2π)/3902 weeks
176-.15093 .02954 (176*2π)/3902 weeks
177-.07381 .02859 (177*2π)/3902 weeks
178-.10742 -.00518 (178*2π)/3902 weeks
179-.21474 -.04928 (179*2π)/3902 weeks
180-.03618 -.01416 (180*2π)/3902 weeks
181-.05688 -.06248 (181*2π)/3902 weeks
182-.02872 -.05598 (182*2π)/3902 weeks
183-.0771 .02361 (183*2π)/3902 weeks
184.02459 .11519 (184*2π)/3902 weeks
185-.09911 -.05518 (185*2π)/3902 weeks
186-.12758 -.03879 (186*2π)/3902 weeks
187-.12434 .15055 (187*2π)/3902 weeks
188-.05698 .03975 (188*2π)/3902 weeks
189-.14241 -.089 (189*2π)/3902 weeks
190-.06473 .05036 (190*2π)/3902 weeks
191-.02466 -.04644 (191*2π)/3902 weeks
192-.06885 -.02162 (192*2π)/3902 weeks
193-.00463 .11124 (193*2π)/3902 weeks
194-.14827 -.02559 (194*2π)/3902 weeks
195-.18624   (195*2π)/3902 weeks
196-.14827 .02559 (196*2π)/3902 weeks
197-.00463 -.11124 (197*2π)/3902 weeks
198-.06885 .02162 (198*2π)/3902 weeks
199-.02466 .04644 (199*2π)/3902 weeks
200-.06473 -.05036 (200*2π)/3902 weeks
201-.14241 .089 (201*2π)/3902 weeks
202-.05698 -.03975 (202*2π)/3902 weeks
203-.12434 -.15055 (203*2π)/3902 weeks
204-.12758 .03879 (204*2π)/3902 weeks
205-.09911 .05518 (205*2π)/3902 weeks
206.02459 -.11519 (206*2π)/3902 weeks
207-.0771 -.02361 (207*2π)/3902 weeks
208-.02872 .05598 (208*2π)/3902 weeks
209-.05688 .06248 (209*2π)/3902 weeks
210-.03618 .01416 (210*2π)/3902 weeks
211-.21474 .04928 (211*2π)/3902 weeks
212-.10742 .00518 (212*2π)/3902 weeks
213-.07381 -.02859 (213*2π)/3902 weeks
214-.15093 -.02954 (214*2π)/3902 weeks
215-.06778 .07797 (215*2π)/3902 weeks
216-.00745 .03867 (216*2π)/3902 weeks
217-.07993 .0306 (217*2π)/3902 weeks
218-.08601 .09356 (218*2π)/3902 weeks
219-.17421 -.02234 (219*2π)/3902 weeks
220-.25663 .02334 (220*2π)/3902 weeks
221-.11934 .01962 (221*2π)/3902 weeks
222-.09672 .00188 (222*2π)/3902 weeks
223-.06652 .05324 (223*2π)/3902 weeks
224-.16279 -.00296 (224*2π)/3902 weeks
225-.11218 .0851 (225*2π)/3902 weeks
226-.12946 .0501 (226*2π)/3902 weeks
227-.10397 .05255 (227*2π)/3902 weeks
228-.16844 -.03771 (228*2π)/3902 weeks
229-.11333 -.00931 (229*2π)/3902 weeks
230-.07979 -.03219 (230*2π)/3902 weeks
231-.1067 -.02604 (231*2π)/3902 weeks
232-.08077 .05196 (232*2π)/3902 weeks
233-.10458 .0931 (233*2π)/3902 weeks
234-.03862 -.05233 (234*2π)/3902 weeks
235-.15643 .02235 (235*2π)/3902 weeks
236-.02369 .02766 (236*2π)/3902 weeks
237-.08449 .03887 (237*2π)/3902 weeks
238-.09677 .16046 (238*2π)/3902 weeks
239-.19644 .00753 (239*2π)/3902 weeks
240-.11163 .03179 (240*2π)/3902 weeks
241-.22865 .03075 (241*2π)/3902 weeks
242-.12859 .07975 (242*2π)/3902 weeks
243-.11578 .00293 (243*2π)/3902 weeks
244-.10776 .00426 (244*2π)/3902 weeks
245-.10735 .04683 (245*2π)/3902 weeks
246-.09771 .17819 (246*2π)/3902 weeks
247-.16002 .15889 (247*2π)/3902 weeks
248-.24153 .06087 (248*2π)/3902 weeks
249-.18516 .01319 (249*2π)/3902 weeks
250-.17817 .02145 (250*2π)/3902 weeks
251-.23092 -.10139 (251*2π)/3902 weeks
252-.13062 .18381 (252*2π)/3902 weeks
253-.07576 .08209 (253*2π)/3902 weeks
254-.22842 .11508 (254*2π)/3902 weeks
255-.13084 .18335 (255*2π)/3902 weeks
256-.24639 .05519 (256*2π)/3902 weeks
257-.16515 .13761 (257*2π)/3902 weeks
258-.08499 .11486 (258*2π)/3902 weeks
259-.1946 .11509 (259*2π)/3902 weeks
260-.08574 .13276 (260*2π)/3902 weeks
261-.14928 .16321 (261*2π)/3901 weeks
262-.08602 .15659 (262*2π)/3901 weeks
263-.03955 .0296 (263*2π)/3901 weeks
264-.06703 .06419 (264*2π)/3901 weeks
265-.09418 .09219 (265*2π)/3901 weeks
266.04516 .18624 (266*2π)/3901 weeks
267.06539 .07739 (267*2π)/3901 weeks
268-.14565 -.02765 (268*2π)/3901 weeks
269-.0131 .06548 (269*2π)/3901 weeks
270-.13849 .09254 (270*2π)/3901 weeks
271-.08966 -.01502 (271*2π)/3901 weeks
272-.16945 -.00985 (272*2π)/3901 weeks
273-.07056 -.03042 (273*2π)/3901 weeks
274-.05991 .10892 (274*2π)/3901 weeks
275-.11935 .01199 (275*2π)/3901 weeks
276-.06141 .00664 (276*2π)/3901 weeks
277-.08227 -.13719 (277*2π)/3901 weeks
278-.08042 .05789 (278*2π)/3901 weeks
279-.16028 .0999 (279*2π)/3901 weeks
280-.06783 .11308 (280*2π)/3901 weeks
281-.09683 .12433 (281*2π)/3901 weeks
282-.23694 .05884 (282*2π)/3901 weeks
283-.21721 .01952 (283*2π)/3901 weeks
284-.24157 .01573 (284*2π)/3901 weeks
285-.15702 .0027 (285*2π)/3901 weeks
286-.14208 .1783 (286*2π)/3901 weeks
287-.06946 .24434 (287*2π)/3901 weeks
288-.21139 .11206 (288*2π)/3901 weeks
289-.18751 .20945 (289*2π)/3901 weeks
290-.20576 .24121 (290*2π)/3901 weeks
291-.08567 .00246 (291*2π)/3901 weeks
292-.1539 .09582 (292*2π)/3901 weeks
293-.11618 .19176 (293*2π)/3901 weeks
294.01147 .05562 (294*2π)/3901 weeks
295-.14004 .15984 (295*2π)/3901 weeks
296.01709 .07435 (296*2π)/3901 weeks
297-.15518 .05623 (297*2π)/3901 weeks
298.01062 .18194 (298*2π)/3901 weeks
299-.03777 .13743 (299*2π)/3901 weeks
300.06022 .18857 (300*2π)/3901 weeks
301-.00267 .11689 (301*2π)/3901 weeks
302-.2565 .33564 (302*2π)/3901 weeks
303-.05255 .16857 (303*2π)/3901 weeks
304.05254 .09106 (304*2π)/3901 weeks
305-.28737 .08292 (305*2π)/3901 weeks
306-.11993 .0547 (306*2π)/3901 weeks
307-.01761 .08639 (307*2π)/3901 weeks
308-.29108 .12307 (308*2π)/3901 weeks
309.11269 .08222 (309*2π)/3901 weeks
310.06081 .15432 (310*2π)/3901 weeks
311-.27006 .0018 (311*2π)/3901 weeks
312-.26649 .26478 (312*2π)/3901 weeks
313-.15332 .13701 (313*2π)/3901 weeks
314-.17248 .15066 (314*2π)/3901 weeks
315-.04436 .29072 (315*2π)/3901 weeks
316-.12845 .10235 (316*2π)/3901 weeks
317-.22414 .0487 (317*2π)/3901 weeks
318-.28821 .42614 (318*2π)/3901 weeks
319.09409 .31687 (319*2π)/3901 weeks
320-.00861 .13885 (320*2π)/3901 weeks
321-.23919 .22888 (321*2π)/3901 weeks
322.01621 .21093 (322*2π)/3901 weeks
323-.21649 .35494 (323*2π)/3901 weeks
324-.19589 .15484 (324*2π)/3901 weeks
325-.25941 .24476 (325*2π)/3901 weeks
326-.07167 .38595 (326*2π)/3901 weeks
327-.00974 .24995 (327*2π)/3901 weeks
328-.18157 .33494 (328*2π)/3901 weeks
329.17285 .43942 (329*2π)/3901 weeks
330-.02412 .50029 (330*2π)/3901 weeks
331-.06555 .40492 (331*2π)/3901 weeks
332-.33587 .25082 (332*2π)/3901 weeks
333-.18262 -.03983 (333*2π)/3901 weeks
334-.00511 .09439 (334*2π)/3901 weeks
335.05447 -.0772 (335*2π)/3901 weeks
336.13293 .34603 (336*2π)/3901 weeks
337-.05268 .34715 (337*2π)/3901 weeks
338.1855 .42974 (338*2π)/3901 weeks
339.00932 .32037 (339*2π)/3901 weeks
340-.02253 .29247 (340*2π)/3901 weeks
341-.15598 .16859 (341*2π)/3901 weeks
342-.21511 .08419 (342*2π)/3901 weeks
343.02522 -.06822 (343*2π)/3901 weeks
344-.24947 .14564 (344*2π)/3901 weeks
345.04558 .35342 (345*2π)/3901 weeks
346-.02433 .51446 (346*2π)/3901 weeks
347-.29339 .38023 (347*2π)/3901 weeks
348-.1955 .41668 (348*2π)/3901 weeks
349.00015 .30788 (349*2π)/3901 weeks
350-.46716 .47599 (350*2π)/3901 weeks
351.04748 .46181 (351*2π)/3901 weeks
352-.16997 .44868 (352*2π)/3901 weeks
353-.44963 .30854 (353*2π)/3901 weeks
354-.02593 .58154 (354*2π)/3901 weeks
355.30051 .79485 (355*2π)/3901 weeks
356-.54001 .2899 (356*2π)/3901 weeks
357.19581 .85235 (357*2π)/3901 weeks
358-.09203 .24259 (358*2π)/3901 weeks
359.00831 .51994 (359*2π)/3901 weeks
360.68361 .80403 (360*2π)/3901 weeks
361-.31657 .98033 (361*2π)/3901 weeks
362.04051 .53329 (362*2π)/3901 weeks
363.06068 .94692 (363*2π)/3901 weeks
364-.36108 .79743 (364*2π)/3901 weeks
365.06766 .35555 (365*2π)/3901 weeks
366.13433 .21187 (366*2π)/3901 weeks
367-.1111 .64956 (367*2π)/3901 weeks
368.345 .40223 (368*2π)/3901 weeks
369.10074 .44705 (369*2π)/3901 weeks
370-.71716 1.18776 (370*2π)/3901 weeks
371-.72722 1.00348 (371*2π)/3901 weeks
372.57783 .14296 (372*2π)/3901 weeks
373-.71991 .3881 (373*2π)/3901 weeks
374-.58454 1.23985 (374*2π)/3901 weeks
375.16782 1.36502 (375*2π)/3901 weeks
376-.85797 1.14614 (376*2π)/3901 weeks
377-.20669 .32058 (377*2π)/3901 weeks
378.85937 1.18911 (378*2π)/3901 weeks
379-1.01024 1.61038 (379*2π)/3901 weeks
380.74053 2.55664 (380*2π)/3901 weeks
381-.68455 2.88438 (381*2π)/3901 weeks
382.08433 2.21033 (382*2π)/3901 weeks
383-1.38341 .33416 (383*2π)/3901 weeks
384-1.22558 3.48397 (384*2π)/3901 weeks
385-.45149 3.80218 (385*2π)/3901 weeks
3861.14906 1.46689 (386*2π)/3901 weeks
3873.56117 6.38637 (387*2π)/3901 weeks
3884.81358 10.0786 (388*2π)/3901 weeks